Theoretical Economics: Recent Articles
http://econtheory.org
Articles recently published or accepted for publicationSat, 31 Jan 2015 15:05:00 ESTen-usSampling best response dynamics and deterministic equilibrium selection
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150243
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150243Fri, 30 Jan 2015 00:00:00 ESTby <b>Daisuke Oyama, William H. Sandholm, and Olivier Tercieux</b><p>Published in Theoretical Economics 10 (1), 243–281 (January 30, 2015)<p>Abstract: We consider a model of evolution in games in which a revising agent observes the actions of a random number of randomly sampled opponents and then chooses a best response to the distribution of actions in the sample. We provide a condition on the distribution of sample sizes under which an iterated $p$-dominant equilibrium is almost globally asymptotically stable under these dynamics. We show under an additional condition on the sample size distribution that in supermodular games, an almost globally asymptotically stable state must be an iterated $p$-dominant equilibrium. Since our selection results are for deterministic dynamics, any selected equilibrium is reached quickly; the long waiting times associated with equilibrium selection in stochastic stability models are absent.Three steps ahead
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150203
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150203Fri, 30 Jan 2015 00:00:00 ESTby <b>Yuval Heller</b><p>Published in Theoretical Economics 10 (1), 203–241 (January 30, 2015)<p>Abstract: We study a variant of the repeated Prisoner's Dilemma with uncertain horizon, in which each player chooses his foresight ability: that is, the timing in which he is informed about the realized length of the interaction. In addition, each player has an independent probability to observe the opponent's foresight ability. We show that if this probability is not too close to zero or one, then the game admits an evolutionarily stable strategy, in which agents who look one step ahead and agents who look three steps ahead co-exist. Moreover, this is the unique evolutionarily stable strategy in which players play efficiently at early stages of the interaction. We interpret our results as a novel evolutionary foundation for limited foresight, and as a new mechanism to induce cooperation in the repeated Prisoner's Dilemma..Breakdowns
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150175
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150175Fri, 30 Jan 2015 00:00:00 ESTby <b>Godfrey Keller and Sven Rady</b><p>Published in Theoretical Economics 10 (1), 175–202 (January 30, 2015)<p>Abstract: We study a continuous-time game of strategic experimentation in which the players try to assess the failure rate of some new equipment or technology. Breakdowns occur at the jump times of a Poisson process whose unknown intensity is either high or low. In marked contrast to existing models, we find that the cooperative value function does not exhibit smooth pasting at the efficient cut-off belief. This finding extends to the boundaries between continuation and stopping regions in Markov perfect equilibria. We characterize the unique symmetric equilibrium, construct a class of asymmetric equilibria, and elucidate the impact of bad versus good Poisson news on equilibrium outcomes.A folk theorem for stochastic games with infrequent state changes
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150131
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150131Fri, 30 Jan 2015 00:00:00 ESTby <b>Marcin Peski and Thomas Wiseman</b><p>Published in Theoretical Economics 10 (1), 131–173 (January 30, 2015)<p>Abstract: We characterize perfect public equilibrium payoffs in dynamic stochastic games, in the case where the length of the period shrinks, but players' rate of time discounting and the transition rate between states remain fixed. We present a meaningful definition of the feasible and individually rational payoff sets for this environment, and we prove a folk theorem under imperfect monitoring. Our setting differs significantly from the case considered in previous literature (Dutta (1995), Fudenberg and Yamamoto (2011), and HÃ¶rner, Sugaya, Takahashi, and Vieille (2011)) where players become very patient. In particular, the set of equilibrium payoffs typically depends on the initial state.Strategic uncertainty and the ex-post Nash property in large games
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150103
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150103Fri, 30 Jan 2015 00:00:00 ESTby <b>M. Ali Khan, Kali P. Rath, Yeneng Sun, and Haomiao Yu</b><p>Published in Theoretical Economics 10 (1), 103–129 (January 30, 2015)<p>Abstract: This paper elucidates the conceptual role that independent randomization plays in non-cooperative game theory. In the context of large (atomless) games in normal form, we present precise formalizations of the notions of a mixed strategy equilibrium (MSE), and of a randomized strategy equilibrium in distributional form (RSED). We offer a resolution of two long-standing open problems and show: (i) any MSE {\it induces} a RSED, and any RSED can be {\it lifted} to a MSE, (ii) a mixed strategy profile is a MSE if and only if
