Learning to Play Nash Equilibrium in Chaotic Dynamics - Mendes, V.; Mendes, D. A. (ICDEA 2021, 2021)
In a bounded rational game where players cannot be as super-rational as in Kalai and Leher (1993), are there simple adaptive heuristics or rules that can be used to secure convergence to Nash equilibria? Robinson (1951) showed that for certain types of games, such rules exist. Nevertheless, the types of games to which they apply are pretty restric- tive. Following Hart and Mas-Colell (2003) terminology, are there games with uncoupled deterministic dynamics in discrete time that converge to Nash equilibrium or not? Young (2009) argues that if an adaptive learning rule follows three conditions { (i) it is uncoupled, (ii) each player's choice of action depends solely on the frequency distribution of past play, and (iii) each player's choice of action, conditional on the state, is deterministic { no such rule leads the players' behavior to converge to the Nash equilibrium. This paper shows that there are simple adaptive rules that secure convergence, in fact, fast convergence, in a fully deterministic and uncoupled game. We use the Cournot model with nonlinear costs and incomplete information for this purpose and illustrate that this convergence can be achieved without any coordination of the players' actions.