Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples
给出了两个贴现随机博弈的例子，每个例子都有连续状态、有限玩家和行动，但不存在平稳均衡，其中第一个例子甚至没有平稳近似均衡或马尔可夫均衡。
We present two examples of discounted stochastic games, each with a continuum of states, finitely many players, and actions, that possess no stationary equilibria. The first example has deterministic transitions—an assumption undertaken in most of the early applications of dynamics games in economics—and perfect information, and does not possess even stationary approximate equilibria or Markovian equilibria. The second example satisfies, in addition to stronger regularity assumptions, that all transitions are absolutely continuous with respect to a fixed measure—an assumption that has been widely used in more recent economic applications. This assumption has been undertaken in several positive results on the existence of stationary equilibria in special cases, and in particular, guarantees the existence of stationary approximate equilibria.