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35,348 | th | It is well known that Random Serial Dictatorship is strategy-proof and leads
to a Pareto-Efficient outcome. We show that this result breaks down when
individuals are allowed to make transfers, and adapt Random Serial Dictatorship
to encompass trades between individuals. Strategic analysis of play under the
new mechanisms we define is given, accompanied by simulations to quantify the
gains from trade. | Random Serial Dictatorship with Transfers | 2023-12-13 12:14:48 | Sudharsan Sundar, Eric Gao, Trevor Chow, Matthew Ding | http://arxiv.org/abs/2312.07999v1, http://arxiv.org/pdf/2312.07999v1 | cs.GT |
35,349 | th | In approval-based committee (ABC) voting, the goal is to choose a subset of
predefined size of the candidates based on the voters' approval preferences
over the candidates. While this problem has attracted significant attention in
recent years, the incentives for voters to participate in an election for a
given ABC voting rule have been neglected so far. This paper is thus the first
to explicitly study this property, typically called participation, for ABC
voting rules. In particular, we show that all ABC scoring rules even satisfy
group participation, whereas most sequential rules severely fail participation.
We furthermore explore several escape routes to the impossibility for
sequential ABC voting rules: we prove for many sequential rules that (i) they
satisfy participation on laminar profiles, (ii) voters who approve none of the
elected candidates cannot benefit by abstaining, and (iii) it is NP-hard for a
voter to decide whether she benefits from abstaining. | Participation Incentives in Approval-Based Committee Elections | 2023-12-14 13:32:59 | Martin Bullinger, Chris Dong, Patrick Lederer, Clara Mehler | http://arxiv.org/abs/2312.08798v1, http://arxiv.org/pdf/2312.08798v1 | cs.GT |
35,350 | th | In approval-based committee (ABC) elections, the goal is to select a
fixed-size subset of the candidates, a so-called committee, based on the
voters' approval ballots over the candidates. One of the most popular classes
of ABC voting rules are ABC scoring rules, which have recently been
characterized by Lackner and Skowron (2021). However, this characterization
relies on a model where the output is a ranking of committees instead of a set
of winning committees and no full characterization of ABC scoring rules exists
in the latter standard setting. We address this issue by characterizing two
important subclasses of ABC scoring rules in the standard ABC election model,
thereby both extending the result of Lackner and Skowron (2021) to the standard
setting and refining it to subclasses. In more detail, by relying on a
consistency axiom for variable electorates, we characterize (i) the prominent
class of Thiele rules and (ii) a new class of ABC voting rules called ballot
size weighted approval voting. Based on these theorems, we also infer
characterizations of three well-known ABC voting rules, namely multi-winner
approval voting, proportional approval voting, and satisfaction approval
voting. | Refined Characterizations of Approval-based Committee Scoring Rules | 2023-12-14 13:34:07 | Chris Dang, Patrick Lederer | http://arxiv.org/abs/2312.08799v1, http://arxiv.org/pdf/2312.08799v1 | cs.GT |
35,351 | th | We provide the first large-scale data collection of real-world approval-based
committee elections. These elections have been conducted on the Polkadot
blockchain as part of their Nominated Proof-of-Stake mechanism and contain
around one thousand candidates and tens of thousands of (weighted) voters each.
We conduct an in-depth study of application-relevant questions, including a
quantitative and qualitative analysis of the outcomes returned by different
voting rules. Besides considering proportionality measures that are standard in
the multiwinner voting literature, we pay particular attention to less-studied
measures of overrepresentation, as these are closely related to the security of
the Polkadot network. We also analyze how different design decisions such as
the committee size affect the examined measures. | Approval-Based Committee Voting in Practice: A Case Study of (Over-)Representation in the Polkadot Blockchain | 2023-12-18 21:15:38 | Niclas Boehmer, Markus Brill, Alfonso Cevallos, Jonas Gehrlein, Luis Sánchez-Fernández, Ulrike Schmidt-Kraepelin | http://arxiv.org/abs/2312.11408v2, http://arxiv.org/pdf/2312.11408v2 | cs.GT |
35,352 | th | In this note, I introduce Estimated Performance Rating (PR$^e$), a novel
system for evaluating player performance in sports and games. PR$^e$ addresses
a key limitation of the Tournament Performance Rating (TPR) system, which is
undefined for zero or perfect scores in a series of games. PR$^e$ is defined as
the rating that solves an optimization problem related to scoring probability,
making it applicable for any performance level. The main theorem establishes
that the PR$^e$ of a player is equivalent to the TPR whenever the latter is
defined. I then apply this system to historically significant win-streaks in
association football, tennis, and chess. Beyond sports, PR$^e$ has broad
applicability in domains where Elo ratings are used, from college rankings to
the evaluation of large language models. | Performance rating in chess, tennis, and other contexts | 2023-12-20 04:47:55 | Mehmet S. Ismail | http://arxiv.org/abs/2312.12700v1, http://arxiv.org/pdf/2312.12700v1 | econ.TH |
35,354 | th | We consider moral hazard problems where a principal has access to rich
monitoring data about an agent's action. Rather than focusing on optimal
contracts (which are known to in general be complicated), we characterize the
optimal rate at which the principal's payoffs can converge to the first-best
payoff as the amount of data grows large. Our main result suggests a novel
rationale for the widely observed binary wage schemes, by showing that such
simple contracts achieve the optimal convergence rate. Notably, in order to
attain the optimal convergence rate, the principal must set a lenient cutoff
for when the agent receives a high vs. low wage. In contrast, we find that
other common contracts where wages vary more finely with observed data (e.g.,
linear contracts) approximate the first-best at a highly suboptimal rate.
Finally, we show that the optimal convergence rate depends only on a simple
summary statistic of the monitoring technology. This yields a detail-free
ranking over monitoring technologies that quantifies their value for incentive
provision in data-rich settings and applies regardless of the agent's specific
utility or cost functions. | Monitoring with Rich Data | 2023-12-28 05:34:18 | Mira Frick, Ryota Iijima, Yuhta Ishii | http://arxiv.org/abs/2312.16789v1, http://arxiv.org/pdf/2312.16789v1 | econ.TH |
35,355 | th | We study the problem of screening in decision-making processes under
uncertainty, focusing on the impact of adding an additional screening stage,
commonly known as a 'gatekeeper.' While our primary analysis is rooted in the
context of job market hiring, the principles and findings are broadly
applicable to areas such as educational admissions, healthcare patient
selection, and financial loan approvals. The gatekeeper's role is to assess
applicants' suitability before significant investments are made. Our study
reveals that while gatekeepers are designed to streamline the selection process
by filtering out less likely candidates, they can sometimes inadvertently
affect the candidates' own decision-making process. We explore the conditions
under which the introduction of a gatekeeper can enhance or impede the
efficiency of these processes. Additionally, we consider how adjusting
gatekeeping strategies might impact the accuracy of selection decisions. Our
research also extends to scenarios where gatekeeping is influenced by
historical biases, particularly in competitive settings like hiring. We
discover that candidates confronted with a statistically biased gatekeeping
process are more likely to withdraw from applying, thereby perpetuating the
previously mentioned historical biases. The study suggests that measures such
as affirmative action can be effective in addressing these biases. While
centered on hiring, the insights and methodologies from our study have
significant implications for a wide range of fields where screening and
gatekeeping are integral. | The Gatekeeper Effect: The Implications of Pre-Screening, Self-selection, and Bias for Hiring Processes | 2023-12-28 20:54:39 | Moran Koren | http://arxiv.org/abs/2312.17167v1, http://arxiv.org/pdf/2312.17167v1 | econ.TH |
35,356 | th | The concept of sequential choice functions is introduced and studied. This
concept applies to the reduction of the problem of stable matchings with
sequential workers to a situation where the workers are linear. | Sequential choice functions and stability problems | 2024-01-01 16:08:56 | Vladimir I. Danilov | http://arxiv.org/abs/2401.00748v1, http://arxiv.org/pdf/2401.00748v1 | math.CO |
35,357 | th | Correlated equilibria are sometimes more efficient than the Nash equilibria
of a game without signals. We investigate whether the availability of quantum
signals in the context of a classical strategic game may allow the players to
achieve even better efficiency than in any correlated equilibrium with
classical signals, and find the answer to be positive. | Correlated Equilibria of Classical Strategic Games with Quantum Signals | 2003-09-03 02:34:49 | Pierfrancesco La Mura | http://dx.doi.org/10.1142/S0219749905000724, http://arxiv.org/abs/quant-ph/0309033v1, http://arxiv.org/pdf/quant-ph/0309033v1 | quant-ph |
35,358 | th | Motivated by several classic decision-theoretic paradoxes, and by analogies
with the paradoxes which in physics motivated the development of quantum
mechanics, we introduce a projective generalization of expected utility along
the lines of the quantum-mechanical generalization of probability theory. The
resulting decision theory accommodates the dominant paradoxes, while retaining
significant simplicity and tractability. In particular, every finite game
within this larger class of preferences still has an equilibrium. | Projective Expected Utility | 2008-02-22 14:00:20 | Pierfrancesco La Mura | http://dx.doi.org/10.1016/j.jmp.2009.02.001, http://arxiv.org/abs/0802.3300v1, http://arxiv.org/pdf/0802.3300v1 | quant-ph |
35,359 | th | In most contemporary approaches to decision making, a decision problem is
described by a sets of states and set of outcomes, and a rich set of acts,
which are functions from states to outcomes over which the decision maker (DM)
has preferences. Most interesting decision problems, however, do not come with
a state space and an outcome space. Indeed, in complex problems it is often far
from clear what the state and outcome spaces would be. We present an
alternative foundation for decision making, in which the primitive objects of
choice are syntactic programs. A representation theorem is proved in the spirit
of standard representation theorems, showing that if the DM's preference
relation on objects of choice satisfies appropriate axioms, then there exist a
set S of states, a set O of outcomes, a way of interpreting the objects of
choice as functions from S to O, a probability on S, and a utility function on
O, such that the DM prefers choice a to choice b if and only if the expected
utility of a is higher than that of b. Thus, the state space and outcome space
are subjective, just like the probability and utility; they are not part of the
description of the problem. In principle, a modeler can test for SEU behavior
without having access to states or outcomes. We illustrate the power of our
approach by showing that it can capture decision makers who are subject to
framing effects. | Constructive Decision Theory | 2009-06-23 21:22:45 | Lawrence Blume, David Easley, Joseph Y. Halpern | http://arxiv.org/abs/0906.4316v2, http://arxiv.org/pdf/0906.4316v2 | cs.GT |
35,360 | th | We consider a large class of social learning models in which a group of
agents face uncertainty regarding a state of the world, share the same utility
function, observe private signals, and interact in a general dynamic setting.
We introduce Social Learning Equilibria, a static equilibrium concept that
abstracts away from the details of the given extensive form, but nevertheless
captures the corresponding asymptotic equilibrium behavior. We establish
general conditions for agreement, herding, and information aggregation in
equilibrium, highlighting a connection between agreement and information
aggregation. | Social learning equilibria | 2012-07-25 08:58:32 | Elchanan Mossel, Manuel Mueller-Frank, Allan Sly, Omer Tamuz | http://dx.doi.org/10.3982/ECTA16465, http://arxiv.org/abs/1207.5895v4, http://arxiv.org/pdf/1207.5895v4 | math.ST |
35,361 | th | We consider a group of strategic agents who must each repeatedly take one of
two possible actions. They learn which of the two actions is preferable from
initial private signals, and by observing the actions of their neighbors in a
social network.
