pwc-archive/papers-with-abstracts huggingface dataset:
A production function with variable elasticity of substitution greater than one
Authors: Constantin Chilarescu
Date: 2021-03-15 00:00:00

The idea of this paper comes from the famous remark of Piketty and Zuckman: "It is natural to imagine that $\sigma$ was much less than one in the eighteenth and nineteenth centuries and became larger than one in the twentieth and twenty-first centuries. One expects a higher elasticity of substitution in high-tech economies where there are lots of alternative uses and forms for capital." The main aim of this paper is to prove the existence of a production function of variable elasticity of substitution with values greater than one.
Optimism and Pessimism in Strategic Interactions under Ignorance
Authors: Pierfrancesco Guarino, Gabriel Ziegler
Date: 2021-03-15 00:00:00

We study players interacting under the veil of ignorance, who have -- coarse -- beliefs represented as subsets of opponents' actions. We analyze when these players follow $\max \min$ or $\max\max$ decision criteria, which we identify with pessimistic or optimistic attitudes, respectively. Explicitly formalizing these attitudes and how players reason interactively under ignorance, we characterize the behavioral implications related to common belief in these events: while optimism is related to Point Rationalizability, a new algorithm -- Wald Rationalizability -- captures pessimism. Our characterizations allow us to uncover novel results: ($i$) regarding optimism, we relate it to wishful thinking \'a la Yildiz (2007) and we prove that dropping the (implicit) "belief-implies-truth" assumption reverses an existence failure described therein; ($ii$) we shed light on the notion of rationality in ordinal games; ($iii$) we clarify the conceptual underpinnings behind a discontinuity in Rationalizability hinted in the analysis of Weinstein (2016).
Pricing decisions under manufacturer's component open-supply strategy
Authors: Peiya Zhu, Xiaofei Qian, Xinbao Liu, Shaojun Lu
Date: 2021-02-20 00:00:00

Faced with huge market potential and increasing competition in emerging industries, product manufacturers with key technologies tend to consider whether to implement a component open supply strategy. This study focuses on a pricing game induced by the component open supply strategy between a vertically integrated manufacturer (who produces key components and end products) and an exterior product manufacturer (who produces end products using purchased key components) with different customer perceived value and different cost structure. This study first establishes a three stage pricing game model and proposes demand functions by incorporating relative customer perceived value. Based on the demand functions, we obtain feasible regions of the exterior manufacturer's sourcing decision and the optimal price decision in each region. Then the effects of relative customer perceived value, cost structure, and market structure on price decisions and optimal profits of the vertically integrated manufacturer are demonstrated. Finally, as for the optimal component supply strategy, we present a generalized closed supply Pareto zone and establish supply strategy Pareto zones under several specific configurations.
Price and Fulfillment Strategies in Omnichannel Retailing
Authors: Yasuyuki Kusuda
Date: 2021-03-12 00:00:00

Omnichannel retailing, a new form of distribution system, seamlessly integrates the Internet and physical stores. This study considers the pricing and fulfillment strategies of a retailer that has two sales channels: online and one physical store. The retailer offers consumers three purchasing options: delivery from the fulfillment center, buy online and pick up in-store (BOPS), and purchasing at the store. Consumers choose one of these options to maximize their utility, dividing them into several segments. Given the retailer can induce consumers to the profitable segment by adjusting the online and store prices, our analysis shows that it has three optimal strategies: (1) The retailer excludes consumers far from the physical store from the market and lets the others choose BOPS or purchasing at the store. (2) It lets consumers far from the physical store choose delivery from the fulfillment center and the others choose BOPS or purchasing at the store. (3) It lets all consumers choose delivery from the fulfillment center. Finally, we present simple dynamic simulations that considers how the retailer's optimal strategy changes as consumers' subjective probability of believing the product is in stock decreases. The results show that the retailer should offer BOPS in later periods of the selling season to maximize its profit as the subjective probability decreases.
Conditional strategy equilibrium
Authors: Lorenzo Bastianello, Mehmet S. Ismail
Date: 2021-03-11 00:00:00

In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players' actions to her own actions. We study the properties of efficiency and coalition-proofness of the conditional strategy equilibrium in $n$-person games.
How to De-Reserves Reserves: Admissions to Technical Colleges in India
Authors: Orhan Aygün, Bertan Turhan
Date: 2021-03-10 00:00:00

