A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.

Suppose the n × n matrix A gives the payoffs for some evolutionary game, and its entries are the values of independent, identically distributed, continuous random variables. The distribution of the pattern of evolutionarily stable strategies for A will depend, if n ≧ 3, on this underlying distribution. A fairly complete picture for n = 3 is found, and some results are obtained for n ≧ 4.

A definition of ESS (evolutionarily stable strategy) is suggested for games in which there are two types of player, each with its own set of strategies, and the fitness of any strategy depends upon the strategy mix, of both types, in the population as a whole. We check that the standard ESS results hold for this definition and discuss a mate-desertion model which has appeared in the literature in which the two types are male and female.