Theoretical Economics Volume 16, Number 4 (November 2021) is now online

Theoretical Economics
Volume 16, Number 4 (November 2021)
Table of contents


Title: Local global equivalence in voting models: a characterization and applications

Pages: 1195-1220

Authors: Ujjwal Kumar, Souvik Roy, Arunava Sen, Sonal Yadav, Huaxia Zeng

Abstract: The paper considers a voting model where each voter's type is her preference.  The type graph for a voter is a graph whose nodes are the possible types of the voter.  A social choice function is locally strategy-proof if no type of a voter can gain by misrepresentation to a type that is connected to her true type by an edge in the type graph. A social choice function is strategy-proof if no type of a voter can gain by misrepresentation to an arbitrary type. Local-Global equivalence
(LGE) is satisfied if local strategy-proofness implies strategy-proofness.
The paper identifies a condition on the graph that characterizes LGE. Our notion of ``localness'' is perfectly general
- we use this feature of our model to identify notions of localness according to which various models of multi-dimensional voting satisfy LGE.
Finally, we show that LGE for deterministic social choice functions does not imply LGE for random social choice functions.

Keywords: Local incentive constraints, strategy-proofness, mechanism design, strategic voting

JEL classification: D71


Title: Subgame-perfect equilibrium in games with almost perfect information: dispensing with public randomization

Pages: 1221-1248

Authors: Paulo Barelli, John Duggan

Abstract: Harris, Reny, and Robson (1995) add a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE).  We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs:  any SPE obtained using public randomization can be ``de-correlated" to produce a payoff-equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun
(2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.

Keywords: Existence, subgame-perfect equilibrium, infinite-action games, stochastic games, public randomization

JEL classification: C72, C73


Title: Minimally unstable Pareto improvements over deferred acceptance

Pages: 1249-1279

Authors: Battal Dogan, Lars Ehlers

Abstract: We investigate efficient and minimally unstable Pareto improvements over the deferred acceptance (DA) mechanism-a popular school choice mechanism which is stable but not efficient. We show that there is no Pareto improvement over the DA mechanism which is minimally unstable among efficient assignments when the stability comparison is based on counting the number of blocking pairs. Our main result characterizes the priority profiles for which there exists a Pareto improvement over the DA assignment that is minimally unstable among efficient assignments. We further consider an alternative natural stability comparison based on the set of blocking students who are involved in at least one blocking pair, show that the impossibilities remain, and characterize the possibility domain of priority profiles.

Keywords: School choice, deferred acceptance, stability comparisons, cardinal minimal instability

JEL classification: C70, D47, D61, D63


Title: Payoff implications of incentive contracting

Pages: 1281-1312

Authors: Daniel F. Garrett

Abstract: In the context of a canonical agency model, we study the payoff implications of introducing optimally-structured incentives. We do so from the perspective of an analyst who does not know the agent's preferences for responding to incentives, but does know that the principal knows them.  We provide, in particular, tight bounds on the principal's expected benefit from optimal incentive contracting across feasible values of the agent's expected rents. We thus show how economically relevant predictions can be made robustly given ignorance of a key primitive.

Keywords: Asymmetric information, mechanism design, robustness, procurement

JEL classification: D82


Title: Monitoring experts

Pages: 1313-1350

Authors: Yaron Azrieli

Abstract: We study the design of contracts that incentivize experts to collect information and truthfully report it to a decision maker. We depart from most of the previous literature by assuming that the transfers cannot depend on the realized state or on the ex-post payoff of the decision maker.
The contract thus has to induce the experts to `monitor each other' by making the transfers contingent on the entire vector of reports. We characterize the least costly contract that implements any given vector of efforts and derive the cost function for the decision maker. We then study properties of optimal contracts by comparing the value of information and its cost.

Keywords: Moral hazard, information acquisition, monitoring, value of information

JEL classification: D82, D86


Title: Robust group strategy-proofness

Pages: 1351-1389

Authors: Steven Kivinen, Norovsambuu Tumennasan

Abstract: Strategy-proofness (SP) is a sought-after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex-post stages.  Group strategy-proofness (GSP), however, is a notion that is applied to the ex-post stage but not to the interim stage.  Thus, we propose a new notion of GSP, coined robust group strategy-proofness (RGSP), which ensures that no group benefits by deviating from truthtelling at the interim stage. We show for the provision of a public good that the Minimum Demand rule (Serizawa,  1999) satisfies RGSP when the production possibilities set satisfies a particular topological property.  In the problem of allocating indivisible objects, an acyclicity condition on the priorities is both necessary and sufficient for the Deferred Acceptance rule to satisfy RGSP, but is only necessary for the  Top Trading Cycles rule. For the allocation of divisible private goods among agents with single-peaked preferences (Sprumont, 1991), only free disposal, group replacement monotonic rules within the class of sequential allotment rules satisfy RGSP.

Keywords: Robust group strategy-proofness, Minimum Demand rule, Top Trading Cycles,  Deferred Acceptance,  Acyclic priorities, Free disposal, Group replacement monotonicity

JEL classification: C71, C78, D70, D80


Title: Relational communication

Pages: 1391-1430

Authors: Anton Kolotilin, Hongyi Li

Abstract: We study a communication game between an informed sender and an uninformed receiver with repeated interactions and voluntary transfers.
Transfers motivate the receiver's decision-making and signal the sender's information. Although full separation can always be supported in equilibrium, partial or complete pooling is optimal if the receiver's decision-making is highly responsive to information. In this case, the receiver's decision-making is disciplined by pooling states where she is most tempted to defect.