We show that the question of whether or not the agents learn efficiently
depends on the topology of the social network. In particular, we identify a
geometric "egalitarianism" condition on the social network that guarantees
learning in infinite networks, or learning with high probability in large
finite networks, in any equilibrium. We also give examples of non-egalitarian
networks with equilibria in which learning fails. | Strategic Learning and the Topology of Social Networks | 2012-09-25 11:13:59 | Elchanan Mossel, Allan Sly, Omer Tamuz | http://dx.doi.org/10.3982/ECTA12058, http://arxiv.org/abs/1209.5527v2, http://arxiv.org/pdf/1209.5527v2 | cs.GT |
35,362 | th | We consider the complexity of finding a correlated equilibrium of an
$n$-player game in a model that allows the algorithm to make queries on
players' payoffs at pure strategy profiles. Randomized regret-based dynamics
are known to yield an approximate correlated equilibrium efficiently, namely,
in time that is polynomial in the number of players $n$. Here we show that both
randomization and approximation are necessary: no efficient deterministic
algorithm can reach even an approximate correlated equilibrium, and no
efficient randomized algorithm can reach an exact correlated equilibrium. The
results are obtained by bounding from below the number of payoff queries that
are needed. | The Query Complexity of Correlated Equilibria | 2013-05-21 19:33:32 | Sergiu Hart, Noam Nisan | http://dx.doi.org/10.1016/j.geb.2016.11.003, http://arxiv.org/abs/1305.4874v2, http://arxiv.org/pdf/1305.4874v2 | cs.GT |
35,365 | th | We consider a model of matching in trading networks in which firms can enter
into bilateral contracts. In trading networks, stable outcomes, which are
immune to deviations of arbitrary sets of firms, may not exist. We define a new
solution concept called trail stability. Trail-stable outcomes are immune to
consecutive, pairwise deviations between linked firms. We show that any trading
network with bilateral contracts has a trail-stable outcome whenever firms'
choice functions satisfy the full substitutability condition. For trail-stable
outcomes, we prove results on the lattice structure, the rural hospitals
theorem, strategy-proofness, and comparative statics of firm entry and exit. We
also introduce weak trail stability which is implied by trail stability under
full substitutability. We describe relationships between the solution concepts. | Trading Networks with Bilateral Contracts | 2015-10-01 18:03:55 | Tamás Fleiner, Zsuzsanna Jankó, Akihisa Tamura, Alexander Teytelboym | http://arxiv.org/abs/1510.01210v3, http://arxiv.org/pdf/1510.01210v3 | cs.GT |
35,366 | th | The first ever human vs. computer no-limit Texas hold 'em competition took
place from April 24-May 8, 2015 at River's Casino in Pittsburgh, PA. In this
article I present my thoughts on the competition design, agent architecture,
and lessons learned. | My Reflections on the First Man vs. Machine No-Limit Texas Hold 'em Competition | 2015-10-29 09:53:15 | Sam Ganzfried | http://arxiv.org/abs/1510.08578v2, http://arxiv.org/pdf/1510.08578v2 | cs.GT |
35,367 | th | We study the problem of Bayesian learning in a dynamical system involving
strategic agents with asymmetric information. In a series of seminal papers in
the literature, this problem has been investigated under a simplifying model
where myopically selfish players appear sequentially and act once in the game,
based on private noisy observations of the system state and public observation
of past players' actions. It has been shown that there exist information
cascades where users discard their private information and mimic the action of
their predecessor. In this paper, we provide a framework for studying Bayesian
learning dynamics in a more general setting than the one described above. In
particular, our model incorporates cases where players are non-myopic and
strategically participate for the whole duration of the game, and cases where
an endogenous process selects which subset of players will act at each time
instance. The proposed framework hinges on a sequential decomposition
methodology for finding structured perfect Bayesian equilibria (PBE) of a
general class of dynamic games with asymmetric information, where user-specific
states evolve as conditionally independent Markov processes and users make
independent noisy observations of their states. Using this methodology, we
study a specific dynamic learning model where players make decisions about
public investment based on their estimates of everyone's types. We characterize
a set of informational cascades for this problem where learning stops for the
team as a whole. We show that in such cascades, all players' estimates of other
players' types freeze even though each individual player asymptotically learns
its own true type. | Decentralized Bayesian learning in dynamic games: A framework for studying informational cascades | 2016-07-23 00:29:18 | Deepanshu Vasal, Achilleas Anastasopoulos | http://arxiv.org/abs/1607.06847v2, http://arxiv.org/pdf/1607.06847v2 | cs.GT |
35,368 | th | We study a sequential-learning model featuring a network of naive agents with
Gaussian information structures. Agents apply a heuristic rule to aggregate
predecessors' actions. They weigh these actions according the strengths of
their social connections to different predecessors. We show this rule arises
endogenously when agents wrongly believe others act solely on private
information and thus neglect redundancies among observations. We provide a
simple linear formula expressing agents' actions in terms of network paths and
use this formula to characterize the set of networks where naive agents
eventually learn correctly. This characterization implies that, on all networks
where later agents observe more than one neighbor, there exist
disproportionately influential early agents who can cause herding on incorrect
actions. Going beyond existing social-learning results, we compute the
probability of such mislearning exactly. This allows us to compare likelihoods
of incorrect herding, and hence expected welfare losses, across network
structures. The probability of mislearning increases when link densities are
higher and when networks are more integrated. In partially segregated networks,
divergent early signals can lead to persistent disagreement between groups. | Network Structure and Naive Sequential Learning | 2017-02-25 09:49:04 | Krishna Dasaratha, Kevin He | http://dx.doi.org/10.3982/TE3388, http://arxiv.org/abs/1703.02105v7, http://arxiv.org/pdf/1703.02105v7 | q-fin.EC |
35,370 | th | Agents learn about a changing state using private signals and their
neighbors' past estimates of the state. We present a model in which Bayesian
agents in equilibrium use neighbors' estimates simply by taking weighted sums
with time-invariant weights. The dynamics thus parallel those of the tractable
DeGroot model of learning in networks, but arise as an equilibrium outcome
rather than a behavioral assumption. We examine whether information aggregation
is nearly optimal as neighborhoods grow large. A key condition for this is
signal diversity: each individual's neighbors have private signals that not
only contain independent information, but also have sufficiently different
distributions. Without signal diversity $\unicode{x2013}$ e.g., if private
signals are i.i.d. $\unicode{x2013}$ learning is suboptimal in all networks and
highly inefficient in some. Turning to social influence, we find it is much
more sensitive to one's signal quality than to one's number of neighbors, in
contrast to standard models with exogenous updating rules. | Learning from Neighbors about a Changing State | 2018-01-06 19:14:47 | Krishna Dasaratha, Benjamin Golub, Nir Hak | http://dx.doi.org/10.1093/restud/rdac077, http://arxiv.org/abs/1801.02042v8, http://arxiv.org/pdf/1801.02042v8 | econ.TH |
35,371 | th | We consider a model of oligopolistic competition in a market with search
frictions, in which competing firms with products of unknown quality advertise
how much information a consumer's visit will glean. In the unique symmetric
equilibrium of this game, the countervailing incentives of attraction and
persuasion yield a payoff function for each firm that is linear in the firm's
realized effective value. If the expected quality of the products is
sufficiently high (or competition is sufficiently fierce), this corresponds to
full information--firms provide the first-best level of information. If not,
this corresponds to information dispersion--firms randomize over signals. | Attraction versus Persuasion: Information Provision in Search Markets | 2018-02-26 18:25:32 | Pak Hung Au, Mark Whitmeyer | http://arxiv.org/abs/1802.09396v7, http://arxiv.org/pdf/1802.09396v7 | math.PR |
35,372 | th | Melamed, Harrell, and Simpson have recently reported on an experiment which
appears to show that cooperation can arise in a dynamic network without
reputational knowledge, i.e., purely via dynamics [1]. We believe that their
experimental design is actually not testing this, in so far as players do know
the last action of their current partners before making a choice on their own
next action and subsequently deciding which link to cut. Had the authors given
no information at all, the result would be a decline in cooperation as shown in
[2]. | Reputation is required for cooperation to emerge in dynamic networks | 2018-03-16 02:39:21 | Jose A. Cuesta, Carlos Gracia-Lázaro, Yamir Moreno, Angel Sánchez | http://arxiv.org/abs/1803.06035v1, http://arxiv.org/pdf/1803.06035v1 | physics.soc-ph |
35,373 | th | I study endogenous learning dynamics for people who misperceive intertemporal
correlations in random sequences. Biased agents face an optimal-stopping
problem. They are uncertain about the underlying distribution and learn its
parameters from predecessors. Agents stop when early draws are "good enough,"
so predecessors' experiences contain negative streaks but not positive streaks.
When agents wrongly expect systematic reversals (the "gambler's fallacy"), they
understate the likelihood of consecutive below-average draws, converge to
over-pessimistic beliefs about the distribution's mean, and stop too early.
Agents uncertain about the distribution's variance overestimate it to an extent
that depends on predecessors' stopping thresholds. I also analyze how other
misperceptions of intertemporal correlation interact with endogenous data
censoring. | Mislearning from Censored Data: The Gambler's Fallacy and Other Correlational Mistakes in Optimal-Stopping Problems | 2018-03-22 02:21:54 | Kevin He | http://dx.doi.org/10.3982/TE4657, http://arxiv.org/abs/1803.08170v6, http://arxiv.org/pdf/1803.08170v6 | q-fin.EC |
35,374 | th | Currency trading (Forex) is the largest world market in terms of volume. We
analyze trading and tweeting about the EUR-USD currency pair over a period of
three years. First, a large number of tweets were manually labeled, and a
Twitter stance classification model is constructed. The model then classifies
all the tweets by the trading stance signal: buy, hold, or sell (EUR vs. USD).
The Twitter stance is compared to the actual currency rates by applying the
event study methodology, well-known in financial economics. It turns out that
there are large differences in Twitter stance distribution and potential
trading returns between the four groups of Twitter users: trading robots,
spammers, trading companies, and individual traders. Additionally, we observe
attempts of reputation manipulation by post festum removal of tweets with poor
predictions, and deleting/reposting of identical tweets to increase the
visibility without tainting one's Twitter timeline. | Forex trading and Twitter: Spam, bots, and reputation manipulation | 2018-04-06 15:36:28 | Igor Mozetič, Peter Gabrovšek, Petra Kralj Novak | http://arxiv.org/abs/1804.02233v2, http://arxiv.org/pdf/1804.02233v2 | cs.SI |
35,375 | th | Creating strong agents for games with more than two players is a major open
problem in AI. Common approaches are based on approximating game-theoretic
solution concepts such as Nash equilibrium, which have strong theoretical
guarantees in two-player zero-sum games, but no guarantees in non-zero-sum
games or in games with more than two players. We describe an agent that is able
to defeat a variety of realistic opponents using an exact Nash equilibrium
strategy in a 3-player imperfect-information game. This shows that, despite a
lack of theoretical guarantees, agents based on Nash equilibrium strategies can
be successful in multiplayer games after all. | Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game | 2018-04-13 08:15:28 | Sam Ganzfried, Austin Nowak, Joannier Pinales | http://arxiv.org/abs/1804.04789v1, http://arxiv.org/pdf/1804.04789v1 | cs.GT |
35,377 | th | We propose a method to design a decentralized energy market which guarantees
individual rationality (IR) in expectation, in the presence of system-level
grid constraints. We formulate the market as a welfare maximization problem
subject to IR constraints, and we make use of Lagrangian duality to model the
problem as a n-person non-cooperative game with a unique generalized Nash
equilibrium (GNE). We provide a distributed algorithm which converges to the
GNE. The convergence and properties of the algorithm are investigated by means
of numerical simulations. | A rational decentralized generalized Nash equilibrium seeking for energy markets | 2018-06-04 15:33:13 | Lorenzo Nespoli, Matteo Salani, Vasco Medici | http://arxiv.org/abs/1806.01072v1, http://arxiv.org/pdf/1806.01072v1 | cs.CE |
35,379 | th | We study online pricing algorithms for the Bayesian selection problem with
production constraints and its generalization to the laminar matroid Bayesian
online selection problem. Consider a firm producing (or receiving) multiple
copies of different product types over time. The firm can offer the products to
arriving buyers, where each buyer is interested in one product type and has a
private valuation drawn independently from a possibly different but known
distribution.
Our goal is to find an adaptive pricing for serving the buyers that maximizes
the expected social-welfare (or revenue) subject to two constraints. First, at
any time the total number of sold items of each type is no more than the number
of produced items. Second, the total number of sold items does not exceed the
total shipping capacity. This problem is a special case of the well-known
matroid Bayesian online selection problem studied in [Kleinberg and Weinberg,
2012], when the underlying matroid is laminar.
We give the first Polynomial-Time Approximation Scheme (PTAS) for the above
problem as well as its generalization to the laminar matroid Bayesian online
selection problem when the depth of the laminar family is bounded by a
constant. Our approach is based on rounding the solution of a hierarchy of
linear programming relaxations that systematically strengthen the commonly used
ex-ante linear programming formulation of these problems and approximate the
optimum online solution with any degree of accuracy. Our rounding algorithm
respects the relaxed constraints of higher-levels of the laminar tree only in
expectation, and exploits the negative dependency of the selection rule of
lower-levels to achieve the required concentration that guarantees the
feasibility with high probability. | Nearly Optimal Pricing Algorithms for Production Constrained and Laminar Bayesian Selection | 2018-07-15 05:19:33 | Nima Anari, Rad Niazadeh, Amin Saberi, Ali Shameli | http://arxiv.org/abs/1807.05477v1, http://arxiv.org/pdf/1807.05477v1 | cs.GT |
35,380 | th | Direct democracy is a special case of an ensemble of classifiers, where every
person (classifier) votes on every issue. This fails when the average voter
competence (classifier accuracy) falls below 50%, which can happen in noisy
settings where voters have only limited information, or when there are multiple
topics and the average voter competence may not be high enough for some topics.
Representative democracy, where voters choose representatives to vote, can be
an elixir in both these situations. Representative democracy is a specific way
to improve the ensemble of classifiers. We introduce a mathematical model for
studying representative democracy, in particular understanding the parameters
of a representative democracy that gives maximum decision making capability.
Our main result states that under general and natural conditions,
1. Representative democracy can make the correct decisions simultaneously for
multiple noisy issues.
2. When the cost of voting is fixed, the optimal representative democracy
requires that representatives are elected from constant sized groups: the
number of representatives should be linear in the number of voters.
