What Information Theory Says about Bounded Rational Best Response

Probability Collectives (PC) provides the information-theoretic extension of conventional full-rationality game theory to bounded rational games. Here an explicit solution to the equations giving the bounded rationality equilibrium of a game is presented. Then PC is used to investigate games in which the players use bounded rational best-response strategies. Next it is shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. It is then shown that for team (shared-payoff) games, this variant of replicator dynamics is identical to Newton-Raphson iterative optimization of the shared utility function.