Keywords: Strategic communication, relational contracts

JEL classification: C73, D82, D83


Title: Robust sequential search

Pages: 1431-1470

Authors: Karl H. Schlag, Andriy Zapechelnyuk

Abstract: We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules robust. The search literature employs optimal rules based on cutoff strategies, and these rules are not robust. We derive robust rules and show that their performance exceeds 1/2 of the optimum against binary i.i.d. environments and 1/4 of the optimum against all i.i.d. environments. This performance improves substantially with the outside option value, for instance, it exceeds 2/3 of the optimum if the outside option exceeds 1/6 of the highest possible alternative.

Keywords: Sequential search, search without priors, robustness, dynamic consistency, competitive ratio

JEL classification: D83, D81, C44


Title: Renegotiation of long-term contracts as part of an implicit agreement

Pages: 1471-1512

Authors: Rumen Kostadinov

Abstract: I study a repeated principal-agent game with long-term output contracts that can be renegotiated at will. Actions are observable but not contractible, so they can only be incentivised through implicit agreements formed in equilibrium. I show that contract renegotiation is a powerful tool for incentive provision, despite the stationarity of the environment.
Continuation contracts are designed to punish deviations in noncontractible behaviour. If the equilibrium actions are observed, these contracts are renegotiated away. This form of anticipated renegotiation results in welfare improvements over outcomes attainable by one-period contracts, or by long-term contracts which are not renegotiated. When the principal is not protected by limited liability, first-best outcomes are attainable regardless of the impatience of the players. Equilibrium strategies are shown to satisfy various concepts of renegotiation-proofness.

Keywords: Long-term contracts, renegotiation, relational contracts

JEL classification: C73, C78, D86


Title: Sustainable debt

Pages: 1513-1555

Authors: Gaetano Bloise, Herakles Polemarchakis, Yiannis Vailakis

Abstract: We show that debt is sustainable at a competitive equilibrium based solely on the reputation for repayment; that is, even without collateral or legal sanctions available to creditors. In an incomplete asset market, when the rate of interest falls recurrently below the rate of growth of the economy, self-insurance is more costly than borrowing, and repayments on loans are enforced by the implicit threat of loss of the risk-sharing advantages of debt contracts. Private debt credibly circulates as a form of inside money, and it is not valued as a speculative bubble. Competitive equilibria with self-enforcing debt exist under a suitable hypothesis of gains from trade.

Keywords: Rate of interest, self-enforcing debt, Ponzi games, incomplete markets, competitive equilibrium, gains from trade

JEL classification: D52, F34, H63


Title: Bayesian privacy

Pages: 1557-1603

Authors: Ran Eilat, Kfir Eliaz, Xiaosheng Mu

Abstract: Modern information technologies make it possible to store, analyze and trade unprecedented amounts of detailed information about individuals.
This has led to public discussions on whether individuals' privacy should be better protected by restricting the amount or the precision of information that is collected by commercial institutions on their participants. We contribute to this discussion by proposing a Bayesian approach to measure loss of privacy in a mechanism. Specifically, we define the loss of privacy associated with a mechanism as the difference between the designer's prior and posterior beliefs about an agent's type, where this difference is calculated using Kullback-Leibler divergence, and where the change in beliefs is triggered by actions taken by the agent in the mechanism. We consider both ex-post (for every realized type, the maximal difference in beliefs cannot exceed some threshold κ) and ex-ante (the expected difference in beliefs over all type realizations cannot exceed some threshold κ) measures of privacy loss. Applying these notions to the monopolistic screening environment of Mussa and Rosen (1978), we study the properties of optimal privacy-constrained mechanisms and the relation between welfare/profits and privacy levels.

Keywords: Privacy, mechanism design, relative entropy

JEL classification: C72, D82, D83


Title: The implications of finite-order reasoning

Pages: 1605-1654

Authors: Adam Brandenburger, Alexander Danieli, Amanda Friedenberg

Abstract: The epistemic conditions of rationality and $m$th-order strong belief of rationality \citep[R$m$SBR,][]{battigalli2002sba} formalize the
idea that players engage in contextualized forward-induction reasoning. This
paper characterizes the behavior consistent with R$m$SBR across all type structures.  In particular, in a class of generic games, R$(m-1)$SBR is characterized by a new solution concept we call an $m$-best response sequence ($m$-BRS). Such sequences are an iterative version of extensive-form best response sets \citep{battigallicontext}.  The strategies that survive $m$ rounds of extensive-form rationalizability are consistent with an $m$-BRS, but there are $m$-BRS’s which are disjoint from the former set. As such, there is behavior that is consistent with R$(m-1)$SBR but inconsistent with $m$ rounds of extensive-form rationalizability.  We use our characterization to draw implications for the interpretation of experimental data.  Specifically, we show that the implications are non-trivial in the $3$-repeated Prisoner’s Dilemma and Centipede games.

Keywords: Epistemic game theory, strategic uncertainty, bounded reasoning, identifying reasoning

JEL classification: D01, D03, D83


Title: Bilateral trade with a benevolent intermediary

Pages: 1655-1714

Authors: Ran Eilat, Ady Pauzner

Abstract: We study intermediaries who seek to maximize gains from trade in bilateral negotiations. Intermediaries are players: they cannot commit to act against their objective function and deny, in some cases, trade they believe to be beneficial. This impairs their ability to assist the parties relative to conventional mechanisms. We analyze this limited commitment environment as a standard mechanism design problem with an additional "credibility" constraint, requiring that every outcome be interim-optimal conditional on available information. We investigate how such intermediaries communicate with the parties, analyze the tradeoffs they face and study the bounds on what they can achieve.

Keywords: Intermediation, mechanism design, imperfect commitment, asymmetric information, bilateral trade

JEL classification: C72, D82, D83


Publication Date: 
Monday, November 8, 2021