Evolution and correlated equilibrium

Metzger, Lars Peter

doi:10.1007/s00191-017-0539-z

Cited by 9 publications

(13 citation statements)

References 18 publications

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“…Our work belongs to a body of game theory that has studied how correlated equilibria can emerge in a decentralized way through evolutionary or learning dynamics (23)(24)(25)(26)(27)(28)(29)(30)(31)(32). The first strand in this body starts with the seminal paper of Selten (23) who proved that evolutionarily stable strategies conditional on cues in the world have to be pure strategies.…”

Section: Significancementioning

confidence: 99%

Evolution of social norms and correlated equilibria

Morsky

Akçay

2019

Proc. Natl. Acad. Sci. U.S.A.

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Social norms regulate and coordinate most aspects of human social life, yet they emerge and change as a result of individual behaviors, beliefs, and expectations. A satisfactory account for the evolutionary dynamics of social norms, therefore, has to link individual beliefs and expectations to population-level dynamics, where individual norms change according to their consequences for individuals. Here, we present a model of evolutionary dynamics of social norms that encompasses this objective and addresses the emergence of social norms. In this model, a norm is a set of behavioral prescriptions and a set of environmental descriptions that describe the expected behaviors of those with whom the norm holder will interact. These prescriptions and descriptions are functions of exogenous environmental events. These events have no intrinsic meaning or effect on the payoffs to individuals, yet beliefs/superstitions regarding them can effectuate coordination. Although a norm’s prescriptions and descriptions are dependent on one another, we show how they emerge from random accumulations of beliefs. We categorize the space of social norms into several natural classes and study the evolutionary competition between these classes of norms. We apply our model to the Game of Chicken and the Nash Bargaining Game. Furthermore, we show how the space of norms and evolutionary stability are dependent on the correlation structure of the environment and under which such correlation structures social dilemmas can be ameliorated or exacerbated.

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Section: Significancementioning

confidence: 99%

Evolution of social norms and correlated equilibria

Morsky

Akçay

2019

Proc. Natl. Acad. Sci. U.S.A.

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“…When a probability distribution over recommended action profiles creates a correlation between the recommendations to different players, it can sometimes be strictly better to obey what the device signaled to a player than to choose any alternative. Strictness lies at the heart of the concept of evolutionary stability, and along these lines, it has been shown that a strict correlated equilibrium strategy is evolutionarily stable [1,2]. I apply this fact to rock-paper-scissors and show that there is an evolutionarily stable strategy, consisting of a strict correlated equilibrium when the game has three players who earn a payoff from three-way ties that exceeds the average of a winning-payoff and a losing-payoff.…”

Section: Introductionmentioning

confidence: 92%

Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors

Grant

2023

Games

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In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.

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“…By contrast, both the stable and (nongeneric) unstable outcomes of introspective equilibrium deliver intuitive comparative statics (Proposition 1(d)). 42 Other adaptive models that predict miscoordination are silent on which outcome is selected (e.g., Foster and Vohra, 1997;Fudenberg and Levine, 1999;Hart and Mas-Colell, 2000;Hart, 2005;Metzger, 2018). These models therefore cannot address the key question of how strategic behavior and the value change when payoffs are varied.…”

Section: Relation To Adaptive Dynamicsmentioning

confidence: 99%

The Value of a Coordination Game

Kets¹,

Kager²,

Sandroni³

2021

Preprint

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The value of a game is the payoff a player can expect (ex ante) from playing the game. Understanding how the value changes with economic primitives is critical for policy design and welfare. However, for games with multiple equilibria, the value is difficult to determine. We therefore develop a new theory of the value of coordination games. The theory delivers testable comparative statics on the value and delivers novel insights relevant to policy design. For example, policies that shift behavior in the desired direction can make everyone worse off, and policies that increase everyone's payoffs can reduce welfare.

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Evolution and correlated equilibrium

Cited by 9 publications

References 18 publications

Evolution of social norms and correlated equilibria

Evolution of social norms and correlated equilibria

Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors

The Value of a Coordination Game

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