Perfect information games where each player acts only once
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Perfect information games where each player acts only once Kutay Cingiz1 · János Flesch2 · P. Jean-Jacques3
· Arkadi Predtetchinski3
Received: 26 February 2018 / Accepted: 17 May 2019 © The Author(s) 2019
Abstract We study perfect information games played by an infinite sequence of players, each acting only once in the course of the game. We introduce a class of frequency-based minority games and show that these games have no subgame perfect -equilibrium for any sufficiently small. Furthermore, we present a number of sufficient conditions to guarantee existence of subgame perfect -equilibrium. Keywords Minority games · Subgame perfect -equilibria · Upper semicontinuous functions · Infinitely many players JEL Classification C72 · C73 · D91
The authors would like to thank Nate Eldredge for an early version of the proof of Theorem 3.3, Natalia Chernova for suggesting the use of coupling, and Abraham Neyman and Jérôme Renault for their valuable comments. We are also grateful to the Editor and two anonymous referees for their helpful questions and suggestions.
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P. Jean-Jacques [email protected] Kutay Cingiz [email protected] János Flesch [email protected] Arkadi Predtetchinski [email protected]
1
Agricultural Economics and Rural Policy Group, Wageningen University, Hollandseweg 1, 6706 KN Wageningen, The Netherlands
2
Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
3
Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
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K. Cingiz et al.
1 Introduction We study perfect information games with infinitely many players where each player is active only once. Our emphasis is on the question of existence of subgame perfect equilibria.1 The references below testify to the increasing attention that the concept has been receiving in the recent game-theoretic literature. In addition to the challenging existence issue, the paper reaches out to a large area of research on topics such as minority games, time-inconsistent preferences, and intergenerational games. The contribution of the paper is twofold. The first contribution is to introduce a class of so-called frequency-based minority games. These are games where a player benefits from choosing an action that is less popular among the players. Minority games have been used to model a variety of different phenomena ranging from congestion, downloading in P2P networks, market entry, to speculative behavior in financial markets. For an extensive list of related works, we refer to Renault et al. (2007) and Renault et al. (2008). Unlike much of the work on minority games that focuses on the setup with simultaneous moves, here we consider sequential games of perfect information. In more detail, we consider perfect information games where each player becomes active exactly once in the course of the game and has a choice between two actions. One is a risky action: It gives a high payoff if a minority of
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