Games that appear to be independent, involving none of the same players, may be related by emotions of reciprocity between the members of the same groups. In the real world, individuals are members of groups and want to reward or punish those groups whose members have been kind or unkind to members of their own. In this paper, we extend Dufwenberg and Kirchsteiger's model of sequential reciprocity (Games Econ Behav 47(2): 2004) to groups of individuals and define a new ''sequential group reciprocity equilibrium'' for which we prove its existence. We study the case of two games with two players in each game, where each player belongs to the same group as a player in the other game. We show that when the payoffs of one game are much higher than the payoffs of the other, the outcome of the game with higher payoffs determines the outcome of the other game. We also find that when the payoffs are very asymmetric, the outcome where the sum of the payoffs is maximized is a sequential group reciprocity equilibrium.
With their Sequential Reciprocity Equilibrium (SRE), Dufwenberg and Kirchsteiger (2004) developed a solution concept that incorporates reciprocity in sequential games. A SRE evaluates the kindness or unkindness of a strategy based purely on the actions it prescribes at the equilibrium path. However, given that it is not the objective of the SRE to evaluate threats and promises, it does not consider the actions outside the equilibrium path, where threats and promises are included. This article develops a new solution concept, Fair Threat Equilibria, which main objective is to give more reasonable predictions when threats and promises are included.
In this paper we extend Rabin's (1993) model of fairness equilibria to groups of individuals and define a new solution concept we name "group-fairness equilibria." We model two games with two players, where each player in each game belongs to one of two groups. We analyze how the outcome of one game may affect the outcome of the other and how the existence of one individual with a particular grudge or liking towards the player she is playing with can impact the outcome of both games. We analyze some applications of our model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.