A Simple Sequential Social Dilemma Game
Ryoichi Takatsuka, Koichi Moriyama, Tohgoroh Matsui, Atsuko Mutoh, Kosuke Shima, Nobuhiro Inuzuka · 2023
A social dilemma in game theory models the situation of agents who do not share a same objective in a multi-agent environment. However, since it ignores various aspects of real social dilemmas, a temporally extended sequential social dilemma (SSD) was proposed. SSD is an extension of Markov game and supposes two sets of policies, i.e., cooperative and defective. It was originally examined in two 2-dimensional grid games, but they were too complicated because we needed simulations to know what policies are in the above two sets. Therefore, we propose a new game that is SSD but has (trivial) cooperative and defective policies. It is a 1-dimensional grid game with two players. We first derive conditions of payoffs the players receive satisfying the constraints of social dilemmas and Markov games. Furthermore, we consider other payoffs that intentionally ignore the Markov property due to the nature of sequential decisions. We see the results of experiments in this game with two tabular Q-learning agents and discuss the learned policies in the game.