Adaptive Heuristics

Adaptive heuristics refer to simple behavioral rules that are directed toward payoff improvement but may be less than fully rational. The number and variety of such rules is virtually unlimited; here we shall survey several prominent examples drawn from psychology, computer science, statistics, and game theory. Of particular interest are the informational inputs required by different learning heuristics and the conditions under which they lead to equilibrium behavior when used by all the players in a game. The empirical validity of various learning procedures is treated elsewhere (see experimental game theory). One of the simplest learning heuristics is cumulative payoff matching, in which the subject plays actions next period with probabilities proportional to their cumulative payoffs to date. Specifically, consider a finite stage game G that is played infinitely often, where all payoffs are assumed to be strictly positive. Let aij(t) denote the cumulative payoff to player i over all those periods 0 ≤ t' ≤ t when he played action j, including some initial propensity aij(0) > 0. The cumulative payoff matching rule stipulates that in period t + 1, player i chooses action j with probability pij(t + 1) = aij(t)/∑kaik(t). (1)