An “Ethical” Game-Theoretic Solution Concept for Two-Player Perfect-Information Games

Abstract

The standard solution concept for perfect-information extensive form games is subgame perfect Nash equilibrium. However, humans do not always play according to a subgame perfect Nash equilibrium, especially in games where it is possible for all the players to obtain much higher payoffs if they place some trust in each other (and this trust is not violated). In this paper, we introduce a new solution concept for two-player perfect-information games that attempts to model this type of trusting behavior (together with the ethical behavior of not violating that trust). The concept takes subgame perfect equilibrium as a starting point, but then repeatedly resolves the game based on the players being able to trust each other. We give two distinct algorithmic definitions of the concept and show that they are equivalent. Finally, we give a fast implementation of one of the algorithms for solving the game, and show that it runs in time O (n logn + nh log(n /h )).