Stubborn Learning

Abstract

The paper studies a specific reinforcement learning rule in two-player games when each player faces a unidimensional strategy set. The essential feature of the rule is that a player keeps on incrementing her strategy in the same direction if and only if her utility increases. The paper concentrates on games on the square [0; 1] x [0; 1] with bilinear payoff functions such as the mixed extensions of 2 x 2 games. It studies the behavior of the system in the interior as well as on the borders of the strategy space. It precisely exhibits the trajectories of the system and the asymptotic states for symmetric, zero-sum, and twin games.