Learning TOMs: Towards Non-Myopic Equilibria

In contrast to classical game theoretic analysis of simultaneous and sequential play in bimatrix games, Steven Brams has proposed an alternative framework called the Theory of Moves (TOM) where players can choose their initial actions and then, in alternating turns, decide to shift or not from its current action. A backward induction process is used to determine a non-myopic action and equilibrium is reached when an agent, on its turn to move, decides to not change its current action. Brams claims that the TOM framework captures the dynamics of a wide range of real-life non-cooperative negotiations ranging over political, historical, and religious disputes. We believe that his analysis is weakened by the assumption that a player has perfect knowledge of the opponent’s payoff. We present a learning approach by which TOM players can learn to converge to Non-Myopic Equilibria (NME) without prior knowledge of its opponent’s preferences and by inducing them from past choices made by the opponent. We present experimental results from all structurally distinct 2-by-2 games without a common preferred outcome showing convergence of our proposed learning player to NMEs. We also discuss the relation between equilibriums in sequential games and NMEs of TOM.