Sequential games as stochastic processes

This paper examines the stochastic processes generated by sequential games that involve repeated play of a specific game. Such sequential games are viewed as adaptive decision-making processes over time wherein each player updates his “state” after every play. This revision may involve one's strategy or one's prior distribution on the competitor's strategies. It is shown that results from the theory of discrete time Markov processes can be applied to gain insight into the asymptotic behavior of the game. This is illustrated with a duopoly game in economics.