We study joint implementation of reservation and de-reservation policies in India that has been enforcing a comprehensive affirmative action since 1950. The landmark judgement of the Supreme Court of India in 2008 mandated that whenever OBC category (with 27 percent reservation) has unfilled positions they must be reverted to general category applicants in admissions to public schools without specifying how to implement it. We disclose the drawbacks of recently reformed allocation procedure in admissions to technical colleges and offer a solution through de-reservation via choice rules. We propose a novel priority design, Backward Transfers (BT) choice rule, for institutions and the deferred acceptance mechanism under these rules (DA-BT) for centralized clearinghouses. We show that DA-BT corrects the shortcomings of existing mechanisms. By formulating the legal requirements and policy goals in India as formal axioms, we show that the DA-BT mechanism is the unique mechanism for concurrent implementation of reservation and de-reservation policies.
Competition in Costly Talk
Authors: Federico Vaccari
Date: 2021-03-09 00:00:00

This paper studies a communication game between an uninformed decision maker and two perfectly informed senders with conflicting interests. Senders can misreport information at a cost that increases with the size of the misrepresentation. The main results show that equilibria where the decision maker obtains the complete-information payoff hinge on beliefs with undesirable properties. The imposition of a minimal and sensible belief structure is sufficient to generate a robust and essentially unique equilibrium with partial information transmission. A complete characterization of this equilibrium unveils the language senders use to communicate.
Core equivalence with large agents
Authors: Aubrey Clark
Date: 2021-03-08 00:00:00

This paper studies the relationship between core and competitive equilibira in economies that consist of a continuum of agents and some large agents. We construct a class of these economies in which the core and competitive allocations do not coincide.
Correlated Choice
Authors: Christopher P. Chambers, Yusufcan Masatlioglu, Christopher Turansick
Date: 2021-03-08 00:00:00

We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each agent can be thought of as acting independently of the other. A random joint choice rule satisfies marginality if for every individual choice set, we can determine the individual's choice probabilities over alternatives independently of the other individual's choice set. We offer two characterizations of random joint choice rules satisfying marginality in terms of separable choice rules. While marginality is a necessary condition for separability, we show that it fails to be sufficient. We provide an additional condition on the marginal choice rules which, along with marginality, is sufficient for separability.
Contracts for acquiring information
Authors: Aubrey Clark, Giovanni Reggiani
Date: 2021-03-05 00:00:00

This paper studies the provision of incentives for information acquisition. Information is costly for an agent to acquire and unobservable to a principal. We show that any Pareto optimal contract has a decomposition into a fraction of output, a state-dependent transfer, and an optimal distortion. Under this decomposition: 1) the fraction of output paid is increasing in the set of experiments available to the agent, 2) the state-dependent transfer indexes contract payments to account for differences in output between states, 3) the optimal distortion exploits complementarities in the cost of information acquisition: experiment probabilities unalterable via contract payments stuck against liability limits are substituted for, the substitution occurring according to complementarities in the cost of information acquisition, and 4) if and only if the agent's cost of experimentation is mutual information, the optimal distortion takes the form of a decision-dependent transfer.
Stable matching: an integer programming approach
Authors: Chao Huang
Date: 2021-03-05 00:00:00

This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete matching market when firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.
Mechanism Design under Approximate Incentive Compatibility
Authors: Santiago Balseiro, Omar Besbes, Francisco Castro
Date: 2021-03-05 00:00:00

A fundamental assumption in classical mechanism design is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or a lack of information, and may not be able to perfectly optimize. This has motivated the introduction of approximate incentive compatibility (IC) as an appealing solution concept for practical mechanism design. While most of the literature focuses on the analysis of particular approximate IC mechanisms, this paper is the first to study the design of optimal mechanisms in the space of approximate IC mechanisms and to explore how much revenue can be garnered by moving from exact to approximate incentive constraints. We study the problem of a seller facing one buyer with private values and analyze optimal selling mechanisms under $\varepsilon$-incentive compatibility. We establish that the gains that can be garnered depend on the local curvature of the seller's revenue function around the optimal posted price when the buyer is a perfect optimizer. If the revenue function behaves locally like an $\alpha$-power for $\alpha \in (1,\infty)$, then no mechanism can garner gains higher than order $\varepsilon^{\alpha/(2\alpha-1)}$. This improves upon state-of-the-art results which imply maximum gains of $\varepsilon^{1/2}$ by providing the first parametric bounds that capture the impact of revenue function's curvature on revenue gains. Furthermore, we establish that an optimal mechanism needs to randomize as soon as $\varepsilon>0$ and construct a randomized mechanism that is guaranteed to achieve order $\varepsilon^{\alpha/(2\alpha-1)}$ additional revenues, leading to a tight characterization of the revenue implications of approximate IC constraints. Our work brings forward the need to optimize not only over allocations and payments but also over best responses, and we develop a new framework to address this challenge.
Decreasing Impatience
Authors: Christopher P. Chambers, Federico Echenique, Alan D. Miller
Date: 2021-03-04 00:00:00

