pwc-archive/papers-with-abstracts huggingface dataset:
Expected utility theory on mixture spaces without the completeness axiom
Authors: David McCarthy, Kalle Mikkola, Teruji Thomas
Date: 2021-02-13 00:00:00
Tasks: Open-Ended Question Answering

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result.
Improving Information from Manipulable Data
Authors: Alex Frankel, Navin Kartik
Date: 2019-08-27 00:00:00

Data-based decisionmaking must account for the manipulation of data by agents who are aware of how decisions are being made and want to affect their allocations. We study a framework in which, due to such manipulation, data becomes less informative when decisions depend more strongly on data. We formalize why and how a decisionmaker should commit to underutilizing data. Doing so attenuates information loss and thereby improves allocation accuracy.
Identification in the Random Utility Model
Authors: Christopher Turansick
Date: 2021-02-10 00:00:00
Tasks: model

The random utility model is known to be unidentified, but there are times when the model admits a unique representation. We offer two characterizations for the existence of a unique random utility representation. Our first characterization puts conditions on a graphical representation of the data set. Non-uniqueness arises when multiple inflows can be assigned to multiple outflows on this graph. Our second characterization provides a direct test for uniqueness given a random utility representation. We also show that the support of a random utility representation is identified if and only if the representation itself is identified.
Extended Gini Index
Authors: Ram Sewak Dubey, Giorgio Laguzzi
Date: 2020-12-08 00:00:00

We propose an extended version of Gini index defined on the set of infinite utility streams, $X=Y^\mathbb{N}$ where $Y\subset \mathbb{R}$. For $Y$ containing at most finitely many elements, the index satisfies the generalized Pigou-Dalton transfer principles in addition to the anonymity axiom.
Comonotonic measures of multivariate risks
Authors: Ivar Ekeland, Alfred Galichon, Marc Henry
Date: 2021-02-08 00:00:00

We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invariance, subadditivity and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.
A Stationary Kyle Setup: Microfounding propagator models
Authors: Michele Vodret, Iacopo Mastromatteo, Bence Tóth, Michael Benzaquen
Date: 2020-11-20 00:00:00

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.
Twofold Multiprior Preferences and Failures of Contingent Reasoning
Authors: Federico Echenique, Masaki Miyashita, Yuta Nakamura, Luciano Pomatto, Jamie Vinson
Date: 2020-12-29 00:00:00

We propose a model of incomplete \textit{twofold multiprior preferences}, in which an act $f$ is ranked above an act $g$ only when $f$ provides higher utility in a worst-case scenario than what $g$ provides in a best-case scenario. The model explains failures of contingent reasoning, captured through a weakening of the state-by-state monotonicity (or dominance) axiom. Our model gives rise to rich comparative statics results, as well as extension exercises, and connections to choice theory. We present an application to second-price auctions.
Can Economic Theory Be Informative for the Judiciary? Affirmative Action in India via Vertical and Horizontal Reservations
Authors: Tayfun Sönmez, M. Bumin Yenmez
Date: 2021-02-05 00:00:00

Sanctioned by its constitution, India is home to the world's most comprehensive affirmative action program, where historically discriminated groups are protected with vertical reservations implemented as "set asides," and other disadvantaged groups are protected with horizontal reservations implemented as "minimum guarantees." A mechanism mandated by the Supreme Court in 1995 suffers from important anomalies, triggering countless litigations in India. Foretelling a recent reform correcting the flawed mechanism, we propose the 2SMG mechanism that resolves all anomalies, and characterize it with desiderata reflecting laws of India. Subsequently rediscovered with a high court judgment and enforced in Gujarat, 2SMG is also endorsed by Saurav Yadav v. State of UP (2020), in a Supreme Court ruling that rescinded the flawed mechanism. While not explicitly enforced, 2SMG is indirectly enforced for an important subclass of applications in India, because no other mechanism satisfies the new mandates of the Supreme Court.
The Refined Assortment Optimization Problem
Authors: Gerardo Berbeglia, Alvaro Flores, Guillermo Gallego
Date: 2021-02-05 00:00:00
Tasks: Assortment Optimization, Discrete Choice Models

