Autocratic strategies for infinitely iterated multiplayer social dilemma games

Abstract

Abstract In this work, we present results on autocratic strategies in infinitely repeated multiplayer games. Extending the previously developed theory for two-player games, we formulate necessary conditions for the existence of autocratic strategies in a standard multiplayer social dilemma game, namely the public goods game. The infinitely repeated game is designed with a discount factor that reduces the values of the future payoffs. The contribution of this work is an adaptation of existing theory on autocratic strategies to multiplayer games with arbitrary action spaces. We first show the existence of an autocratic strategy that uses a finite set of points from a continuous action space. Then, using a strategy concentrated on two points of the continuous interval representing the autocrat’s available actions, we show the necessary conditions for the existence of autocratic strategies in the context of the public goods game.