3. When the cost and benefit of voting are both polynomial, the optimal group
size is close to linear in the number of voters. This work sets the
mathematical foundation for studying the quality-quantity tradeoff in a
representative democracy-type ensemble (fewer highly qualified representatives
versus more less qualified representatives). | A Mathematical Model for Optimal Decisions in a Representative Democracy | 2018-07-17 03:09:53 | Malik Magdon-Ismail, Lirong Xia | http://arxiv.org/abs/1807.06157v1, http://arxiv.org/pdf/1807.06157v1 | cs.GT |
35,381 | th | Cooperative behavior in real social dilemmas is often perceived as a
phenomenon emerging from norms and punishment. To overcome this paradigm, we
highlight the interplay between the influence of social networks on
individuals, and the activation of spontaneous self-regulating mechanisms,
which may lead them to behave cooperatively, while interacting with others and
taking conflicting decisions over time. By extending Evolutionary game theory
over networks, we prove that cooperation partially or fully emerges whether
self-regulating mechanisms are sufficiently stronger than social pressure.
Interestingly, even few cooperative individuals act as catalyzing agents for
the cooperation of others, thus activating a recruiting mechanism, eventually
driving the whole population to cooperate. | Self-regulation promotes cooperation in social networks | 2018-07-20 17:06:43 | Dario Madeo, Chiara Mocenni | http://arxiv.org/abs/1807.07848v1, http://arxiv.org/pdf/1807.07848v1 | physics.soc-ph |
35,383 | th | This paper introduces a unified framework called cooperative extensive form
games, which (i) generalizes standard non-cooperative games, and (ii) allows
for more complex coalition formation dynamics than previous concepts like
coalition-proof Nash equilibrium. Central to this framework is a novel solution
concept called cooperative equilibrium system (CES). CES differs from Nash
equilibrium in two important respects. First, a CES is immune to both
unilateral and multilateral `credible' deviations. Second, unlike Nash
equilibrium, whose stability relies on the assumption that the strategies of
non-deviating players are held fixed, CES allows for the possibility that
players may regroup and adjust their strategies in response to a deviation. The
main result establishes that every cooperative extensive form game, possibly
with imperfect information, possesses a CES. For games with perfect
information, the proof is constructive. This framework is broadly applicable in
contexts such as oligopolistic markets and dynamic political bargaining. | The strategy of conflict and cooperation | 2018-08-21 06:27:42 | Mehmet S. Ismail | http://arxiv.org/abs/1808.06750v7, http://arxiv.org/pdf/1808.06750v7 | econ.TH |
35,384 | th | We study a two-stage model, in which students are 1) admitted to college on
the basis of an entrance exam which is a noisy signal about their
qualifications (type), and then 2) those students who were admitted to college
can be hired by an employer as a function of their college grades, which are an
independently drawn noisy signal of their type. Students are drawn from one of
two populations, which might have different type distributions. We assume that
the employer at the end of the pipeline is rational, in the sense that it
computes a posterior distribution on student type conditional on all
information that it has available (college admissions, grades, and group
membership), and makes a decision based on posterior expectation. We then study
what kinds of fairness goals can be achieved by the college by setting its
admissions rule and grading policy. For example, the college might have the
goal of guaranteeing equal opportunity across populations: that the probability
of passing through the pipeline and being hired by the employer should be
independent of group membership, conditioned on type. Alternately, the college
might have the goal of incentivizing the employer to have a group blind hiring
rule. We show that both goals can be achieved when the college does not report
grades. On the other hand, we show that under reasonable conditions, these
goals are impossible to achieve even in isolation when the college uses an
(even minimally) informative grading policy. | Downstream Effects of Affirmative Action | 2018-08-27 22:15:15 | Sampath Kannan, Aaron Roth, Juba Ziani | http://arxiv.org/abs/1808.09004v1, http://arxiv.org/pdf/1808.09004v1 | cs.GT |
35,385 | th | We map the recently proposed notions of algorithmic fairness to economic
models of Equality of opportunity (EOP)---an extensively studied ideal of
fairness in political philosophy. We formally show that through our conceptual
mapping, many existing definition of algorithmic fairness, such as predictive
value parity and equality of odds, can be interpreted as special cases of EOP.
In this respect, our work serves as a unifying moral framework for
understanding existing notions of algorithmic fairness. Most importantly, this
framework allows us to explicitly spell out the moral assumptions underlying
each notion of fairness, and interpret recent fairness impossibility results in
a new light. Last but not least and inspired by luck egalitarian models of EOP,
we propose a new family of measures for algorithmic fairness. We illustrate our
proposal empirically and show that employing a measure of algorithmic
(un)fairness when its underlying moral assumptions are not satisfied, can have
devastating consequences for the disadvantaged group's welfare. | A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity | 2018-09-10 18:33:51 | Hoda Heidari, Michele Loi, Krishna P. Gummadi, Andreas Krause | http://arxiv.org/abs/1809.03400v2, http://arxiv.org/pdf/1809.03400v2 | cs.LG |
35,386 | th | In nature and society problems arise when different interests are difficult
to reconcile, which are modeled in game theory. While most applications assume
uncorrelated games, a more detailed modeling is necessary to consider the
correlations that influence the decisions of the players. The current theory
for correlated games, however, enforces the players to obey the instructions
from a third party or "correlation device" to reach equilibrium, but this
cannot be achieved for all initial correlations. We extend here the existing
framework of correlated games and find that there are other interesting and
previously unknown Nash equilibria that make use of correlations to obtain the
best payoff. This is achieved by allowing the players the freedom to follow or
not to follow the suggestions of the correlation device. By assigning
independent probabilities to follow every possible suggestion, the players
engage in a response game that turns out to have a rich structure of Nash
equilibria that goes beyond the correlated equilibrium and mixed-strategy
solutions. We determine the Nash equilibria for all possible correlated
Snowdrift games, which we find to be describable by Ising Models in thermal
equilibrium. We believe that our approach paves the way to a study of
correlations in games that uncovers the existence of interesting underlying
interaction mechanisms, without compromising the independence of the players. | Nash Equilibria in the Response Strategy of Correlated Games | 2018-09-07 15:52:12 | A. D. Correia, H. T. C. Stoof | http://dx.doi.org/10.1038/s41598-018-36562-2, http://arxiv.org/abs/1809.03860v1, http://arxiv.org/pdf/1809.03860v1 | physics.soc-ph |
35,390 | th | Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditional optimal mechanism design
approach is ill-suited---either because it makes overly strong assumptions, or
because it advocates overly complex designs. This survey reviews several common
issues with optimal mechanisms, including exorbitant communication,
computation, and informational requirements; and it presents several examples
demonstrating that passing to the relaxed goal of an approximately optimal
mechanism allows us to reason about fundamental questions that seem out of
reach of the traditional theory. | Approximately Optimal Mechanism Design | 2018-12-31 19:54:47 | Tim Roughgarden, Inbal Talgam-Cohen | http://arxiv.org/abs/1812.11896v2, http://arxiv.org/pdf/1812.11896v2 | econ.TH |
35,391 | th | This paper shows that the fuzzy temporal logic can model figures of thought
to describe decision-making behaviors. In order to exemplify, some economic
behaviors observed experimentally were modeled from problems of choice
containing time, uncertainty and fuzziness. Related to time preference, it is
noted that the subadditive discounting is mandatory in positive rewards
situations and, consequently, results in the magnitude effect and time effect,
where the last has a stronger discounting for earlier delay periods (as in, one
hour, one day), but a weaker discounting for longer delay periods (for
instance, six months, one year, ten years). In addition, it is possible to
explain the preference reversal (change of preference when two rewards proposed
on different dates are shifted in the time). Related to the Prospect Theory, it
is shown that the risk seeking and the risk aversion are magnitude dependents,
where the risk seeking may disappear when the values to be lost are very high. | Decision-making and Fuzzy Temporal Logic | 2019-01-07 21:56:24 | José Cláudio do Nascimento | http://arxiv.org/abs/1901.01970v2, http://arxiv.org/pdf/1901.01970v2 | cs.AI |
35,394 | th | As financial instruments grow in complexity more and more information is
neglected by risk optimization practices. This brings down a curtain of opacity
on the origination of risk, that has been one of the main culprits in the
2007-2008 global financial crisis. We discuss how the loss of transparency may
be quantified in bits, using information theoretic concepts. We find that {\em
i)} financial transformations imply large information losses, {\em ii)}
portfolios are more information sensitive than individual stocks only if
fundamental analysis is sufficiently informative on the co-movement of assets,
that {\em iii)} securitisation, in the relevant range of parameters, yields
assets that are less information sensitive than the original stocks and that
{\em iv)} when diversification (or securitisation) is at its best (i.e. when
assets are uncorrelated) information losses are maximal. We also address the
issue of whether pricing schemes can be introduced to deal with information
losses. This is relevant for the transmission of incentives to gather
information on the risk origination side. Within a simple mean variance scheme,
we find that market incentives are not generally sufficient to make information
harvesting sustainable. | Lost in Diversification | 2019-01-28 19:39:51 | Marco Bardoscia, Daniele d'Arienzo, Matteo Marsili, Valerio Volpati | http://dx.doi.org/10.1016/j.crhy.2019.05.015, http://arxiv.org/abs/1901.09795v1, http://arxiv.org/pdf/1901.09795v1 | q-fin.GN |
35,395 | th | The standard solution concept for stochastic games is Markov perfect
equilibrium (MPE); however, its computation becomes intractable as the number
of players increases. Instead, we consider mean field equilibrium (MFE) that
has been popularized in the recent literature. MFE takes advantage of averaging
effects in models with a large number of players. We make three main
contributions. First, our main result provides conditions that ensure the
uniqueness of an MFE. We believe this uniqueness result is the first of its
nature in the class of models we study. Second, we generalize previous MFE
existence results. Third, we provide general comparative statics results. We
apply our results to dynamic oligopoly models and to heterogeneous agent
macroeconomic models commonly used in previous work in economics and
operations. | Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics | 2019-03-06 12:56:58 | Bar Light, Gabriel Weintraub | http://arxiv.org/abs/1903.02273v3, http://arxiv.org/pdf/1903.02273v3 | econ.TH |
35,397 | th | We consider a stochastic game of contribution to the common good in which the
players have continuous control over the degree of contribution, and we examine
the gradualism arising from the free rider effect. This game belongs to the
class of variable concession games which generalize wars of attrition.
Previously known examples of variable concession games in the literature yield
equilibria characterized by singular control strategies without any delay of
concession. However, these no-delay equilibria are in contrast to mixed
strategy equilibria of canonical wars of attrition in which each player delays
concession by a randomized time. We find that a variable contribution game with
a single state variable, which extends the Nerlove-Arrow model, possesses an
equilibrium characterized by regular control strategies that result in a
gradual concession. This equilibrium naturally generalizes the mixed strategy
equilibria from the canonical wars of attrition. Stochasticity of the problem
accentuates the qualitative difference between a singular control solution and
a regular control equilibrium solution. We also find that asymmetry between the
players can mitigate the inefficiency caused by the gradualism. | Game of Variable Contributions to the Common Good under Uncertainty | 2019-04-01 01:41:25 | H. Dharma Kwon | http://dx.doi.org/10.1287/opre.2019.1879, http://arxiv.org/abs/1904.00500v1, http://arxiv.org/pdf/1904.00500v1 | math.OC |
35,399 | th | Journal ranking is becoming more important in assessing the quality of
academic research. Several indices have been suggested for this purpose,
typically on the basis of a citation graph between the journals. We follow an
axiomatic approach and find an impossibility theorem: any self-consistent
ranking method, which satisfies a natural monotonicity property, should depend
on the level of aggregation. Our result presents a trade-off between two
axiomatic properties and reveals a dilemma of aggregation. | Journal ranking should depend on the level of aggregation | 2019-04-08 16:27:34 | László Csató | http://dx.doi.org/10.1016/j.joi.2019.100975, http://arxiv.org/abs/1904.06300v4, http://arxiv.org/pdf/1904.06300v4 | cs.DL |
35,402 | th | We develop original models to study interacting agents in financial markets
and in social networks. Within these models randomness is vital as a form of
shock or news that decays with time. Agents learn from their observations and
learning ability to interpret news or private information in time-varying
networks. Under general assumption on the noise, a limit theorem is developed
for the generalised DeGroot framework for certain type of conditions governing
the learning. In this context, the agents beliefs (properly scaled) converge in
distribution that is not necessarily normal. Fresh insights are gained not only
from proposing a new setting for social learning models but also from using
different techniques to study discrete time random linear dynamical systems. | Averaging plus Learning Models and Their Asymptotics | 2019-04-17 11:34:14 | Ionel Popescu, Tushar Vaidya | http://dx.doi.org/10.1098/rspa.2022.0681, http://arxiv.org/abs/1904.08131v5, http://arxiv.org/pdf/1904.08131v5 | q-fin.MF |
35,403 | th | We consider an agent who represents uncertainty about the environment via a
possibly misspecified model. Each period, the agent takes an action, observes a
consequence, and uses Bayes' rule to update her belief about the environment.