We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example, offer fares with severe restrictions rather than making them unavailable. This is a more subtle way of handling the trade-off between demand induction and demand cannibalization. For the latent class MNL model, a firm that engages in refined assortment optimization can make up to $\min(n,m)$ times more than one that insists on traditional assortment optimization, where $n$ is the number of products and $m$ the number of customer types. Surprisingly, the revenue-ordered assortment heuristic has the same performance guarantees relative to {\em personalized} refined assortment optimization as it does to traditional assortment optimization. Based on this finding, we construct refinements of the revenue-order heuristic and measure their improved performance relative to the revenue-ordered assortment and the optimal traditional assortment optimization problem. We also provide tight bounds on the ratio of the expected revenues for the refined versus the traditional assortment optimization for some well known discrete choice models.
Equitable preference relations on infinite utility streams
Authors: Ram S. Dubey, Giorgio Laguzzi
Date: 2020-11-12 00:00:00
Tasks: Relation

We propose generalized versions of strong equity and Pigou-Dalton transfer principle. We study the existence and the real valued representation of social welfare relations satisfying these two generalized equity principles. Our results characterize the restrictions on one period utility domains for the equitable social welfare relation (i) to exist; and (ii) to admit real-valued representations.
Choice with Endogenous Categorization
Authors: Andrew Ellis, Yusufcan Masatlioglu
Date: 2020-05-11 00:00:00

We propose and axiomatize the categorical thinking model (CTM) in which the framing of the decision problem affects how agents categorize alternatives, that in turn affects their evaluation of it. Prominent models of salience, status quo bias, loss-aversion, inequality aversion, and present bias all fit under the umbrella of CTM. This suggests categorization is an underlying mechanism of key departures from the neoclassical model of choice. We specialize CTM to provide a behavioral foundation for the salient thinking model of Bordalo et al. (2013) that highlights its strong predictions and distinctions from other models.
Robust double auction mechanisms
Authors: Kiho Yoon
Date: 2021-02-01 00:00:00

We study the robust double auction mechanisms, that is, the double auction mechanisms that satisfy dominant strategy incentive compatibility, ex-post individual rationality and ex-post budget balance. We first establish that the price in any robust mechanism does not depend on the valuations of the trading players. We next establish that, with a non-bossiness assumption, the price in any robust mechanism does not depend on players' valuations at all, whether trading or non-trading. Our main result is the characterization result that, with a non-bossy assumption along with other assumptions on the properties of the mechanism, the generalized posted mechanism in which a constant price is posted for each possible set of traders is the only robust double auction mechanism. We also show that, even without the non-bossiness assumption, it is quite difficult to find a reasonable robust double auction mechanism other than the generalized posted price mechanism.
Monotone additive statistics
Authors: Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz
Date: 2021-02-01 00:00:00
Tasks: Decision Making, Descriptive

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. We also offer a novel class of nonexpected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.
Electoral Accountability and Selection with Personalized Information Aggregation
Authors: Anqi Li, Lin Hu
Date: 2020-09-03 00:00:00

We study a model of electoral accountability and selection whereby heterogeneous voters aggregate incumbent politician's performance data into personalized signals through paying limited attention. Extreme voters' signals exhibit an own-party bias, which hampers their ability to discern the good and bad performances of the incumbent. While this effect alone would undermine electoral accountability and selection, there is a countervailing effect stemming from partisan disagreement, which makes the centrist voter more likely to be pivotal. In case the latter's unbiased signal is very informative about the incumbent's performance, the combined effect on electoral accountability and selection can actually be a positive one. For this reason, factors that carry a negative connotation in every political discourse -- such as increasing mass polarization and shrinking attention span -- have ambiguous accountability and selection effects in general. Correlating voters' signals, if done appropriately, unambiguously improves electoral accountability and selection and, hence, voter welfare.
Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange
Authors: Péter Biró, Flip Klijn, Xenia Klimentova, Ana Viana
Date: 2021-01-30 00:00:00
Tasks: Blocking

