Breeding hybrid strategies: optimal behaviour for oligopolists

Abstract

Oligopolistic pricing decisions-in which the choice variable is not dichotomous as in the simple prisoner's dilemma but continuous-have been modeled as a generalized prisoner's dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtain an effective generalization of Rapoport's Tit for Tat for the three-person repeated game. Holland's genetic algorithm and Axelrod's representation of contingent strategies provide a means of generating new strategies in the computer, through machine learning, without outside submissions.

The paper discusses how findings from two-person tournaments can be extended to the GPD, in particular how the author's winning strategy in the Second MIT Competitive Strategy Tournament could be bettered. The paper provides insight into how oligopolistic pricing competitors can successfully compete, and underlines the importance of “niche” strategies, successful against a particular environment of competitors.

Bootstrapping, or breeding strategies against their peers, provides a means of examining whether “repetition leads to cooperation”: we show that it can, under certain conditions, for simple and extended two- and three-person GPD repeated games. The paper concludes with a discussion of the relationship between Selten's trembling-hand perfect equilibrium and Maynard Smith's evolutionarily stable strategies, with practical simulations of successful and unsuccessful “invasions” by new strategies.