Global games and equilibrium selection

Global games and equilibrium selection

1990 | Carlsson, H.; van Damme, E.E.C.
**Summary:** This paper presents a framework for analyzing equilibrium selection in games with incomplete information, known as "global games." The authors consider a class of games where the actual payoff structure is determined by a random draw from a given set of games, and each player observes the selected game with some noise. The key result is that, in such games, players' behavior under vanishing noise leads them to conform to the risk dominance criterion introduced by Harsanyi and Selten. For 2x2 games, this implies that players will coordinate on the risk dominant equilibrium when uncertainty is sufficiently large. The paper shows that in a global game with vanishing noise, players' strategies are determined by their beliefs about the underlying game structure and the noisy observations. The authors demonstrate that the risk dominance criterion can be derived through repeated elimination of dominated strategies in the global game. This approach allows for the identification of unique equilibria in many 2x2 games with two strict Nash equilibria. The paper also discusses the implications of this result for the broader literature on game theory, particularly in relation to Harsanyi's games with randomly disturbed payoffs. It highlights that the proposed framework provides a novel way to eliminate strict equilibria and leads to unique solutions in many cases. The analysis is supported by examples and mathematical proofs, showing that the risk dominance criterion is robust under certain conditions. The paper concludes that the global game framework offers a powerful tool for understanding equilibrium selection in games with incomplete information.**Summary:** This paper presents a framework for analyzing equilibrium selection in games with incomplete information, known as "global games." The authors consider a class of games where the actual payoff structure is determined by a random draw from a given set of games, and each player observes the selected game with some noise. The key result is that, in such games, players' behavior under vanishing noise leads them to conform to the risk dominance criterion introduced by Harsanyi and Selten. For 2x2 games, this implies that players will coordinate on the risk dominant equilibrium when uncertainty is sufficiently large. The paper shows that in a global game with vanishing noise, players' strategies are determined by their beliefs about the underlying game structure and the noisy observations. The authors demonstrate that the risk dominance criterion can be derived through repeated elimination of dominated strategies in the global game. This approach allows for the identification of unique equilibria in many 2x2 games with two strict Nash equilibria. The paper also discusses the implications of this result for the broader literature on game theory, particularly in relation to Harsanyi's games with randomly disturbed payoffs. It highlights that the proposed framework provides a novel way to eliminate strict equilibria and leads to unique solutions in many cases. The analysis is supported by examples and mathematical proofs, showing that the risk dominance criterion is robust under certain conditions. The paper concludes that the global game framework offers a powerful tool for understanding equilibrium selection in games with incomplete information.
Reach us at info@study.space