The Maximal Domain for the Revelation Principle when Preferences are Menu Dependent

We extend the domain of preferences to include menu-dependent preferences and characterize the maximal subset of this domain in which the revelation principle holds. Minimax-regret preference is shown to be outside this subset.microeconomics ;

Bargaining with Behavioral Players: Strategic Deception and More Trade

Previous literature proved the existence of an upper bound on the probability of trade in a bilateral trading problem when the valuations are distributed uniformly on [0,1]. This upper bound is achieved in the ½-double auction when the players play the Chatterjee-Samuelson strategies. We introduce behavioral-type players in a ½-double auction preceded by cheap talk. The behavioral-type players always declare a keenness to trade in the cheap-talk stage and play the Chatterjee-Samuelson strategies if they hear the “Keen” message. In equilibrium, the probability of trade between the strategic types increases monotonically as the probability of the behavioral types increases. If the probability of the behavioral types is high enough, the probability of trade between the strategic types is greater than the upper bound.microeconomics ;

How Communication Improves Efficiency in Bargaining: Reconciling Theory with Evidence

Previous theoretical literature proved the existence of an upper bound on efficiency in bilateral bargaining. In contrast, experiments consistently find players obtaining higher efficiency than the upper bound if they are allowed to communicate before the 1/2-double auction. We bridge this gap between theory and experiments by introducing an epsilon proportion of behavioral-type players who always truthfully reveal their valuations and declare a keenness to trade before bidding in the 1/2-double auction. Preplay communication is used by the strategic types to communicate their "tougher'''' bargaining position, forcing the behavioral types to adopt a "weaker'''' position. This further induces the strategic types to decrease the shading/exaggeration in the announcement of their valuations lest they miss the chance to trade with the "weaker'''' behavioral types. As a result, for any epsilon>0, the efficiency in equilibrium is greater than the upper bound.microeconomics ;

Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values

In contexts in which players have no priors, we analyze a learning pro- cess based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are ran- domly matched to play the game (random matching). The relevant long run predictions are minimal sets that are closed under “the same or better reply” operations. Under additional assumptions in each case, the prediction boils down to pure Nash equilibria, pure ex-post equilibria or pure minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in second-price auctions, first-price auctions and Bertrand duopolies.Fixed and Random Matching; Incomplete Information; Ex-Post Regret Learning; Nash Equilibrium; Ex-Post Equilibrium; Minimax Regret

Whose Opinion Counts? Political Processes and the Implementation Problem

The mechanism used in Nash implementation is a form of direct democracy, taking everyone''s opinion into account. We augment this mechanism with a political process that selects the opinions of a subset of the individuals. We study three such processes -- oligarchy, oligarchic democracy and random sampling -- and compare the social choice rules (SCRs) that can be implemented using each of these processes with those that can be Nash implemented. In oligarchy, only the opinions of a fixed subset of the individuals -- the oligarchs -- determine the implemented alternative. We obtain a negative result for oligarchies: there exist Nash implementable SCRs that cannot be implemented by any oligarchy. Oligarchic democracy is a perturbation of oligarchy, in which the opinions of the oligarchs “almost always” determine the implemented alternative but sometimes, everyone''s opinions are considered. In a sharp contrast to the negative result for oligarchies, we show that in economic environments, every Nash implementable SCR can be implemented by an oligarchic democracy in which any three individuals act as oligarchs. In random sampling, opinions of a fixed number of individuals are selected randomly, which then determine the implemented alternative. We show that in economic environments, every Nash implementable SCR can be implemented by randomly sampling opinions of four individuals.microeconomics ;

Ex-post regret learning in games with fixed and random matching: The case of private values

In contexts in which players have no priors, we analyze a learning process based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are randomly matched to play the game (random matching). The relevant long run predictions are minimal sets that are closed under “the same or better reply” operations. Under additional assumptions in each case, the prediction boils down to pure Nash equilibria, pure ex-post equilibria or pure minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in second-price auctions, first-price auctions and Bertrand duopolies.fixed and random matching; incomplete information; ex-post regret learning; nash equilibrium; ex-post equilibrium; minimax regret equilibrium; second-price auction;first-price auction;bertrand duopoly

Regret Matching with Finite Memory

We consider the regret matching process with finite memory. For general games in normal form, it is shown that any recurrent class of the dynamics must be such that the action profiles that appear in it constitute a closed set under the “same or better reply” correspondence (CUSOBR set) that does not contain a smaller product set that is closed under “same or better replies,” i.e., a smaller PCUSOBR set. Two characterizations of the recurrent classes are offered. First, for the class of weakly acyclic games under better replies, each recurrent class is monomorphic and corresponds to each pure Nash equilibrium. Second, for a modified process with random sampling, if the sample size is sufficiently small with respect to the memory bound, the recurrent classes consist of action profiles that are minimal PCUSOBR sets. Our results are used in a robust example that shows that the limiting empirical distribution of play can be arbitrarily far from correlated equilibria for any large but finite choice of the memory bound.Regret Matching; Nash Equilibria; Closed Sets under Same or Better Replies; Correlated Equilibria.

In Bargaining We Trust

We introduce trustworthy traders in bilateral trading. Trustworthy traders do not misrepresent their private information. We prove that an increase in the levels of trust (probabilities that traders are trustworthy) can reduce the maximum attainable probability of trade among the strategic traders in the set of k-double auctions. In contrast, if the levels of trust increase, then we can construct direct mechanisms with a higher probability of trade among the strategic traders. In fact, there exist ex-post efficient direct mechanisms if the levels of trust are high but k-double auctions are inefficient for all levels of trust. We prove that k-double auctions are constraint-inefficient for generic levels of trust when players have uniform priors.microeconomics ;