Game Theory

Summary

^*Game-theoretic models provide a substantial amount of generalization of the basic notions of mathematical economics, such as core, equilibria, saddle points and intertempolar optimum. In this chapter, we deal with different models in game theory. We start with noncooperative games which lead to the notion of “Nash equilibria”. Then we pass to cooperative games, for which we can define the notion of core. After that we consider random games with a continuum of players. For such games, we show the existence of Cournot–Nash equilibria. We also consider Bayesian games stochastic 2-player, and zero-sum games. Finally, using the notion of ε-subdifferential of convex functions, we prove the existence of approximate Nash equilibria for noncooperative games.