Evolutionary Stability in Games of Communication

doi:10.1006/game.1993.1031

Games and Economic Behavior

Volume 5, Issue 4, October 1993, Pages 547-575

https://doi.org/10.1006/game.1993.1031 Get rights and content

Abstract

This paper identifies evolutionarily stable outcomes in games in which one player has private information and the other takes a payoff-relevant action. The informed player can communicate at little cost. Outcomes satisfying a set-valued evolutionary stability condition must exist and be efficient in common-interest games. When there is a small cost associated with using each message the outcome preferred by the informed player is stable. The paper introduces a nonequilibrium, set-valued stability notion of entry resistant sets. For games with partial common interest, the no-communication outcome is never an element of an entry resistant set. Journal of Economic Literature Classification Numbers: C72,D82.

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The evolution of taking roles
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Citation Excerpt :
Farrell allows only for a specific type of communication that corresponds to our hierarchical structure in anti-coordination games and analyzes the corresponding Nash equilibria. Most of this related cheap-talk literature, including Robson (1990), Sobel (1993), Blume et al. (1993), Schlag (1993), Wärneryd (1993), Schlag (1995), Kim and Sobel (1995), Bhaskar (1998), Banerjee and Weibull (2000), and Hurkens and Schlag (2003), focusses on coordination games and investigates how far cheap talk does – or does not – support selection against inefficient equilibria. The most closely related formal setup to our work is that described in Hurkens and Schlag (2003) and Banerjee and Weibull (2000).
Individuals are randomly matched to play an ex-ante symmetric hawk-dove game. Individuals assume one of a finite set of observable labels and condition their action choice on their opponent’s label. We study the evolutionary stability of chosen labels and their social interaction structure. Evolutionarily stable social structures differ for games in which a dove player prefers the opponent to play hawk (anti-coordination games), and those in which everyone prefers their opponent to play dove (conflict games). Non-trivial hierarchical social structures can only emerge in anti-coordination games. Egalitarian social structures can emerge in both, but are more fragile in conflict games.
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Citation Excerpt :
Unfortunately, both Farrell's neologism proofness and Matthews et al.'s (strong) announcement proofness criteria eliminate all equilibria in many games, including the original Crawford–Sobel game.4 Several other types of concepts have been proposed that distinguish between stable and unstable equilibria (or profiles), such as Partial Common Interest (PCI) (Blume et al., 1993), the recurrent mop (Rabin and Sobel, 1996) and No Incentive To Separate (NITS) (Chen et al., 2008). These criteria often select a plausible equilibrium in specific settings, but fail to discriminate successfully across a wider range of cheap talk games.
In the past, many refinements have been proposed to select equilibria in cheap talk games. Usually, these refinements were motivated by a discussion of how rational agents would reason in some particular cheap talk games. In this paper, we propose a new refinement and stability measure that is intended to predict actual behavior in a wide range of cheap talk games. According to our Average Credible Deviation Criterion (ACDC), the stability of an equilibrium is determined by the frequency and size of credible deviations. ACDC organizes the results from several cheap talk experiments in which behavior converges to equilibrium, even in cases where other criteria do not make a prediction.

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Special Issue ArticleEvolutionary Stability in Games of Communication

Abstract

Special Issue Article
Evolutionary Stability in Games of Communication