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. In this paper we show that in the case of strict preferences the unique strong core allocation (or competitive allocation) respects improvement: if an agent's object becomes more attractive for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We obtain a general result in case of ties in the preferences and provide new integer programming formulations for computing (strong) core and competitive allocations. Finally, we conduct computer simulations to compare the game-theoretical solutions with maximum size and maximum weight exchanges for markets that resemble the pools of kidney exchange programmes.
Conservative Updating
Authors: Matthew Kovach
Date: 2021-01-30 00:00:00

This paper provides a behavioral analysis of conservatism in beliefs. I introduce a new axiom, Dynamic Conservatism, that relaxes Dynamic Consistency when information and prior beliefs "conflict." When the agent is a subjective expected utility maximizer, Dynamic Conservatism implies that conditional beliefs are a convex combination of the prior and the Bayesian posterior. Conservatism may result in belief dynamics consistent with confirmation bias, representativeness, and the good news-bad news effect, suggesting a deeper behavioral connection between these biases. An index of conservatism and a notion of comparative conservatism are characterized. Finally, I extend conservatism to the case of an agent with incomplete preferences that admit a multiple priors representation.
Dynamic Random Choice
Authors: Ricky Li
Date: 2021-01-30 00:00:00

I study dynamic random utility with finite choice sets and exogenous total menu variation, which I refer to as stochastic utility (SU). First, I characterize SU when each choice set has three elements. Next, I prove several mathematical identities for joint, marginal, and conditional Block--Marschak sums, which I use to obtain two characterizations of SU when each choice set but the last has three elements. As a corollary under the same cardinality restrictions, I sharpen an axiom to obtain a characterization of SU with full support over preference tuples. I conclude by characterizing SU without cardinality restrictions. All of my results hold over an arbitrary finite discrete time horizon.
New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting
Authors: Peter G. Hansen
Date: 2021-01-28 00:00:00

I introduce novel preference formulations which capture aversion to ambiguity about unknown and potentially time-varying volatility. I compare these preferences with Gilboa and Schmeidler's maxmin expected utility as well as variational formulations of ambiguity aversion. The impact of ambiguity aversion is illustrated in a simple static model of portfolio choice, as well as a dynamic model of optimal contracting under repeated moral hazard. Implications for investor beliefs, optimal design of corporate securities, and asset pricing are explored.
Multinomial logit processes and preference discovery: inside and outside the black box
Authors: Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
Date: 2020-04-28 00:00:00

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation \[ p_{t}\left( a,A\right) =\dfrac{e^{\frac{u\left( a\right) }{\lambda \left( t\right) }+\alpha \left( a\right) }}{\sum_{b\in A}e^{\frac{u\left( b\right) }{\lambda \left( t\right) }+\alpha \left( b\right) }}% \] where $p_{t}\left( a,A\right) $ is the probability that alternative $a$ is selected from the set $A$ of feasible alternatives if $t$ is the time available to decide, $\lambda$ is a time dependent noise parameter measuring the unit cost of information, $u$ is a time independent utility function, and $\alpha$ is an alternative-specific bias that determines the initial choice probabilities reflecting prior information and memory anchoring. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when $\alpha$ is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).
Relative Maximum Likelihood Updating of Ambiguous Beliefs
Authors: Xiaoyu Cheng
Date: 2019-11-06 00:00:00
Tasks: Open-Ended Question Answering

This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear contraction of C towards its subset ascribing a maximal probability to the observed event. The degree of contraction captures the extent of willingness to discard priors based on likelihood when updating. Two well-known updating rules of multiple priors, Full Bayesian (FB) and Maximum Likelihood (ML), are included as special cases of RML. An axiomatic characterization of conditional preferences generated by RML updating is provided when the preferences admit Maxmin Expected Utility representations. The axiomatization relies on weakening the axioms characterizing FB and ML. The axiom characterizing ML is identified for the first time in this paper, addressing a long-standing open question in the literature.
Strength in Numbers: Robust Mechanisms for Public Goods with Many Agents
Authors: Jin Xi, Haitian Xie
Date: 2021-01-07 00:00:00