We characterize decreasing impatience, a common behavioral phenomenon in intertemporal choice. Discount factors that display decreasing impatience are characterized through a convexit y axiom for investments at fixed interest rates. Then we show that they are equivalent to a geometric average of generalized quasi-hype rbolic discount rates. Finally, they emerge through parimutuel preference aggregation of exponential discount factors.
Informational Robustness of Common Belief in Rationality
Authors: Gabriel Ziegler
Date: 2021-03-03 00:00:00
Tasks: valid

In this note, I explore the implications of informational robustness under the assumption of common belief in rationality. That is, predictions for incomplete-information games which are valid across all possible information structures. First, I address this question from a global perspective and then generalize the analysis to allow for localized informational robustness.
Information Design in Multi-stage Games
Authors: Miltiadis Makris, Ludovic Renou
Date: 2021-02-26 00:00:00

This paper generalizes the concept of Bayes correlated equilibrium (Bergemann and Morris, 2016) to multi-stage games. We demonstrate the power of our characterization results by applying them to a number of illustrative examples and applications.
On the Basis of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics
Authors: Yuhki Hosoya
Date: 2021-02-15 00:00:00

We consider the classical Ramsey-Cass-Koopmans capital accumulation model and present three examples in which the Hamilton-Jacobi-Bellman (HJB) equation is neither necessary nor sufficient for a function to be the value function. Next, we present assumptions under which the HJB equation becomes a necessary and sufficient condition for a function to be the value function, and using this result, we propose a new method for solving the original problem using the solution to the HJB equation. Our assumptions are so mild that many macroeconomic growth models satisfy them. Therefore, our results ensure that the solution to the HJB equation is rigorously the value function in many macroeconomic models, and present a new solving method for these models.
Dynamically Stable Matching
Authors: Laura Doval
Date: 2019-06-26 00:00:00
Tasks: Blocking, Form

I introduce a stability notion, dynamic stability, for two-sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent's payoff from remaining unmatched cannot be defined independently of what other contemporaneous agents' outcomes are. Dynamically stable matchings always exist. Dynamic stability is a necessary condition to ensure timely participation in the economy by ensuring that agents do not strategically delay the time at which they are available to match.
Ambiguity and Partial Bayesian Updating
Authors: Matthew Kovach
Date: 2021-02-23 00:00:00

Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a general method for updating a set of priors, partial bayesian updating (PB), in which the decision maker (i) utilizes an event-dependent threshold to determine whether a prior is likely enough, conditional on observed information, and then (ii) applies Bayes' rule to the sufficiently likely priors. I show that PB nests FB and ML and explore its behavioral properties.
Local Utility and Multivariate Risk Aversion
Authors: Arthur Charpentier, Alfred Galichon, Marc Henry
Date: 2021-02-08 00:00:00

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. We show that for non-expected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions, thereby generalizing Machina's result in Machina (1982). To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of Galichon and Henry (2011), we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in Landsberger and Meilijson (1994) still holds in the multivariate case.
Minimal entropy and uniqueness of price equilibria in a pure exchange economy
Authors: Andrea Loi, Stefano Matta
Date: 2021-02-19 00:00:00

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.
Incentives for accelerating the production of Covid-19 vaccines in the presence of adjustment costs
Authors: Claudius Gros, Daniel Gros
Date: 2021-02-19 00:00:00

Delays in the availability of vaccines are costly as the pandemic continues. However, in the presence of adjustment costs firms have an incentive to increase production capacity only gradually. The existing contracts specify only a fixed quantity to be supplied over a certain period and thus provide no incentive for an accelerated buildup in capacity. A high price does not change this. The optimal contract would specify a decreasing price schedule over time which can replicate the social optimum.
Price Discrimination in the Presence of Customer Loyalty and Differing Firm Costs
Authors: Theja Tulabandhula, Aris Ouksel, Son Nguyen
Date: 2021-02-16 00:00:00

