be equal at every value of t. Dynamic formulation and evolutionarily stable strategy The unique evolutionarily stable strategy coincides with the symmetric Nash equilibrium. This follows from the fact that any ESS must be a Nash equilibrium and the fact that no pure persistence time can be an ESS. That no pure persistence time is an ESS can be demonstrated simply by considering a putative ESS bid of x, which will be beaten by a bid of x+. It has also been shown that even if the individuals can only play pure strategies, the time average of the strategy value of all individuals converges precisely to the calculated ESS. In such a setting, one can observe a cyclic behavior of the competing individuals. See also Evolutionary game theory Bishop-Cannings theorem Rubinstein bargaining model Hawk-dove game Dollar auction Attrition warfare References Non-cooperative games