This framework has become increasingly popular in economics to study behavior
driven by incorrect or biased beliefs. Current literature has characterized
asymptotic behavior under fairly specific assumptions. By first showing that
the key element to predict the agent's behavior is the frequency of her past
actions, we are able to characterize asymptotic behavior in general settings in
terms of the solutions of a generalization of a differential equation that
describes the evolution of the frequency of actions. We then present a series
of implications that can be readily applied to economic applications, thus
providing off-the-shelf tools that can be used to characterize behavior under
misspecified learning. | Asymptotic Behavior of Bayesian Learners with Misspecified Models | 2019-04-18 03:58:32 | Ignacio Esponda, Demian Pouzo, Yuichi Yamamoto | http://arxiv.org/abs/1904.08551v2, http://arxiv.org/pdf/1904.08551v2 | econ.TH |
35,404 | th | The literature specifies extensive-form games in many styles, and eventually
I hope to formally translate games across those styles. Toward that end, this
paper defines $\mathbf{NCF}$, the category of node-and-choice forms. The
category's objects are extensive forms in essentially any style, and the
category's isomorphisms are made to accord with the literature's small handful
of ad hoc style equivalences.
Further, this paper develops two full subcategories: $\mathbf{CsqF}$ for
forms whose nodes are choice-sequences, and $\mathbf{CsetF}$ for forms whose
nodes are choice-sets. I show that $\mathbf{NCF}$ is "isomorphically enclosed"
in $\mathbf{CsqF}$ in the sense that each $\mathbf{NCF}$ form is isomorphic to
a $\mathbf{CsqF}$ form. Similarly, I show that $\mathbf{CsqF_{\tilde a}}$ is
isomorphically enclosed in $\mathbf{CsetF}$ in the sense that each
$\mathbf{CsqF}$ form with no-absentmindedness is isomorphic to a
$\mathbf{CsetF}$ form. The converses are found to be almost immediate, and the
resulting equivalences unify and simplify two ad hoc style equivalences in
Kline and Luckraz 2016 and Streufert 2019.
Aside from the larger agenda, this paper already makes three practical
contributions. Style equivalences are made easier to derive by [1] a natural
concept of isomorphic invariance and [2] the composability of isomorphic
enclosures. In addition, [3] some new consequences of equivalence are
systematically deduced. | The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms | 2019-04-27 04:30:55 | Peter A. Streufert | http://dx.doi.org/10.1007/978-981-15-1342-8_2, http://arxiv.org/abs/1904.12085v1, http://arxiv.org/pdf/1904.12085v1 | econ.TH |
35,405 | th | We study repeated independent Blackwell experiments; standard examples
include drawing multiple samples from a population, or performing a measurement
in different locations. In the baseline setting of a binary state of nature, we
compare experiments in terms of their informativeness in large samples.
Addressing a question due to Blackwell (1951), we show that generically an
experiment is more informative than another in large samples if and only if it
has higher Renyi divergences.
We apply our analysis to the problem of measuring the degree of dissimilarity
between distributions by means of divergences. A useful property of Renyi
divergences is their additivity with respect to product distributions. Our
characterization of Blackwell dominance in large samples implies that every
additive divergence that satisfies the data processing inequality is an
integral of Renyi divergences. | From Blackwell Dominance in Large Samples to Renyi Divergences and Back Again | 2019-06-07 02:15:02 | Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz | http://arxiv.org/abs/1906.02838v5, http://arxiv.org/pdf/1906.02838v5 | math.ST |
35,407 | th | With vast databases at their disposal, private tech companies can compete
with public statistical agencies to provide population statistics. However,
private companies face different incentives to provide high-quality statistics
and to protect the privacy of the people whose data are used. When both privacy
protection and statistical accuracy are public goods, private providers tend to
produce at least one suboptimally, but it is not clear which. We model a firm
that publishes statistics under a guarantee of differential privacy. We prove
that provision by the private firm results in inefficiently low data quality in
this framework. | Suboptimal Provision of Privacy and Statistical Accuracy When They are Public Goods | 2019-06-22 02:42:46 | John M. Abowd, Ian M. Schmutte, William Sexton, Lars Vilhuber | http://arxiv.org/abs/1906.09353v1, http://arxiv.org/pdf/1906.09353v1 | econ.TH |
35,408 | th | Poker is a large complex game of imperfect information, which has been
singled out as a major AI challenge problem. Recently there has been a series
of breakthroughs culminating in agents that have successfully defeated the
strongest human players in two-player no-limit Texas hold 'em. The strongest
agents are based on algorithms for approximating Nash equilibrium strategies,
which are stored in massive binary files and unintelligible to humans. A recent
line of research has explored approaches for extrapolating knowledge from
strong game-theoretic strategies that can be understood by humans. This would
be useful when humans are the ultimate decision maker and allow humans to make
better decisions from massive algorithmically-generated strategies. Using
techniques from machine learning we have uncovered a new simple, fundamental
rule of poker strategy that leads to a significant improvement in performance
over the best prior rule and can also easily be applied by human players. | Most Important Fundamental Rule of Poker Strategy | 2019-06-09 01:42:24 | Sam Ganzfried, Max Chiswick | http://arxiv.org/abs/1906.09895v3, http://arxiv.org/pdf/1906.09895v3 | cs.AI |
35,409 | th | We propose new Degroot-type social learning models with feedback in a
continuous time, to investigate the effect of a noisy information source on
consensus formation in a social network. Unlike the standard Degroot framework,
noisy information models destroy consensus formation. On the other hand, the
noisy opinion dynamics converge to the equilibrium distribution that
encapsulates correlations among agents' opinions. Interestingly, such an
equilibrium distribution is also a non-equilibrium steady state (NESS) with a
non-zero probabilistic current loop. Thus, noisy information source leads to a
NESS at long times that encodes persistent correlated opinion dynamics of
learning agents. Our model provides a simple realization of NESS in the context
of social learning. Other phenomena such as synchronization of opinions when
agents are subject to a common noise are also studied. | Broken Detailed Balance and Non-Equilibrium Dynamics in Noisy Social Learning Models | 2019-06-27 11:00:36 | Tushar Vaidya, Thiparat Chotibut, Georgios Piliouras | http://dx.doi.org/10.1016/j.physa.2021.125818, http://arxiv.org/abs/1906.11481v2, http://arxiv.org/pdf/1906.11481v2 | physics.soc-ph |
35,411 | th | We study the problem of allocating divisible bads (chores) among multiple
agents with additive utilities when monetary transfers are not allowed. The
competitive rule is known for its remarkable fairness and efficiency properties
in the case of goods. This rule was extended to chores in prior work by
Bogomolnaia, Moulin, Sandomirskiy, and Yanovskaya (2017). The rule produces
Pareto optimal and envy-free allocations for both goods and chores. In the case
of goods, the outcome of the competitive rule can be easily computed.
Competitive allocations solve the Eisenberg-Gale convex program; hence the
outcome is unique and can be approximately found by standard gradient methods.
An exact algorithm that runs in polynomial time in the number of agents and
goods was given by Orlin (2010).
In the case of chores, the competitive rule does not solve any convex
optimization problem; instead, competitive allocations correspond to local
minima, local maxima, and saddle points of the Nash social welfare on the
Pareto frontier of the set of feasible utilities. The Pareto frontier may
contain many such points; consequently, the competitive rule's outcome is no
longer unique.
In this paper, we show that all the outcomes of the competitive rule for
chores can be computed in strongly polynomial time if either the number of
agents or the number of chores is fixed. The approach is based on a combination
of three ideas: all consumption graphs of Pareto optimal allocations can be
listed in polynomial time; for a given consumption graph, a candidate for a
competitive utility profile can be constructed via an explicit formula; each
candidate can be checked for competitiveness, and the allocation can be
reconstructed using a maximum flow computation.
Our algorithm gives an approximately-fair allocation of indivisible chores by
the rounding technique of Barman and Krishnamurthy (2018). | Algorithms for Competitive Division of Chores | 2019-07-03 09:55:04 | Simina Brânzei, Fedor Sandomirskiy | http://arxiv.org/abs/1907.01766v2, http://arxiv.org/pdf/1907.01766v2 | cs.GT |
35,413 | th | We study a model of vendors competing to sell a homogeneous product to
customers spread evenly along a linear city. This model is based on Hotelling's
celebrated paper in 1929. Our aim in this paper is to present a necessary and
sufficient condition for the equilibrium. This yields a representation for the
equilibrium. To achieve this, we first formulate the model mathematically.
Next, we prove that the condition holds if and only if vendors are equilibrium. | Necessary and sufficient condition for equilibrium of the Hotelling model | 2019-07-14 13:26:40 | Satoshi Hayashi, Naoki Tsuge | http://arxiv.org/abs/1907.06200v1, http://arxiv.org/pdf/1907.06200v1 | econ.TH |
35,414 | th | We investigate a multi-household DSGE model in which past aggregate
consumption impacts the confidence, and therefore consumption propensity, of
individual households. We find that such a minimal setup is extremely rich, and
leads to a variety of realistic output dynamics: high output with no crises;
high output with increased volatility and deep, short lived recessions;
alternation of high and low output states where relatively mild drop in
economic conditions can lead to a temporary confidence collapse and steep
decline in economic activity. The crisis probability depends exponentially on
the parameters of the model, which means that markets cannot efficiently price
the associated risk premium. We conclude by stressing that within our
framework, {\it narratives} become an important monetary policy tool, that can
help steering the economy back on track. | Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model | 2019-07-17 13:13:35 | Federico Guglielmo Morelli, Michael Benzaquen, Marco Tarzia, Jean-Philippe Bouchaud | http://arxiv.org/abs/1907.07425v1, http://arxiv.org/pdf/1907.07425v1 | q-fin.GN |
35,416 | th | How does supply uncertainty affect the structure of supply chain networks? To
answer this question we consider a setting where retailers and suppliers must
establish a costly relationship with each other prior to engaging in trade.
Suppliers, with uncertain yield, announce wholesale prices, while retailers
must decide which suppliers to link to based on their wholesale prices.
Subsequently, retailers compete with each other in Cournot fashion to sell the
acquired supply to consumers. We find that in equilibrium retailers concentrate
their links among too few suppliers, i.e., there is insufficient
diversification of the supply base. We find that either reduction of supply
variance or increase of mean supply, increases a supplier's profit. However,
these two ways of improving service have qualitatively different effects on
welfare: improvement of the expected supply by a supplier makes everyone better
off, whereas improvement of supply variance lowers consumer surplus. | Yield Uncertainty and Strategic Formation of Supply Chain Networks | 2019-07-20 19:19:46 | Victor Amelkin, Rakesh Vohra | http://dx.doi.org/10.1002/net.22186, http://arxiv.org/abs/1907.09943v1, http://arxiv.org/pdf/1907.09943v1 | cs.GT |
35,417 | th | Motivated by the problem of market power in electricity markets, we
introduced in previous works a mechanism for simplified markets of two agents
with linear cost. In standard procurement auctions, the market power resulting
from the quadratic transmission losses allows the producers to bid above their
true values, which are their production cost. The mechanism proposed in the
previous paper optimally reduces the producers' margin to the society's
benefit. In this paper, we extend those results to a more general market made
of a finite number of agents with piecewise linear cost functions, which makes
the problem more difficult, but simultaneously more realistic. We show that the
methodology works for a large class of externalities. We also provide an
algorithm to solve the principal allocation problem. Our contribution provides
a benchmark to assess the sub-optimality of the mechanisms used in practice. | Optimal auctions for networked markets with externalities | 2019-07-23 21:02:28 | Benjamin Heymann, Alejandro Jofré | http://arxiv.org/abs/1907.10080v1, http://arxiv.org/pdf/1907.10080v1 | econ.TH |
35,418 | th | Exchanges acquire excess processing capacity to accommodate trading activity
surges associated with zero-sum high-frequency trader (HFT) "duels." The idle
capacity's opportunity cost is an externality of low-latency trading. We build
a model of decentralized exchanges (DEX) with flexible capacity. On DEX, HFTs
acquire speed in real-time from peer-to-peer networks. The price of speed
surges during activity bursts, as HFTs simultaneously race to market. Relative
to centralized exchanges, HFTs acquire more speed on DEX, but for shorter
timespans. Low-latency "sprints" speed up price discovery without harming
liquidity. Overall, speed rents decrease and fewer resources are locked-in to
support zero-sum HFT trades. | Liquid Speed: On-Demand Fast Trading at Distributed Exchanges | 2019-07-24 23:56:12 | Michael Brolley, Marius Zoican | http://arxiv.org/abs/1907.10720v1, http://arxiv.org/pdf/1907.10720v1 | q-fin.TR |
35,419 | th | The stochastic multi-armed bandit model captures the tradeoff between
exploration and exploitation. We study the effects of competition and
cooperation on this tradeoff. Suppose there are $k$ arms and two players, Alice
and Bob. In every round, each player pulls an arm, receives the resulting
reward, and observes the choice of the other player but not their reward.
Alice's utility is $\Gamma_A + \lambda \Gamma_B$ (and similarly for Bob), where
$\Gamma_A$ is Alice's total reward and $\lambda \in [-1, 1]$ is a cooperation
parameter. At $\lambda = -1$ the players are competing in a zero-sum game, at
$\lambda = 1$, they are fully cooperating, and at $\lambda = 0$, they are
neutral: each player's utility is their own reward. The model is related to the
economics literature on strategic experimentation, where usually players
observe each other's rewards.
With discount factor $\beta$, the Gittins index reduces the one-player
problem to the comparison between a risky arm, with a prior $\mu$, and a
predictable arm, with success probability $p$. The value of $p$ where the
player is indifferent between the arms is the Gittins index $g = g(\mu,\beta) >
m$, where $m$ is the mean of the risky arm.
