Abstract
Axelrod's The Evolution of Cooperation (1984) asserts, both from results of computer tournaments he organized and from a mathematical analysis of a model he constructed, that Tit-for-Tat is a powerful strategy. However, the conceptual scheme on the basis of which he computed the expected value has some theoretical flaws. The present paper attempts to re-formulate his conceptual scheme by the introduction of the notion of ‘inbreeding bias’ which is now nicely treated in literature of social networks, and by dropping the idea of ‘discount parameter’ which we see does not fit into the problems of collective stability of a certain strategy. We find that Tit-for-Tat remains somewhat strong under our re-formulation, but is so only under some restricted conditions.