This study examines the mechanism design problem for public goods provision in a large economy with $n$ independent agents. We propose a class of dominant-strategy incentive compatible and ex-post individually rational mechanisms, which we call the adjusted mean-thresholding (AMT) mechanisms. We show that when the cost of provision grows slower than the $\sqrt{n}$-rate, the AMT mechanisms are both eventually ex-ante budget balanced and asymptotically efficient. When the cost grows faster than the $\sqrt{n}$-rate, in contrast, we show that any incentive compatible, individually rational, and eventually ex-ante budget balanced mechanism must have provision probability converging to zero and hence cannot be asymptotically efficient. The AMT mechanisms have a simple form and are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of an AMT mechanism depends only on the first moment of the valuation distribution.
Machine Learning for Strategic Inference
Authors: In-Koo Cho, Jonathan Libgober
Date: 2021-01-24 00:00:00
Tasks: BIG-bench Machine Learning

We study interactions between strategic players and markets whose behavior is guided by an algorithm. Algorithms use data from prior interactions and a limited set of decision rules to prescribe actions. While as-if rational play need not emerge if the algorithm is constrained, it is possible to guide behavior across a rich set of possible environments using limited details. Provided a condition known as weak learnability holds, Adaptive Boosting algorithms can be specified to induce behavior that is (approximately) as-if rational. Our analysis provides a statistical perspective on the study of endogenous model misspecification.
Fair Allocation of Vaccines, Ventilators and Antiviral Treatments: Leaving No Ethical Value Behind in Health Care Rationing
Authors: Parag A. Pathak, Tayfun Sönmez, M. Utku Ünver, M. Bumin Yenmez
Date: 2020-08-02 00:00:00

A priority system has traditionally been the protocol of choice for the allocation of scarce life-saving resources during public health emergencies. Covid-19 revealed the limitations of this allocation rule. Many argue that priority systems abandon ethical values such as equity by discriminating against disadvantaged communities. We show that a restrictive feature of the traditional priority system largely drives these limitations. Following minimalist market design, an institution design paradigm that integrates research and policy efforts, we formulate pandemic allocation of scarce life-saving resources as a new application of market design. Interfering only with the restrictive feature of the priority system to address its shortcomings, we formulate a reserve system as an alternative allocation rule. Our theoretical analysis develops a general theory of reserve design. We relate our analysis to debates during Covid-19 and describe the impact of our paper on policy and practice.
Assignment mechanisms: common preferences and information acquisition
Authors: Georgy Artemov
Date: 2021-01-18 00:00:00

I study costly information acquisition in a two-sided matching problem, such as matching applicants to schools. An applicant's utility is a sum of common and idiosyncratic components. The idiosyncratic component is unknown to the applicant but can be learned at a cost. When applicants are assigned using an ordinal strategy-proof mechanism, too few acquire information, generating a significant welfare loss. Affirmative action and other realistic policies may lead to a Pareto improvement. As incentives to acquire information differ across mechanisms, ignoring such incentives may lead to incorrect welfare assessments, for example, in comparing a popular Immediate Assignment and an ordinal strategy-proof mechanism.
DKPRG or how to succeed in the Kolkata Paise Restaurant gamevia TSP
Authors: Kalliopi Kastampolidou, Christos Papalitsas, Theodore Andronikos
Date: 2021-01-16 00:00:00

The Kolkata Paise Restaurant Problem is a challenging game, in which $n$ agents must decide where to have lunch during their lunch break. The game is very interesting because there are exactly $n$ restaurants and each restaurant can accommodate only one agent. If two or more agents happen to choose the same restaurant, only one gets served and the others have to return back to work hungry. In this paper we tackle this problem from an entirely new angle. We abolish certain implicit assumptions, which allows us to propose a novel strategy that results in greater utilization for the restaurants. We emphasize the spatially distributed nature of our approach, which, for the first time, perceives the locations of the restaurants as uniformly distributed in the entire city area. This critical change in perspective has profound ramifications in the topological layout of the restaurants, which now makes it completely realistic to assume that every agent has a second chance. Every agent now may visit, in case of failure, more than one restaurants, within the predefined time constraints.