it has the ex-post Nash property. Our substantive results are a direct consequence of an {\it exact} law of large numbers (ELLN) that can be formalized in the analytic framework of a Fubini extension. We discuss how the \lq measurability' problem associated with a MSE of a large game is automatically resolved in such a framework. We also illustrate our ideas by an approximate result pertaining to a sequence of large but finite games.Communication with tokens in repeated games on networks
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150067
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150067Fri, 30 Jan 2015 00:00:00 ESTby <b>Alexander Wolitzky</b><p>Published in Theoretical Economics 10 (1), 67–101 (January 30, 2015)<p>Abstract: A key obstacle to coordination and cooperation in many networked environments is that behavior in each bilateral relationship is not observable to individuals outside that relationship: that is, information is local. This paper investigates when players can use communication to replicate any outcome that would have been sustainable were this information public. A benchmark result is that if only cheap talk communication is possible then public information can only be replicated if the network is 2-connected: that is, if no player can prevent the flow of information to another. In contrast, the main result is that public information can always be replicated if in addition to cheap talk the players have access to undifferentiated tokens that can be freely transferred among neighbors (which bear some resemblance to certain models of fiat money). Sufficient conditions are provided for such tokens to expand the equilibrium payoff set, relative to what would be achievable without explicit communication or with cheap talk communication only.Is utility transferable? a revealed preference analysis
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150051
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150051Fri, 30 Jan 2015 00:00:00 ESTby <b>Laurens Cherchye, Thomas Demuynck, and Bram De Rock</b><p>Published in Theoretical Economics 10 (1), 51–65 (January 30, 2015)<p>Abstract: The transferable utility hypothesis underlies important theoretical results in household economics. We provide a revealed preference framework for bringing this (theoretically appealing) hypothesis to observational data. We establish revealed preference conditions that must be satisfied for observed household consumption behavior to be consistent with transferable utility. We also show that these conditions are testable by means of integer programming methods.Unraveling in a repeated moral hazard model with multiple agents
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150011
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150011Fri, 30 Jan 2015 00:00:00 ESTby <b>Madhav Chandrasekher</b><p>Published in Theoretical Economics 10 (1), 11–49 (January 30, 2015)<p>Abstract: This paper studies an infinite horizon repeated moral hazard problem where a single principal employs several agents. We assume that the principal cannot observe the agents' effort choices; however, agents can observe each other and can be contractually required to make observation reports to the principal. Observation reports, if truthful, can serve as a monitoring instrument to discipline the agents. However, reports are cheap talk so that it is also possible for agents to collude, i.e. where they shirk, earn rents, and report otherwise to the principal. The main result of the paper constructs a class of collusion-proof contracts with two properties. First, equilibrium payoffs to both the principal and the agents approach their first-best benchmarks as the discount factor tends to unity. These payoff bounds apply to all subgame perfect equilibria in the game induced by the contract. Second, while equilibria themselves depend on the discount factor, the contract which induces these equilibria is independent of the discount factor.The Foster-Hart measure of riskiness for general gambles
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150001
http://econtheory.org/ojs/index.php/te/article/viewArticle/20150001Fri, 30 Jan 2015 00:00:00 ESTby <b>Frank Riedel and Tobias Hellmann</b><p>Published in Theoretical Economics 10 (1), 1–9 (January 30, 2015)<p>Abstract: Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst--case risk measure, i.e. the maximal possible loss incurred by that gamble. For many discrete gambles with a large number of values, the Foster--Hart riskiness is close to the maximal loss. We give a simple characterization of gambles whose riskiness is or is close to the maximal loss.Fragility of asymptotic agreement under Bayesian learning
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/436/12247/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/436/12247/1Sun, 25 Jan 2015 00:00:00 ESTby <b>Daron Acemoglu, Victor Chernozhukov, and Muhamet Yildiz</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on January 25, 2015<p>Abstract: Under the assumption that individuals know the conditional distributions of signals given the payoff-relevant parameters, existing results conclude that as individuals observe infinitely many signals, their beliefs about the parameters will eventually merge. We first show that these results are fragile when individuals are uncertain about the signal distributions: given any such model, vanishingly small individual uncertainty about the signal distributions can lead to substantial (non-vanishing) differences in asymptotic beliefs. Under a uniform convergence assumption, we then characterize the conditions under which a small amount of uncertainty leads to significant asymptotic disagreement.Reputation without commitment in finitely-repeated games