We show that competing players explore less than a single player: there is
$p^* \in (m, g)$ so that for all $p > p^*$, the players stay at the predictable
arm. However, the players are not myopic: they still explore for some $p > m$.
On the other hand, cooperating players explore more than a single player. We
also show that neutral players learn from each other, receiving strictly higher
total rewards than they would playing alone, for all $ p\in (p^*, g)$, where
$p^*$ is the threshold from the competing case.
Finally, we show that competing and neutral players eventually settle on the
same arm in every Nash equilibrium, while this can fail for cooperating
players. | Multiplayer Bandit Learning, from Competition to Cooperation | 2019-08-03 11:20:54 | Simina Brânzei, Yuval Peres | http://arxiv.org/abs/1908.01135v3, http://arxiv.org/pdf/1908.01135v3 | cs.GT |
35,420 | th | We outline a token model for Truebit, a retrofitting, blockchain enhancement
which enables secure, community-based computation. The model addresses the
challenge of stable task pricing, as raised in the Truebit whitepaper, without
appealing to external oracles, exchanges, or hierarchical nodes. The system's
sustainable economics and fair market pricing derive from a mintable token
format which leverages existing tokens for liquidity. Finally, we introduce a
governance layer whose lifecycles culminates with permanent dissolution into
utility tokens, thereby tending the network towards autonomous
decentralization. | Bootstrapping a stable computation token | 2019-08-08 09:41:13 | Jason Teutsch, Sami Mäkelä, Surya Bakshi | http://arxiv.org/abs/1908.02946v1, http://arxiv.org/pdf/1908.02946v1 | cs.CR |
35,421 | th | In December 2015, a bounty emerged to establish both reliable communication
and secure transfer of value between the Dogecoin and Ethereum blockchains.
This prized "Dogethereum bridge" would allow parties to "lock" a DOGE coin on
Dogecoin and in exchange receive a newly minted WOW token in Ethereum. Any
subsequent owner of the WOW token could burn it and, in exchange, earn the
right to "unlock" a DOGE on Dogecoin.
We describe an efficient, trustless, and retrofitting Dogethereum
construction which requires no fork but rather employs economic collateral to
achieve a "lock" operation in Dogecoin. The protocol relies on bulletproofs,
Truebit, and parametrized tokens to efficiently and trustlessly relay events
from the "true" Dogecoin blockchain into Ethereum. The present construction not
only enables cross-platform exchange but also allows Ethereum smart contracts
to trustlessly access Dogecoin. A similar technique adds Ethereum-based smart
contracts to Bitcoin and Bitcoin data to Ethereum smart contracts. | Retrofitting a two-way peg between blockchains | 2019-08-12 07:41:13 | Jason Teutsch, Michael Straka, Dan Boneh | http://arxiv.org/abs/1908.03999v1, http://arxiv.org/pdf/1908.03999v1 | cs.CR |
35,422 | th | Ethereum has emerged as a dynamic platform for exchanging cryptocurrency
tokens. While token crowdsales cannot simultaneously guarantee buyers both
certainty of valuation and certainty of participation, we show that if each
token buyer specifies a desired purchase quantity at each valuation then
everyone can successfully participate. Our implementation introduces smart
contract techniques which recruit outside participants in order to circumvent
computational complexity barriers. | Interactive coin offerings | 2019-08-12 07:30:55 | Jason Teutsch, Vitalik Buterin, Christopher Brown | http://arxiv.org/abs/1908.04295v1, http://arxiv.org/pdf/1908.04295v1 | econ.TH |
35,423 | th | We provide elementary proofs of several results concerning the possible
outcomes arising from a fixed profile within the class of positional voting
systems. Our arguments enable a simple and explicit construction of paradoxical
profiles, and we also demonstrate how to choose weights that realize desirable
results from a given profile. The analysis ultimately boils down to thinking
about positional voting systems in terms of doubly stochastic matrices. | Positional Voting and Doubly Stochastic Matrices | 2019-08-18 22:48:33 | Jacqueline Anderson, Brian Camara, John Pike | http://arxiv.org/abs/1908.06506v2, http://arxiv.org/pdf/1908.06506v2 | math.CO |
35,431 | th | For a discrete time Markov chain and in line with Strotz' consistent planning
we develop a framework for problems of optimal stopping that are
time-inconsistent due to the consideration of a non-linear function of an
expected reward. We consider pure and mixed stopping strategies and a (subgame
perfect Nash) equilibrium. We provide different necessary and sufficient
equilibrium conditions including a verification theorem. Using a fixed point
argument we provide equilibrium existence results. We adapt and study the
notion of the myopic adjustment process and introduce different kinds of
equilibrium stability. We show that neither existence nor uniqueness of
equilibria should generally be expected. The developed theory is applied to a
mean-variance problem and a variance problem. | Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application | 2019-09-26 09:17:03 | Sören Christensen, Kristoffer Lindensjö | http://arxiv.org/abs/1909.11921v2, http://arxiv.org/pdf/1909.11921v2 | math.OC |
35,426 | th | The Shapley value has become a popular method to attribute the prediction of
a machine-learning model on an input to its base features. The use of the
Shapley value is justified by citing [16] showing that it is the \emph{unique}
method that satisfies certain good properties (\emph{axioms}).
There are, however, a multiplicity of ways in which the Shapley value is
operationalized in the attribution problem. These differ in how they reference
the model, the training data, and the explanation context. These give very
different results, rendering the uniqueness result meaningless. Furthermore, we
find that previously proposed approaches can produce counterintuitive
attributions in theory and in practice---for instance, they can assign non-zero
attributions to features that are not even referenced by the model.
In this paper, we use the axiomatic approach to study the differences between
some of the many operationalizations of the Shapley value for attribution, and
propose a technique called Baseline Shapley (BShap) that is backed by a proper
uniqueness result. We also contrast BShap with Integrated Gradients, another
extension of Shapley value to the continuous setting. | The many Shapley values for model explanation | 2019-08-22 19:13:10 | Mukund Sundararajan, Amir Najmi | http://arxiv.org/abs/1908.08474v2, http://arxiv.org/pdf/1908.08474v2 | cs.AI |
35,427 | th | In this article we solve the problem of maximizing the expected utility of
future consumption and terminal wealth to determine the optimal pension or
life-cycle fund strategy for a cohort of pension fund investors. The setup is
strongly related to a DC pension plan where additionally (individual)
consumption is taken into account. The consumption rate is subject to a
time-varying minimum level and terminal wealth is subject to a terminal floor.
Moreover, the preference between consumption and terminal wealth as well as the
intertemporal coefficient of risk aversion are time-varying and therefore
depend on the age of the considered pension cohort. The optimal consumption and
investment policies are calculated in the case of a Black-Scholes financial
market framework and hyperbolic absolute risk aversion (HARA) utility
functions. We generalize Ye (2008) (2008 American Control Conference, 356-362)
by adding an age-dependent coefficient of risk aversion and extend Steffensen
(2011) (Journal of Economic Dynamics and Control, 35(5), 659-667), Hentschel
(2016) (Doctoral dissertation, Ulm University) and Aase (2017) (Stochastics,
89(1), 115-141) by considering consumption in combination with terminal wealth
and allowing for consumption and terminal wealth floors via an application of
HARA utility functions. A case study on fitting several models to realistic,
time-dependent life-cycle consumption and relative investment profiles shows
that only our extended model with time-varying preference parameters provides
sufficient flexibility for an adequate fit. This is of particular interest to
life-cycle products for (private) pension investments or pension insurance in
general. | Optimal life-cycle consumption and investment decisions under age-dependent risk preferences | 2019-08-27 04:17:52 | Andreas Lichtenstern, Pavel V. Shevchenko, Rudi Zagst | http://dx.doi.org/10.1007/s11579-020-00276-9, http://arxiv.org/abs/1908.09976v1, http://arxiv.org/pdf/1908.09976v1 | q-fin.MF |
35,429 | th | Our research is concerned with studying behavioural changes within a dynamic
system, i.e. health care, and their effects on the decision-making process.
Evolutionary Game theory is applied to investigate the most probable
strategy(ies) adopted by individuals in a finite population based on the
interactions among them with an eye to modelling behaviour using the following
metrics: cost of investment, cost of management, cost of treatment, reputation
benefit for the provider(s), and the gained health benefit for the patient. | Modelling Cooperation in a Dynamic Healthcare System | 2019-09-06 20:23:39 | Zainab Alalawi, Yifeng Zeng, The Anh Han, Aiman Elragig | http://arxiv.org/abs/1909.03070v1, http://arxiv.org/pdf/1909.03070v1 | cs.GT |
35,430 | th | We introduce and analyze new envy-based fairness concepts for agents with
weights that quantify their entitlements in the allocation of indivisible
items. We propose two variants of weighted envy-freeness up to one item (WEF1):
strong, where envy can be eliminated by removing an item from the envied
agent's bundle, and weak, where envy can be eliminated either by removing an
item (as in the strong version) or by replicating an item from the envied
agent's bundle in the envying agent's bundle. We show that for additive
valuations, an allocation that is both Pareto optimal and strongly WEF1 always
exists and can be computed in pseudo-polynomial time; moreover, an allocation
that maximizes the weighted Nash social welfare may not be strongly WEF1, but
always satisfies the weak version of the property. Moreover, we establish that
a generalization of the round-robin picking sequence algorithm produces in
polynomial time a strongly WEF1 allocation for an arbitrary number of agents;
for two agents, we can efficiently achieve both strong WEF1 and Pareto
optimality by adapting the adjusted winner procedure. Our work highlights
several aspects in which weighted fair division is richer and more challenging
than its unweighted counterpart. | Weighted Envy-Freeness in Indivisible Item Allocation | 2019-09-23 20:44:59 | Mithun Chakraborty, Ayumi Igarashi, Warut Suksompong, Yair Zick | http://dx.doi.org/10.1145/3457166, http://arxiv.org/abs/1909.10502v7, http://arxiv.org/pdf/1909.10502v7 | cs.AI |
35,432 | th | This paper studies dynamic mechanism design in a quasilinear Markovian
environment and analyzes a direct mechanism model of a principal-agent
framework in which the agent is allowed to exit at any period. We consider that
the agent's private information, referred to as state, evolves over time. The
agent makes decisions of whether to stop or continue and what to report at each
period. The principal, on the other hand, chooses decision rules consisting of
an allocation rule and a set of payment rules to maximize her ex-ante expected
payoff. In order to influence the agent's stopping decision, one of the
terminal payment rules is posted-price, i.e., it depends only on the realized
stopping time of the agent. We define the incentive compatibility in this
dynamic environment in terms of Bellman equations, which is then simplified by
establishing a one-shot deviation principle. Given the optimality of the
stopping rule, a sufficient condition for incentive compatibility is obtained
by constructing the state-dependent payment rules in terms of a set of
functions parameterized by the allocation rule. A necessary condition is
derived from envelope theorem, which explicitly formulates the state-dependent
payment rules in terms of allocation rules. A class of monotone environment is
considered to characterize the optimal stopping by a threshold rule. The
posted-price payment rules are then pinned down in terms of the allocation rule
and the threshold function up to a constant. The incentive compatibility
constraints restrict the design of the posted-price payment rule by a regular
condition. | On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment | 2019-09-30 17:05:50 | Tao Zhang, Quanyan Zhu | http://arxiv.org/abs/1909.13720v4, http://arxiv.org/pdf/1909.13720v4 | math.DS |
35,435 | th | We use machine learning to provide a tractable measure of the amount of
predictable variation in the data that a theory captures, which we call its
"completeness." We apply this measure to three problems: assigning certain
equivalents to lotteries, initial play in games, and human generation of random
sequences. We discover considerable variation in the completeness of existing
models, which sheds light on whether to focus on developing better models with
the same features or instead to look for new features that will improve
predictions. We also illustrate how and why completeness varies with the
experiments considered, which highlights the role played in choosing which
experiments to run. | Measuring the Completeness of Theories | 2019-10-15 22:46:54 | Drew Fudenberg, Jon Kleinberg, Annie Liang, Sendhil Mullainathan | http://arxiv.org/abs/1910.07022v1, http://arxiv.org/pdf/1910.07022v1 | econ.TH |
35,437 | th | This survey explores the literature on game-theoretic models of network
formation under the hypothesis of mutual consent in link formation. The
introduction of consent in link formation imposes a coordination problem in the
network formation process. This survey explores the conclusions from this
theory and the various methodologies to avoid the main pitfalls. The main
insight originates from Myerson's work on mutual consent in link formation and
his main conclusion that the empty network (the network without any links)
always emerges as a strong Nash equilibrium in any game-theoretic model of
network formation under mutual consent and positive link formation costs.