We study how loyalty behavior of customers and differing costs to produce undifferentiated products by firms can influence market outcomes. In prior works that study such markets, firm costs have generally been assumed negligible or equal, and loyalty is modeled as an additive bias in customer valuations. We extend these previous treatments by explicitly considering cost asymmetry and richer customer loyalty behavior in a game-theoretic model. Thus, in the setting where firms incur different non-negligible product costs, and customers have firm-specific loyalty levels, we comprehensively characterize the effects of loyalty and product cost difference on market outcomes such as prices, market shares, and profits. Our analysis and numerical simulations provide new insights into how firms can price, how they can survive competition even with higher product costs, and how they can control these costs and/or increase customer loyalty to change their market position.
Bounds and Heuristics for Multi-Product Personalized Pricing
Authors: Guillermo Gallego, Gerardo Berbeglia
Date: 2021-02-05 00:00:00
Tasks: BIG-bench Machine Learning, Clustering

We present tight bounds and heuristics for personalized, multi-product pricing problems. Under mild conditions we show that the best price in the direction of a positive vector results in profits that are guaranteed to be at least as large as a fraction of the profits from optimal personalized pricing. For unconstrained problems, the fraction depends on the factor and on optimal price vectors for the different customer types. For constrained problems the factor depends on the factor and a ratio of the constraints. Using a factor vector with equal components results in uniform pricing and has exceedingly mild sufficient conditions for the bound to hold. A robust factor is presented that achieves the best possible performance guarantee. As an application, our model yields a tight lower-bound on the performance of linear pricing relative to optimal personalized non-linear pricing, and suggests effective non-linear price heuristics relative to personalized solutions. Additionally, our model provides guarantees for simple strategies such as bundle-size pricing and component-pricing with respect to optimal personalized mixed bundle pricing. Heuristics to cluster customer types are also developed with the goal of improving performance by allowing each cluster to price along its own factor. Numerical results are presented for a variety of demand models that illustrate the tradeoffs between using the economic factor and the robust factor for each cluster, as well as the tradeoffs between using a clustering heuristic with a worst case performance of two and a machine learning clustering algorithm. In our experiments economically motivated factors coupled with machine learning clustering heuristics performed best.
A Theory of Choice Bracketing under Risk
Authors: Mu Zhang
Date: 2021-02-15 00:00:00

Aggregating risks from multiple sources can be complex and demanding, and decision makers usually adopt heuristics to simplify the evaluation process. This paper axiomatizes two closed related and yet different heuristics, narrow bracketing and correlation neglect, by relaxing the independence axiom in the expected utility theory. The flexibility of our framework allows for applications in various economic problems. First, our model can explain the experimental evidence of narrow bracketing over monetary gambles. Second, when one source represents background risk, we can accommodate Rabin (2000)'s critique and explain risk aversion over small gambles. Finally, when different sources represent consumptions in different periods, we unify three seemingly distinct models of time preferences and propose a novel model that simultaneously satisfies indifference to temporal resolution of uncertainty, separation of time and risk preferences, and recursivity in the domain of lotteries. As a direct application to macroeconomics and finance, we provide an alternative to Epstein and Zin (1989) which avoids the unreasonably high timing premium discussed in Epstein, Farhi, and Strzalecki (2014).
An Axiom for Concavifiable Preferences in View of Alt's Theory
Authors: Yuhki Hosoya
Date: 2021-02-14 00:00:00

We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can be seen as an extension of Gossen's first law, and thus has an economic interpretation. Together with the above results, we provide a necessary and sufficient condition for Alt's utility to be continuously differentiable.
Learning from Manipulable Signals
Authors: Mehmet Ekmekci, Leandro Gorno, Lucas Maestri, Jian Sun, Dong Wei
Date: 2020-07-17 00:00:00

We study a dynamic stopping game between a principal and an agent. The agent is privately informed about his type. The principal learns about the agent's type from a noisy performance measure, which can be manipulated by the agent via a costly and hidden action. We fully characterize the unique Markov equilibrium of this game. We find that terminations/market crashes are often preceded by a spike in (expected) performance. Our model also predicts that, due to endogenous signal manipulation, too much transparency can inhibit learning. As the players get arbitrarily patient, the principal elicits no useful information from the observed signal.