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1893/12233/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1893/12233/1Fri, 23 Jan 2015 00:00:00 ESTby <b>Jonathan Weinstein and Muhamet Yildiz</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on January 23, 2015<p>Abstract: In the reputation literature, players have \emph{commitment types} which
represent the possibility that they do not have standard payoffs but instead
are constrained to follow a particular plan. In this paper, we show that
arbitrary commitment types can emerge from incomplete information about the
stage payoffs. In particular, any finitely repeated game with commitment
types is strategically equivalent to a standard finitely repeated game with
incomplete information about the stage payoffs. Then, classic reputation
results can be achieved with uncertainty concerning only the stage payoffs.Optimally constraining a bidder using a simple budget
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1745/12177/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1745/12177/1Sun, 18 Jan 2015 00:00:00 ESTby <b>Justin Burkett</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on January 18, 2015<p>Abstract: I study a principal's optimal choice of constraint for an agent participating in an auction (or auction-like allocation mechanism). I give necessary and sufficient conditions on the principal's beliefs about the value of the item for a simple budget constraint to be the optimal contract. The results link the observed use of budget constraints to their use in models incorporating budget-constrained bidders. Other implications of the model are that a general revenue equivalence result applies and that the optimal auction with budget-constrained bidders has a standard solution analogous to the one for classic models.Dynamics in stochastic evolutionary models
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1978/12043/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1978/12043/1Wed, 17 Dec 2014 00:00:00 ESTby <b>David Knudsen Levine and Salvatore Modica</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on December 17, 2014<p>Abstract: We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict and illustrate the theory with the fall of the Qing Dynasty and rise of Communism in China.Approximate efficiency in repeated games with side-payments and correlated signals
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1369/11946/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1369/11946/1Mon, 01 Dec 2014 00:00:00 ESTby <b>Jimmy H. Chan and Wenzhang Zhang</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on December 1, 2014<p>Abstract: Side-payments are common in many long-term relationships. We show that when players can exchange side-payments, approximate efficiency is achievable in any repeated game with private monitoring and communication, so long as the players can observe their own payoffs and are sufficiently patient, the efficient stage-game outcome is unique, and the signal distribution has full support. Unlike existing results in the literature, our result does not require deviations be statistically detectable.On the impossibility of core-selecting auctions
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1198/11945/1
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/1198/11945/1Mon, 01 Dec 2014 00:00:00 ESTby <b>Jacob K. Goeree and Yuanchuan Lien</b><p>To be published in Theoretical Economics. First available as a "Paper to appear" on December 1, 2014<p>Abstract: When goods are substitutes, the Vickrey outcome is in the core and yields competitive seller revenue. In contrast, with complements, the Vickrey outcome is efficient but not necessarily in the core and revenue can be low. Non-core outcomes may be perceived as unfair since there are bidders willing to pay more than the winners' payments. Moreover, non-core outcomes render the auction vulnerable to defections as the seller can attract better offers afterwards. To avoid instabilities of this type, Day and Raghavan (2007), Day and Milgrom (2008), and Day and Cramton (2012) have suggested adapting the Vickrey pricing rule so that outcomes are in the core with respect to bidders' {\em reported} values.
If truthful bidding were an equilibrium of the resulting auction then the outcome would also be in the core with respect to bidders' {\em true} values. We show, however, that when the equilibrium outcome of any auction is in the core, it is equivalent to the Vickrey outcome. In other words, if the Vickrey outcome is not in the core, no core-selecting auction exists. Our results further imply that the competitive equilibrium outcome, which always exists when goods are substitutes, can only be implemented when it coincides with the Vickrey outcome. Finally, for a simple environment we show that compared to Vickrey prices the adapted pricing rule yields lower expected efficiency and revenue as well as outcomes that are on average further from the core.