Jackson and Wolinsky introduced a cooperative framework to avoid this main
pitfall. They devised the notion of a pairwise stable network to arrive at
equilibrium networks that are mainly non-trivial. Unfortunately, this notion of
pairwise stability requires coordinated action by pairs of decision makers in
link formation. I survey the possible solutions in a purely non-cooperative
framework of network formation under mutual consent by exploring potential
refinements of the standard Nash equilibrium concept to explain the emergence
of non-trivial networks. This includes the notions of unilateral and monadic
stability. The first one is founded on advanced rational reasoning of
individuals about how others would respond to one's efforts to modify the
network. The latter incorporates trusting, boundedly rational behaviour into
the network formation process. The survey is concluded with an initial
exploration of external correlation devices as an alternative framework to
address mutual consent in network formation. | Building social networks under consent: A survey | 2019-10-25 16:04:55 | Robert P. Gilles | http://arxiv.org/abs/1910.11693v2, http://arxiv.org/pdf/1910.11693v2 | econ.TH |
35,439 | th | Mean field game theory studies the behavior of a large number of interacting
individuals in a game theoretic setting and has received a lot of attention in
the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In
this work, we derive mean field game partial differential equation systems from
deterministic microscopic agent dynamics. The dynamics are given by a
particular class of ordinary differential equations, for which an optimal
strategy can be computed (Bressan, Milan Journal of Mathematics, 2011). We use
the concept of Nash equilibria and apply the dynamic programming principle to
derive the mean field limit equations and we study the scaling behavior of the
system as the number of agents tends to infinity and find several mean field
game limits. Especially we avoid in our derivation the notion of measure
derivatives. Novel scales are motivated by an example of an agent-based
financial market model. | Microscopic Derivation of Mean Field Game Models | 2019-10-30 00:12:16 | Martin Frank, Michael Herty, Torsten Trimborn | http://arxiv.org/abs/1910.13534v1, http://arxiv.org/pdf/1910.13534v1 | math.OC |
35,441 | th | The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely
studied in terms of its theoretical analysis as well as in its applications,
ranging from sociology and biology to economics. Many experimental results of
the RPS game indicate that this game is better modelled by the discretized
best-response dynamics rather than continuous time dynamics. In this work we
show that the attractor of the discrete time best-response dynamics of the RPS
game is finite and periodic. Moreover we also describe the bifurcations of the
attractor and determine the exact number, period and location of the periodic
strategies. | Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game | 2019-12-14 15:20:12 | José Pedro Gaivão, Telmo Peixe | http://dx.doi.org/10.1007/s13235-020-00371-y, http://arxiv.org/abs/1912.06831v1, http://arxiv.org/pdf/1912.06831v1 | math.DS |
35,442 | th | For object reallocation problems, if preferences are strict but otherwise
unrestricted, the Top Trading Cycles rule (TTC) is the leading rule: It is the
only rule satisfying efficiency, individual rationality, and
strategy-proofness. However, on the subdomain of single-peaked preferences,
Bade (2019) defines a new rule, the "crawler", which also satisfies these three
properties. (i) The crawler selects an allocation by "visiting" agents in a
specific order. A natural "dual" rule can be defined by proceeding in the
reverse order. Our first theorem states that the crawler and its dual are
actually the same. (ii) Single-peakedness of a preference profile may in fact
hold for more than one order and its reverse. Our second theorem states that
the crawler is invariant to the choice of the order. (iii) For object
allocation problems (as opposed to reallocation problems), we define a
probabilistic version of the crawler by choosing an endowment profile at random
according to a uniform distribution, and applying the original definition. Our
third theorem states that this rule is the same as the "random priority rule". | The Crawler: Three Equivalence Results for Object (Re)allocation Problems when Preferences Are Single-peaked | 2019-12-14 22:27:12 | Yuki Tamura, Hadi Hosseini | http://arxiv.org/abs/1912.06909v2, http://arxiv.org/pdf/1912.06909v2 | econ.TH |
35,445 | th | In the past few years, several new matching models have been proposed and
studied that take into account complex distributional constraints. Relevant
lines of work include (1) school choice with diversity constraints where
students have (possibly overlapping) types and (2) hospital-doctor matching
where various regional quotas are imposed. In this paper, we present a
polynomial-time reduction to transform an instance of (1) to an instance of (2)
and we show how the feasibility and stability of corresponding matchings are
preserved under the reduction. Our reduction provides a formal connection
between two important strands of work on matching with distributional
constraints. We then apply the reduction in two ways. Firstly, we show that it
is NP-complete to check whether a feasible and stable outcome for (1) exists.
Due to our reduction, these NP-completeness results carry over to setting (2).
In view of this, we help unify some of the results that have been presented in
the literature. Secondly, if we have positive results for (2), then we have
corresponding results for (1). One key conclusion of our results is that
further developments on axiomatic and algorithmic aspects of hospital-doctor
matching with regional quotas will result in corresponding results for school
choice with diversity constraints. | From Matching with Diversity Constraints to Matching with Regional Quotas | 2020-02-17 05:51:46 | Haris Aziz, Serge Gaspers, Zhaohong Sun, Toby Walsh | http://arxiv.org/abs/2002.06748v1, http://arxiv.org/pdf/2002.06748v1 | cs.GT |
35,446 | th | In a second-price auction with i.i.d. (independent identically distributed)
bidder valuations, adding bidders increases expected buyer surplus if the
distribution of valuations has a sufficiently heavy right tail. While this does
not imply that a bidder in an auction should prefer for more bidders to join
the auction, it does imply that a bidder should prefer it in exchange for the
bidder being allowed to participate in more auctions. Also, for a heavy-tailed
valuation distribution, marginal expected seller revenue per added bidder
remains strong even when there are already many bidders. | Heavy Tails Make Happy Buyers | 2020-02-20 23:47:42 | Eric Bax | http://arxiv.org/abs/2002.09014v1, http://arxiv.org/pdf/2002.09014v1 | cs.GT |
35,447 | th | A Euclidean path integral is used to find an optimal strategy for a firm
under a Walrasian system, Pareto optimality and a non-cooperative feedback Nash
Equilibrium. We define dynamic optimal strategies and develop a Feynman type
path integration method to capture all non-additive convex strategies. We also
show that the method can solve the non-linear case, for example
Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum
principle cannot solve in closed form. Furthermore, under Walrasian system we
are able to solve for the optimal strategy under a linear constraint with a
linear objective function with respect to strategy. | Optimization of a Dynamic Profit Function using Euclidean Path Integral | 2020-02-21 19:22:48 | P. Pramanik, A. M. Polansky | http://arxiv.org/abs/2002.09394v1, http://arxiv.org/pdf/2002.09394v1 | econ.TH |
35,448 | th | A well-known axiom for proportional representation is Proportionality of
Solid Coalitions (PSC). We characterize committees satisfying PSC as possible
outcomes of the Minimal Demand rule, which generalizes an approach pioneered by
Michael Dummett. | A characterization of proportionally representative committees | 2020-02-22 04:48:56 | Haris Aziz, Barton E. Lee | http://arxiv.org/abs/2002.09598v2, http://arxiv.org/pdf/2002.09598v2 | cs.GT |
35,449 | th | We study the set of possible joint posterior belief distributions of a group
of agents who share a common prior regarding a binary state, and who observe
some information structure. For two agents we introduce a quantitative version
of Aumann's Agreement Theorem, and show that it is equivalent to a
characterization of feasible distributions due to Dawid et al. (1995). For any
number of agents, we characterize feasible distributions in terms of a
"no-trade" condition. We use these characterizations to study information
structures with independent posteriors. We also study persuasion problems with
multiple receivers, exploring the extreme feasible distributions. | Feasible Joint Posterior Beliefs | 2020-02-26 12:01:10 | Itai Arieli, Yakov Babichenko, Fedor Sandomirskiy, Omer Tamuz | http://arxiv.org/abs/2002.11362v4, http://arxiv.org/pdf/2002.11362v4 | econ.TH |
35,450 | th | We develop a theory for continuous-time non-Markovian stochastic control
problems which are inherently time-inconsistent. Their distinguishing feature
is that the classical Bellman optimality principle no longer holds. Our
formulation is cast within the framework of a controlled non-Markovian forward
stochastic differential equation, and a general objective functional setting.
We adopt a game-theoretic approach to study such problems, meaning that we seek
for sub-game perfect Nash equilibrium points. As a first novelty of this work,
we introduce and motivate a refinement of the definition of equilibrium that
allows us to establish a direct and rigorous proof of an extended dynamic
programming principle, in the same spirit as in the classical theory. This in
turn allows us to introduce a system consisting of an infinite family of
backward stochastic differential equations analogous to the classical HJB
equation. We prove that this system is fundamental, in the sense that its
well-posedness is both necessary and sufficient to characterise the value
function and equilibria. As a final step we provide an existence and uniqueness
result. Some examples and extensions of our results are also presented. | Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents | 2020-02-28 09:54:54 | Camilo Hernández, Dylan Possamaï | http://arxiv.org/abs/2002.12572v2, http://arxiv.org/pdf/2002.12572v2 | math.OC |
35,451 | th | In non-truthful auctions, agents' utility for a strategy depends on the
strategies of the opponents and also the prior distribution over their private
types; the set of Bayes Nash equilibria generally has an intricate dependence
on the prior. Using the First Price Auction as our main demonstrating example,
we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents
suffice for an algorithm to learn the interim utilities for all monotone
bidding strategies. As a consequence, this number of samples suffice for
learning all approximate equilibria. We give almost matching (up to polylog
factors) lower bound on the sample complexity for learning utilities. We also
consider a setting where agents must pay a search cost to discover their own
types. Drawing on a connection between this setting and the first price
auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde
O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated
in a near welfare-optimal descending auction in this setting. En route, we
improve the sample complexity bound, recently obtained by Guo et al. (2021),
for the Pandora's Box problem, which is a classical model for sequential
consumer search. | Learning Utilities and Equilibria in Non-Truthful Auctions | 2020-07-03 17:44:33 | Hu Fu, Tao Lin | http://arxiv.org/abs/2007.01722v3, http://arxiv.org/pdf/2007.01722v3 | cs.GT |
35,452 | th | The prisoner's dilemma (PD) is a game-theoretic model studied in a wide array
of fields to understand the emergence of cooperation between rational
self-interested agents. In this work, we formulate a spatial iterated PD as a
discrete-event dynamical system where agents play the game in each time-step
and analyse it algebraically using Krohn-Rhodes algebraic automata theory using
a computational implementation of the holonomy decomposition of transformation
semigroups. In each iteration all players adopt the most profitable strategy in
their immediate neighbourhood. Perturbations resetting the strategy of a given
player provide additional generating events for the dynamics. Our initial study
shows that the algebraic structure, including how natural subsystems comprising
permutation groups acting on the spatial distributions of strategies, arise in
certain parameter regimes for the pay-off matrix, and are absent for other
parameter regimes. Differences in the number of group levels in the holonomy
decomposition (an upper bound for Krohn-Rhodes complexity) are revealed as more
pools of reversibility appear when the temptation to defect is at an
intermediate level. Algebraic structure uncovered by this analysis can be
interpreted to shed light on the dynamics of the spatial iterated PD. | Spatial Iterated Prisoner's Dilemma as a Transformation Semigroup | 2020-07-03 21:20:30 | Isaiah Farahbakhsh, Chrystopher L. Nehaniv | http://arxiv.org/abs/2007.01896v2, http://arxiv.org/pdf/2007.01896v2 | math.DS |
35,453 | th | We investigate how to model the beliefs of an agent who becomes more aware.
We use the framework of Halpern and Rego (2013) by adding probability, and
define a notion of a model transition that describes constraints on how, if an
agent becomes aware of a new formula $\phi$ in state $s$ of a model $M$, she
transitions to state $s^*$ in a model $M^*$. We then discuss how such a model
can be applied to information disclosure. | Dynamic Awareness | 2020-07-06 18:28:22 | Joseph Y. Halpern, Evan Piermont | http://arxiv.org/abs/2007.02823v1, http://arxiv.org/pdf/2007.02823v1 | cs.AI |
35,454 | th | This paper provides a complete review of the continuous-time optimal
contracting problem introduced by Sannikov, in the extended context allowing
for possibly different discount rates for both parties. The agent's problem is
to seek for optimal effort, given the compensation scheme proposed by the
principal over a random horizon. Then, given the optimal agent's response, the
principal determines the best compensation scheme in terms of running payment,
retirement, and lump-sum payment at retirement. A Golden Parachute is a
situation where the agent ceases any effort at some positive stopping time, and
receives a payment afterwards, possibly under the form of a lump sum payment,
or of a continuous stream of payments. We show that a Golden Parachute only
exists in certain specific circumstances. This is in contrast with the results
claimed by Sannikov, where the only requirement is a positive agent's marginal
cost of effort at zero. Namely, we show that there is no Golden Parachute if
this parameter is too large. Similarly, in the context of a concave marginal
utility, there is no Golden Parachute if the agent's utility function has a too
negative curvature at zero. In the general case, we prove that an agent with
positive reservation utility is either never retired by the principal, or
retired above some given threshold (as in Sannikov's solution). We show that
different discount factors induce a face-lifted utility function, which allows
to reduce the analysis to a setting similar to the equal discount rates one.
Finally, we also confirm that an agent with small reservation utility may have
an informational rent, meaning that the principal optimally offers him a
contract with strictly higher utility than his participation value. | Is there a Golden Parachute in Sannikov's principal-agent problem? | 2020-07-10 15:50:49 | Dylan Possamaï, Nizar Touzi | http://arxiv.org/abs/2007.05529v2, http://arxiv.org/pdf/2007.05529v2 | econ.TH |
35,457 | th | Convex analysis is fundamental to proving inequalities that have a wide
variety of applications in economics and mathematics. In this paper we provide
Jensen-type inequalities for functions that are, intuitively, "very" convex.
