We prove for a large class of stochastic games with discontinuous payoffs, a stationary Markov perfect equilibrium exists under the condition of “continuation payoff security.” This condition is easy to verify and holds in many economic games. Roughly, a game belongs to this class if for any action/state profiles and continuation payoff, a player can identify another action at the current stage with the payoff not much worse than her current one, even if other players perturb actions slightly. As an illustrative application of the equilibrium existence result, we provide a stochastic dynamic oligopoly model of firm entry, exit, and price competitions.

我们证明了对于一大类具有不连续收益的随机博弈，在“持续收益安全”的条件下存在平稳的马尔可夫完美均衡。这个条件很容易验证并在许多经济游戏中成立。粗略地说，如果对于任何动作/状态配置文件和持续收益，玩家可以识别当前阶段的另一个动作，其收益不会比她当前的差多少，即使其他玩家稍微干扰动作，游戏也属于这一类。作为均衡存在结果的说明性应用，我们提供了企业进入、退出和价格竞争的随机动态寡头模型。