 The initial population in an EPD can be represented by a set of pairs \(\{(p_1, s_1), \ldots (p_n, s_n)\}\) where \(p_1 \ldots p_n\) are the proportions of the population playing strategies \(\bs_1, \ldots, \bs_n\), respectively. The description of EPDs given above does not specify exactly how the population of strategies is to be reconstituted after each IPD. The usual assumption, and the most sensible one for biological applications, is that a score in any round indicates the relative number of “offspring” in the next. It is assumed that the size of the entire population stays fixed, so that births of more successful strategies are exactly offset by deaths of less successful ones. This amounts to the condition that the proportion \(p_i^*\) of each strategy \(s_i\) in the successor population is determined by the equation \(p_i^* = p_i(V_i / V)\), where \(V_i\) is the score of \(s_i\) in the previous round and \(V\) is the average of all scores in the population. Thus every strategy that scores above the population average will increase in number and every one that scores below the average will decrease. This kind of evolution is referred to as “replicator dynamics” or evolution according to the “proportional fitness” rule. Other rules of evolution are possible. Bendor and Swistak argue that, for social applications, it makes more sense to think of the players as switching from one strategy to another rather than as coming into and of existence. Since rational players would presumably switch only to strategies that received the highest payoff in previous rounds, only the highest scoring strategies would increase in numbers. Batali and Kitcher employ a dynamics in which lowest scoring strategies are replaced by strategies that mix characteristics of the highest scoring strategies. A variety of other possible evolutionary dynamics are described and compared in Kuhn 2004. Discussion here, however, will primarily concern EPDs with the proportional fitness rule.