These inequalities are simple to apply and can be used to generalize and extend
previous results or to derive new results. We apply our inequalities to
quantify the notion "more risk averse" provided in \cite{pratt1978risk}. We
also apply our results in other applications from different fields, including
risk measures, Poisson approximation, moment generating functions,
log-likelihood functions, and Hermite-Hadamard type inequalities. | New Jensen-type inequalities and their applications | 2020-07-18 01:08:02 | Bar Light | http://arxiv.org/abs/2007.09258v3, http://arxiv.org/pdf/2007.09258v3 | math.OC |
35,458 | th | Most online platforms strive to learn from interactions with users, and many
engage in exploration: making potentially suboptimal choices for the sake of
acquiring new information. We study the interplay between exploration and
competition: how such platforms balance the exploration for learning and the
competition for users. Here users play three distinct roles: they are customers
that generate revenue, they are sources of data for learning, and they are
self-interested agents which choose among the competing platforms.
We consider a stylized duopoly model in which two firms face the same
multi-armed bandit problem. Users arrive one by one and choose between the two
firms, so that each firm makes progress on its bandit problem only if it is
chosen. Through a mix of theoretical results and numerical simulations, we
study whether and to what extent competition incentivizes the adoption of
better bandit algorithms, and whether it leads to welfare increases for users.
We find that stark competition induces firms to commit to a "greedy" bandit
algorithm that leads to low welfare. However, weakening competition by
providing firms with some "free" users incentivizes better exploration
strategies and increases welfare. We investigate two channels for weakening the
competition: relaxing the rationality of users and giving one firm a
first-mover advantage. Our findings are closely related to the "competition vs.
innovation" relationship, and elucidate the first-mover advantage in the
digital economy. | Competing Bandits: The Perils of Exploration Under Competition | 2020-07-20 17:19:08 | Guy Aridor, Yishay Mansour, Aleksandrs Slivkins, Zhiwei Steven Wu | http://arxiv.org/abs/2007.10144v7, http://arxiv.org/pdf/2007.10144v7 | cs.GT |
35,459 | th | This paper studies continuous-time optimal contracting in a hierarchy problem
which generalises the model of Sung (2015). The hierarchy is modeled by a
series of interlinked principal-agent problems, leading to a sequence of
Stackelberg equilibria. More precisely, the principal can contract with the
managers to incentivise them to act in her best interest, despite only
observing the net benefits of the total hierarchy. Managers in turn subcontract
with the agents below them. Both agents and managers independently control in
continuous time a stochastic process representing their outcome. First, we show
through a continuous-time adaptation of Sung's model that, even if the agents
only control the drift of their outcome, their manager controls the volatility
of their continuation utility. This first simple example justifies the use of
recent results on optimal contracting for drift and volatility control, and
therefore the theory of second-order backward stochastic differential
equations, developed in the theoretical part of this paper, dedicated to a more
general model. The comprehensive approach we outline highlights the benefits of
considering a continuous-time model and opens the way to obtain comparative
statics. We also explain how the model can be extended to a large-scale
principal-agent hierarchy. Since the principal's problem can be reduced to only
an $m$-dimensional state space and a $2m$-dimensional control set, where $m$ is
the number of managers immediately below her, and is therefore independent of
the size of the hierarchy below these managers, the dimension of the problem
does not explode. | Continuous-time incentives in hierarchies | 2020-07-21 15:47:29 | Emma Hubert | http://arxiv.org/abs/2007.10758v1, http://arxiv.org/pdf/2007.10758v1 | math.OC |
35,460 | th | In multi-agent environments in which coordination is desirable, the history
of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies
with a significant environmental footprint or high social cost persist despite
the successful development of more environmentally friendly and/or socially
efficient alternatives. The displacement of the status quo is hindered by
entrenched economic interests and network effects. To exacerbate matters, the
standard mechanism design approaches based on centralized authorities with the
capacity to use preferential subsidies to effectively dictate system outcomes
are not always applicable to modern decentralized economies. What other types
of mechanisms are feasible? In this paper, we develop and analyze a mechanism
that induces transitions from inefficient lock-ins to superior alternatives.
This mechanism does not exogenously favor one option over another -- instead,
the phase transition emerges endogenously via a standard evolutionary learning
model, Q-learning, where agents trade-off exploration and exploitation.
Exerting the same transient influence to both the efficient and inefficient
technologies encourages exploration and results in irreversible phase
transitions and permanent stabilization of the efficient one. On a technical
level, our work is based on bifurcation and catastrophe theory, a branch of
mathematics that deals with changes in the number and stability properties of
equilibria. Critically, our analysis is shown to be structurally robust to
significant and even adversarially chosen perturbations to the parameters of
both our game and our behavioral model. | Catastrophe by Design in Population Games: Destabilizing Wasteful Locked-in Technologies | 2020-07-25 10:55:15 | Stefanos Leonardos, Iosif Sakos, Costas Courcoubetis, Georgios Piliouras | http://arxiv.org/abs/2007.12877v1, http://arxiv.org/pdf/2007.12877v1 | cs.GT |
35,462 | th | We here study the Battle of the Sexes game, a textbook case of asymmetric
games, on small networks. Due to the conflicting preferences of the players,
analytical approaches are scarce and most often update strategies are employed
in numerical simulations of repeated games on networks until convergence is
reached. As a result, correlations between the choices of the players emerge.
Our approach is to study these correlations with a generalized Ising model.
Using the response strategy framework, we describe how the actions of the
players can bring the network into a steady configuration, starting from an
out-of-equilibrium one. We obtain these configurations using game-theoretical
tools, and describe the results using Ising parameters. We exhaust the
two-player case, giving a detailed account of all the equilibrium
possibilities. Going to three players, we generalize the Ising model and
compare the equilibrium solutions of three representative types of network. We
find that players that are not directly linked retain a degree of correlation
that is proportional to their initial correlation. We also find that the local
network structure is the most relevant for small values of the magnetic field
and the interaction strength of the Ising model. Finally, we conclude that
certain parameters of the equilibrium states are network independent, which
opens up the possibility of an analytical description of asymmetric games
played on networks. | Asymmetric games on networks: towards an Ising-model representation | 2020-11-05 13:23:38 | A. D. Correia, L. L. Leestmaker, H. T. C. Stoof | http://arxiv.org/abs/2011.02739v3, http://arxiv.org/pdf/2011.02739v3 | physics.soc-ph |
35,463 | th | We present a linear--quadratic Stackelberg game with a large number of
followers and we also derive the mean field limit of infinitely many followers.
The relation between optimization and mean-field limit is studied and
conditions for consistency are established. Finally, we propose a numerical
method based on the derived models and present numerical results. | Multiscale Control of Stackelberg Games | 2020-11-06 18:05:43 | Michael Herty, Sonja Steffensen, Anna Thünen | http://arxiv.org/abs/2011.03405v1, http://arxiv.org/pdf/2011.03405v1 | math.OC |
35,465 | th | Understanding the likelihood for an election to be tied is a classical topic
in many disciplines including social choice, game theory, political science,
and public choice. Despite a large body of literature and the common belief
that ties are rare, little is known about how rare ties are in large elections
except for a few simple positional scoring rules under the i.i.d. uniform
distribution over the votes, known as the Impartial Culture (IC) in social
choice. In particular, little progress was made after Marchant explicitly posed
the likelihood of k-way ties under IC as an open question in 2001.
We give an asymptotic answer to the open question for a wide range of
commonly studied voting rules under a model that is much more general and
realistic than i.i.d. models (especially IC) -- the smoothed social choice
framework by Xia that was inspired by the celebrated smoothed complexity
analysis by Spielman and Teng. We prove dichotomy theorems on the smoothed
likelihood of ties under positional scoring rules, edge-order-based rules, and
some multi-round score-based elimination rules, which include commonly studied
voting rules such as plurality, Borda, veto, maximin, Copeland, ranked pairs,
Schulze, STV, and Coombs as special cases. We also complement the theoretical
results by experiments on synthetic data and real-world rank data on Preflib.
Our main technical tool is an improved dichotomous characterization on the
smoothed likelihood for a Poisson multinomial variable to be in a polyhedron,
which is proved by exploring the interplay between the V-representation and the
matrix representation of polyhedra and might be of independent interest. | How Likely Are Large Elections Tied? | 2020-11-07 18:16:04 | Lirong Xia | http://arxiv.org/abs/2011.03791v3, http://arxiv.org/pdf/2011.03791v3 | cs.GT |
35,493 | th | This paper is an axiomatic study of consistent approval-based multi-winner
rules, i.e., voting rules that select a fixed-size group of candidates based on
approval ballots. We introduce the class of counting rules and provide an
axiomatic characterization of this class based on the consistency axiom.
Building upon this result, we axiomatically characterize three important
consistent multi-winner rules: Proportional Approval Voting, Multi-Winner
Approval Voting and the Approval Chamberlin--Courant rule. Our results
demonstrate the variety of multi-winner rules and illustrate three different,
orthogonal principles that multi-winner voting rules may represent: individual
excellence, diversity, and proportionality. | Consistent Approval-Based Multi-Winner Rules | 2017-04-08 10:29:43 | Martin Lackner, Piotr Skowron | http://arxiv.org/abs/1704.02453v6, http://arxiv.org/pdf/1704.02453v6 | cs.GT |
35,467 | th | I relate bipartite graph matchings to stable matchings. I prove a necessary
and sufficient condition for the existence of a saturating stable matching,
where every agent on one side is matched, for all possible preferences. I
extend my analysis to perfect stable matchings, where every agent on both sides
is matched. | Saturating stable matchings | 2020-11-11 22:59:50 | Muhammad Maaz | http://dx.doi.org/10.1016/j.orl.2021.06.013, http://arxiv.org/abs/2011.06046v2, http://arxiv.org/pdf/2011.06046v2 | cs.GT |
35,468 | th | We study a market of investments on networks, where each agent (vertex) can
invest in any enterprise linked to her, and at the same time, raise capital for
her firm's enterprise from other agents she is linked to. Failing to raise
sufficient capital results with the firm defaulting, being unable to invest in
others. Our main objective is to examine the role of collateral contracts in
handling the strategic risk that can propagate to a systemic risk throughout
the network in a cascade of defaults. We take a mechanism-design approach and
solve for the optimal scheme of collateral contracts that capital raisers offer
their investors. These contracts aim at sustaining the efficient level of
investment as a unique Nash equilibrium, while minimizing the total collateral.
Our main results contrast the network environment with its non-network
counterpart (where the sets of investors and capital raisers are disjoint). We
show that for acyclic investment networks, the network environment does not
necessitate any additional collaterals, and systemic risk can be fully handled
by optimal bilateral collateral contracts between capital raisers and their
investors. This is, unfortunately, not the case for cyclic investment networks.
We show that bilateral contracting will not suffice to resolve systemic risk,
and the market will need an external entity to design a global collateral
scheme for all capital raisers. Furthermore, the minimum total collateral that
will sustain the efficient level of investment as a unique equilibrium may be
arbitrarily higher, even in simple cyclic investment networks, compared with
its corresponding non-network environment. Additionally, we prove
computational-complexity results, both for a single enterprise and for
networks. | Optimal Collaterals in Multi-Enterprise Investment Networks | 2020-11-12 10:59:46 | Moshe Babaioff, Yoav Kolumbus, Eyal Winter | http://dx.doi.org/10.1145/3485447.3512053, http://arxiv.org/abs/2011.06247v3, http://arxiv.org/pdf/2011.06247v3 | cs.GT |
35,470 | th | We provide an economically sound micro-foundation to linear price impact
models, by deriving them as the equilibrium of a suitable agent-based system.
Our setup generalizes the well-known Kyle model, by dropping the assumption of
a terminal time at which fundamental information is revealed so to describe a
stationary market, while retaining agents' rationality and asymmetric
information. We investigate the stationary equilibrium for arbitrary Gaussian
noise trades and fundamental information, and show that the setup is compatible
with universal price diffusion at small times, and non-universal mean-reversion
at time scales at which fluctuations in fundamentals decay. Our model provides
a testable relation between volatility of prices, magnitude of fluctuations in
fundamentals and level of volume traded in the market. | A Stationary Kyle Setup: Microfounding propagator models | 2020-11-20 10:23:35 | Michele Vodret, Iacopo Mastromatteo, Bence Tóth, Michael Benzaquen | http://dx.doi.org/10.1088/1742-5468/abe702, http://arxiv.org/abs/2011.10242v3, http://arxiv.org/pdf/2011.10242v3 | q-fin.TR |
35,472 | th | The expectation is an example of a descriptive statistic that is monotone
with respect to stochastic dominance, and additive for sums of independent
random variables. We provide a complete characterization of such statistics,
and explore a number of applications to models of individual and group
decision-making. These include a representation of stationary monotone time
preferences, extending the work of Fishburn and Rubinstein (1982) to time
lotteries. This extension offers a new perspective on risk attitudes toward
time, as well as on the aggregation of multiple discount factors. | Monotone additive statistics | 2021-02-01 06:43:06 | Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz | http://arxiv.org/abs/2102.00618v4, http://arxiv.org/pdf/2102.00618v4 | econ.TH |
35,494 | th | I study the measurement of scientists' influence using bibliographic data.
