Abstract:

For population games with uncertain parameters, a weak NS equilibrium is firstly proposed based on the fact that switching strategies cause corresponding costs. The underlying idea of a weak NS equilibrium is that the agents' new gained payoffs from strategy switch are less than or equal to the increased cost for a given uncertainty parameter; simultaneously, each population can not obtain strictly poor net profits under uncertain parameters, thus each agent in every population has no motivation to unilaterally change the current strategy and then they achieve a weak NS equilibrium. Secondly, the existence of weak NS equilibria is proven by Kakutani's fixed point theorem. Thirdly, by constructing an abstract rational function, a corresponding bounded rational model is established, and it is shown structural stability implying robustness. Therefore, the generic stability of weak NS equilibria for population games with uncertain parameters under bounded rationality is also obtained when the net profit function is perturbed. Finally, an example is illustrated the correctness of the above results.

Key words: Population games, Weak NS equilibria, Bounded rationality, Uncertainty, Structural stability