Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature

Simon Weidenholzer
2010 Games  
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more » ... bedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: We survey the recent literature on coordination games, where there is a conflict between risk dominance and payoff dominance. Our main focus is on models of local interactions, where players only interact with small subsets of the overall population rather than with society as a whole. We use Ellison's [1] Radius-Coradius Theorem to present prominent results on local interactions. Amongst others, we discuss best reply learning in a global-and in a local-interaction framework and best reply learning in multiple location models and in a network formation context. Further, we discuss imitation learning in a localand in a global-interactions setting. 552 with use than by the overall distribution of technology standards. Similarly, it is also reasonable to think that e.g., family members, neighbors, or business partners interact more often with each other than with anybody chosen randomly from the entire population. In such situations we speak of "local interactions". Further, note that in many situations people can benefit from coordinating on the same action. Typical examples include common technology standards, as e.g. the aforementioned choice of a text editing programme, common legal standards, as e.g., driving on the left versus the right side of the road, or common social norms, as e.g., the affirmative versus the disapproving meaning of shaking one's head in different parts of the world. These situations give rise to coordination games. In these coordination games the problem of equilibrium selection is probably most evident, as classical game theory can not provide an answer to the question which convention or equilibrium will eventually arise. The reason for this shortcoming is that no equilibrium refinement concept can discard a strict Nash equilibrium. This paper aims at providing a detailed overview of the answers models of local interaction can give to the question which equilibrium will be adopted in the long run. 1 We further provide insight on the main technical tools employed, the main forces at work, and the most prominent results of the game theoretic literature on coordination games under local interactions. Jackson [2], Goyal [3], and Vega-Redondo [4] also provide surveys on the topic of networks and local interactions. These authors consider economics and networks in general, whereas we almost entirely concentrate on the coordination games under local interactions. This allows us to give a more detailed picture of the literature within this particular area. Starting with the seminal works of Foster and Young [5], Kandori, Mailath, and Rob [6], henceforth KMR, and Young [7] a growing literature on equilibrium selection in models of bounded rationality has evolved over the past two decades. Typically, in these models a finite set of players is assumed to be pairwise matched according to some matching rule and each pair plays a coordination game against each other in discrete time. Rather than assuming that players are fully rational, these models postulate a certain degree of bounded rationality on the side of the players: Instead of reasoning about other players' future behavior players just use simple adjustment rules. This survey concentrates on two prominent dynamic adjustment rules used in these models of bounded rationality. 2 The first is based on myopic best reply, as e.g., in Ellison [1, 9] or Kandori and Rob [10, 11] . Under myopic best response learning players play a best response to the current strategies of their opponents. This is meant to capture the idea that players cannot forecast what their opponents will do and, hence, react to the current distribution of play. The second model dynamic is imitative, as e.g., in KMR, [12], Eshel, Samuelson, and Shaked [13], 15] . Under imitation rules players merely mimic the most successful behavior they observe. While myopic best reponse assumes a certain degree of rationality and knowledge of the underlying game, imitation is an even more "boundedly rational" rule of thumb and can be justified under lack of information or in the presence of decision costs. Both, myopic best reply and imitation rules, give rise to an adjustment process which depends only on the distribution of play in the previous period, i.e., a Markov process. For coordination games this process will (after some time) converge to a convention, i.e., a state where all players use the same strategy. Further, once the process has settled down at a convention it will stay there forever. To which particular 1 Of course, the articles presented in this survey just reflect a selection of the literature within this field. 2 See Sobel [8] for a review of various learning theories used in models of bounded rationality. 5 See Alós-Ferrer and Schlag [36] for a detailed survey on imitation learning. 6 See also Kandori and Rob [10,11] for variations and applications of the basic model.
doi:10.3390/g1040551 fatcat:3d7zmcycx5bjzoc3fbdgkbpwqq