The main result is an axiomatic characterization of the family of
citation-counting indices, a broad class of influence measures which includes
the renowned h-index. The result highlights several limitations of these
indices: they are not suitable to compare scientists across different fields,
and they cannot account for indirect influence. I explore how these limitations
can be overcome by using richer bibliographic information. | The Limits of Citation Counts | 2017-11-07 22:22:02 | Antonin Macé | http://arxiv.org/abs/1711.02695v3, http://arxiv.org/pdf/1711.02695v3 | cs.DL |
35,473 | th | We study network games in which players choose both the partners with whom
they associate and an action level (e.g., effort) that creates spillovers for
those partners. We introduce a framework and two solution concepts, extending
standard approaches for analyzing each choice in isolation: Nash equilibrium in
actions and pairwise stability in links. Our main results show that, under
suitable order conditions on incentives, stable networks take simple forms. The
first condition concerns whether links create positive or negative payoff
spillovers. The second concerns whether actions are strategic complements to
links, or strategic substitutes. Together, these conditions yield a taxonomy of
the relationship between network structure and economic primitives organized
around two network architectures: ordered overlapping cliques and nested split
graphs. We apply our model to understand the consequences of competition for
status, to microfound matching models that assume clique formation, and to
interpret empirical findings that highlight unintended consequences of group
design. | Games on Endogenous Networks | 2021-02-02 19:27:00 | Evan Sadler, Benjamin Golub | http://arxiv.org/abs/2102.01587v7, http://arxiv.org/pdf/2102.01587v7 | econ.TH |
35,474 | th | We introduce a new two-sided stable matching problem that describes the
summer internship matching practice of an Australian university. The model is a
case between two models of Kamada and Kojima on matchings with distributional
constraints. We study three solution concepts, the strong and weak stability
concepts proposed by Kamada and Kojima, and a new one in between the two,
called cutoff stability. Kamada and Kojima showed that a strongly stable
matching may not exist in their most restricted model with disjoint regional
quotas. Our first result is that checking its existence is NP-hard. We then
show that a cutoff stable matching exists not just for the summer internship
problem but also for the general matching model with arbitrary heredity
constraints. We present an algorithm to compute a cutoff stable matching and
show that it runs in polynomial time in our special case of summer internship
model. However, we also show that finding a maximum size cutoff stable matching
is NP-hard, but we provide a Mixed Integer Linear Program formulation for this
optimisation problem. | Cutoff stability under distributional constraints with an application to summer internship matching | 2021-02-05 03:11:46 | Haris Aziz, Anton Baychkov, Peter Biro | http://arxiv.org/abs/2102.02931v2, http://arxiv.org/pdf/2102.02931v2 | cs.GT |
35,477 | th | We study a game theoretic model of standardized testing for college
admissions. Students are of two types; High and Low. There is a college that
would like to admit the High type students. Students take a potentially costly
standardized exam which provides a noisy signal of their type.
The students come from two populations, which are identical in talent (i.e.
the type distribution is the same), but differ in their access to resources:
the higher resourced population can at their option take the exam multiple
times, whereas the lower resourced population can only take the exam once. We
study two models of score reporting, which capture existing policies used by
colleges. The first policy (sometimes known as "super-scoring") allows students
to report the max of the scores they achieve. The other policy requires that
all scores be reported.
We find in our model that requiring that all scores be reported results in
superior outcomes in equilibrium, both from the perspective of the college (the
admissions rule is more accurate), and from the perspective of equity across
populations: a student's probability of admission is independent of their
population, conditional on their type. In particular, the false positive rates
and false negative rates are identical in this setting, across the highly and
poorly resourced student populations. This is the case despite the fact that
the more highly resourced students can -- at their option -- either report a
more accurate signal of their type, or pool with the lower resourced population
under this policy. | Best vs. All: Equity and Accuracy of Standardized Test Score Reporting | 2021-02-15 22:27:22 | Sampath Kannan, Mingzi Niu, Aaron Roth, Rakesh Vohra | http://arxiv.org/abs/2102.07809v1, http://arxiv.org/pdf/2102.07809v1 | cs.GT |
35,488 | th | In this paper, we investigate two heterogeneous triopoly games where the
demand function of the market is isoelastic. The local stability and the
bifurcation of these games are systematically analyzed using the symbolic
approach proposed by the author. The novelty of the present work is twofold. On
one hand, the results of this paper are analytical, which are different from
the existing results in the literature based on observations through numerical
simulations. In particular, we rigorously prove the existence of double routes
to chaos through the period-doubling bifurcation and through the Neimark-Sacker
bifurcation. On the other hand, for the special case of the involved firms
having identical marginal costs, we acquire the necessary and sufficient
conditions of the local stability for both models. By further analyzing these
conditions, it seems that that the presence of the local monopolistic
approximation (LMA) mechanism might have a stabilizing effect for heterogeneous
triopoly games with the isoelastic demand. | Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand | 2021-12-11 14:01:20 | Xiaoliang Li | http://arxiv.org/abs/2112.05950v1, http://arxiv.org/pdf/2112.05950v1 | math.DS |
35,478 | th | Bilateral trade, a fundamental topic in economics, models the problem of
intermediating between two strategic agents, a seller and a buyer, willing to
trade a good for which they hold private valuations. Despite the simplicity of
this problem, a classical result by Myerson and Satterthwaite (1983) affirms
the impossibility of designing a mechanism which is simultaneously efficient,
incentive compatible, individually rational, and budget balanced. This
impossibility result fostered an intense investigation of meaningful trade-offs
between these desired properties. Much work has focused on approximately
efficient fixed-price mechanisms, i.e., Blumrosen and Dobzinski (2014; 2016),
Colini-Baldeschi et al. (2016), which have been shown to fully characterize
strong budget balanced and ex-post individually rational direct revelation
mechanisms. All these results, however, either assume some knowledge on the
priors of the seller/buyer valuations, or a black box access to some samples of
the distributions, as in D{\"u}tting et al. (2021). In this paper, we cast for
the first time the bilateral trade problem in a regret minimization framework
over rounds of seller/buyer interactions, with no prior knowledge on the
private seller/buyer valuations. Our main contribution is a complete
characterization of the regret regimes for fixed-price mechanisms with
different models of feedback and private valuations, using as benchmark the
best fixed price in hindsight. More precisely, we prove the following bounds on
the regret:
$\bullet$ $\widetilde{\Theta}(\sqrt{T})$ for full-feedback (i.e., direct
revelation mechanisms);
$\bullet$ $\widetilde{\Theta}(T^{2/3})$ for realistic feedback (i.e.,
posted-price mechanisms) and independent seller/buyer valuations with bounded
densities;
$\bullet$ $\Theta(T)$ for realistic feedback and seller/buyer valuations with
bounded densities;
$\bullet$ $\Theta(T)$ for realistic feedback and independent seller/buyer
valuations;
$\bullet$ $\Theta(T)$ for the adversarial setting. | A Regret Analysis of Bilateral Trade | 2021-02-16 11:53:17 | Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi | http://dx.doi.org/10.1145/3465456.3467645, http://arxiv.org/abs/2102.08754v1, http://arxiv.org/pdf/2102.08754v1 | cs.LG |
35,479 | th | Critical decisions like loan approvals, medical interventions, and college
admissions are guided by predictions made in the presence of uncertainty. In
this paper, we prove that uncertainty has a disparate impact. While it imparts
errors across all demographic groups, the types of errors vary systematically:
Groups with higher average outcomes are typically assigned higher false
positive rates, while those with lower average outcomes are assigned higher
false negative rates. We show that additional data acquisition can eliminate
the disparity and broaden access to opportunity. The strategy, which we call
Affirmative Information, could stand as an alternative to Affirmative Action. | The Disparate Impact of Uncertainty: Affirmative Action vs. Affirmative Information | 2021-02-19 19:40:47 | Claire Lazar Reich | http://arxiv.org/abs/2102.10019v4, http://arxiv.org/pdf/2102.10019v4 | stat.ML |
35,481 | th | We study a repeated persuasion setting between a sender and a receiver, where
at each time $t$, the sender observes a payoff-relevant state drawn
independently and identically from an unknown prior distribution, and shares
state information with the receiver, who then myopically chooses an action. As
in the standard setting, the sender seeks to persuade the receiver into
choosing actions that are aligned with the sender's preference by selectively
sharing information about the state. However, in contrast to the standard
models, the sender does not know the prior, and has to persuade while gradually
learning the prior on the fly.
We study the sender's learning problem of making persuasive action
recommendations to achieve low regret against the optimal persuasion mechanism
with the knowledge of the prior distribution. Our main positive result is an
algorithm that, with high probability, is persuasive across all rounds and
achieves $O(\sqrt{T\log T})$ regret, where $T$ is the horizon length. The core
philosophy behind the design of our algorithm is to leverage robustness against
the sender's ignorance of the prior. Intuitively, at each time our algorithm
maintains a set of candidate priors, and chooses a persuasion scheme that is
simultaneously persuasive for all of them. To demonstrate the effectiveness of
our algorithm, we further prove that no algorithm can achieve regret better
than $\Omega(\sqrt{T})$, even if the persuasiveness requirements were
significantly relaxed. Therefore, our algorithm achieves optimal regret for the
sender's learning problem up to terms logarithmic in $T$. | Learning to Persuade on the Fly: Robustness Against Ignorance | 2021-02-20 00:02:15 | You Zu, Krishnamurthy Iyer, Haifeng Xu | http://arxiv.org/abs/2102.10156v1, http://arxiv.org/pdf/2102.10156v1 | cs.GT |
35,482 | th | We introduce a new algorithm for finding stable matchings in multi-sided
matching markets. Our setting is motivated by a PhD market of students,
advisors, and co-advisors, and can be generalized to supply chain networks
viewed as $n$-sided markets. In the three-sided PhD market, students primarily
care about advisors and then about co-advisors (consistent preferences), while
advisors and co-advisors have preferences over students only (hence they are
cooperative). A student must be matched to one advisor and one co-advisor, or
not at all. In contrast to previous work, advisor-student and
student-co-advisor pairs may not be mutually acceptable (e.g., a student may
not want to work with an advisor or co-advisor and vice versa). We show that
three-sided stable matchings always exist, and present an algorithm that, in
time quadratic in the market size (up to log factors), finds a three-sided
stable matching using any two-sided stable matching algorithm as matching
engine. We illustrate the challenges that arise when not all advisor-co-advisor
pairs are compatible. We then generalize our algorithm to $n$-sided markets
with quotas and show how they can model supply chain networks. Finally, we show
how our algorithm outperforms the baseline given by [Danilov, 2003] in terms of
both producing a stable matching and a larger number of matches on a synthetic
dataset. | Finding Stable Matchings in PhD Markets with Consistent Preferences and Cooperative Partners | 2021-02-23 21:10:46 | Maximilian Mordig, Riccardo Della Vecchia, Nicolò Cesa-Bianchi, Bernhard Schölkopf | http://arxiv.org/abs/2102.11834v2, http://arxiv.org/pdf/2102.11834v2 | cs.GT |
35,489 | th | Spin models of markets inspired by physics models of magnetism, as the Ising
model, allow for the study of the collective dynamics of interacting agents in
a market. The number of possible states has been mostly limited to two (buy or
sell) or three options. However, herding effects of competing stocks and the
collective dynamics of a whole market may escape our reach in the simplest
models. Here I study a q-spin Potts model version of a simple Ising market
model to represent the dynamics of a stock market index in a spin model. As a
result, a self-organized gain-loss asymmetry in the time series of an index
variable composed of stocks in this market is observed. | A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon | 2021-12-12 21:15:33 | Stefan Bornholdt | http://arxiv.org/abs/2112.06290v1, http://arxiv.org/pdf/2112.06290v1 | physics.soc-ph |
35,483 | th | Consider a coordination game played on a network, where agents prefer taking
actions closer to those of their neighbors and to their own ideal points in
action space. We explore how the welfare outcomes of a coordination game depend
on network structure and the distribution of ideal points throughout the
network. To this end, we imagine a benevolent or adversarial planner who
intervenes, at a cost, to change ideal points in order to maximize or minimize
utilitarian welfare subject to a constraint. A complete characterization of
optimal interventions is obtained by decomposing interventions into principal
components of the network's adjacency matrix. Welfare is most sensitive to
interventions proportional to the last principal component, which focus on
local disagreement. A welfare-maximizing planner optimally works to reduce
local disagreement, bringing the ideal points of neighbors closer together,
whereas a malevolent adversary optimally drives neighbors' ideal points apart
to decrease welfare. Such welfare-maximizing/minimizing interventions are very
different from ones that would be done to change some traditional measures of
discord, such as the cross-sectional variation of equilibrium actions. In fact,
an adversary sowing disagreement to maximize her impact on welfare will
minimize her impact on global variation in equilibrium actions, underscoring a
tension between improving welfare and increasing global cohesion of equilibrium
behavior. | Discord and Harmony in Networks | 2021-02-26 08:56:01 | Andrea Galeotti, Benjamin Golub, Sanjeev Goyal, Rithvik Rao | http://arxiv.org/abs/2102.13309v1, http://arxiv.org/pdf/2102.13309v1 | econ.TH |