Communication and Equilibrium in Discontinuous Games of Incomplete Information (original) (raw)
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Corrigendum to "Communication and Equilibrium in Discontinuous Games of Incomplete Information
Econometrica, 2004
This paper o ers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payo s. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules which resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy pro les satisfying the usual best-response criteria. It is shown that that the introduction of incentive compatible communication (cheap talk) restores existence.
Discontinuous Payoff Functions under Incomplete Information
1994
Abstract: Discontinuous payoff functions have attracted some attention in the literature, especially in economic games. This paper considers such functions when the location of the discontinuity is known incompletely. Under this scenario, the presence of a discontinuity ...
A note on the equilibrium existence problem in discontinuous games
2012
In this note we prove an equilibrium existence theorem for games with discontinuous pay- offs and convex and compact strategy spaces. It generalizes the classical result of Reny (1999) [Econometrica 67, p. 1029-1056], as well as the recent paper of McLennan, Monteiro, and Tourky (2011) [Econometrica 79, p. 1643-1664]. Our condition is simple and easy to verify. Importantly, an example
On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games
2013
New relaxations of the Nash equilibrium concept are shown to exist in any strategic game with discontinuous payoff functions. The new concepts are used (1) to show the equivalence between Reny's better-reply security condition [28] and Simon-Zame's endogenous tie-breaking rule equilibrium concept [32], (2) to obtain conditions for the existence of approximated equilibria in a class of discontinuous games that naturally extends Reny's better-reply secure games, and (3) to show the existence of approximated equilibria in a large family of two-player games that contains all standard models of auctions.
On the existence of approximate equilibria and sharing rule solutions in discontinuous games
Theoretical Economics, 2017
This paper studies the existence of some known equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition [34], and its recent improvements [3, 25, 35, 36]. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame [38]). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that in any general equilibrium model with discontinuous preferences, there is a sharing rule solution.
Single-crossing properties and existence of pure-strrategy equilibria in games of incomplete informa
2001
This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash Ž . Ž . equilibria PSNE under a condition we call the single crossing condition SCC , roughly Ž described as follows: whenever each opponent uses a nondecreasing strategy in the sense . that higher types choose higher actions , a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite-action games that converges to a PSNE of the continuum-action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first-price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first-price, multi-unit, and all-pay auctions; pricing games with incomplete information about costs; and noisy signaling games.
Communication in games of incomplete information: Two players
Journal of Economic Theory, 2007
We study the effect of communication in two-person games of incomplete information. We show that for any two-player game of incomplete information, any rational mediated communication mechanism outcome (satisfying a Nash domination condition) can be implemented as the perfect Bayesian equilibrium of a cheap-communication extension of the original game.
On the stability of equilibria in incomplete information games under ambiguity
2013
In this paper, we look at the (Kajii and Ui) mixed equilibrium notion, which has been recognized by previous literature as a natural solution concept for incomplete information games in which players have multiple priors on the space of payoff relevant states. We investigate the problem of stability of mixed equilibria with respect to perturbations on the sets of multiple priors. We find out that the (Painlevé-Kuratowski) convergence of posteriors ensures that stability holds; whereas, convergence of priors is not enough to obtain stability since it does not always implies convergence of posteriors when we consider updating rules (for multiple priors) based on the classical Bayesian approach.
Econometrica, 2001
This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash Ž . Ž . equilibria PSNE under a condition we call the single crossing condition SCC , roughly Ž described as follows: whenever each opponent uses a nondecreasing strategy in the sense . that higher types choose higher actions , a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite-action games that converges to a PSNE of the continuum-action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first-price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first-price, multi-unit, and all-pay auctions; pricing games with incomplete information about costs; and noisy signaling games.