论文标题
在不确定性下的流失战争中的混合策略平衡
Mixed-Strategy Equilibria in the War of Attrition under Uncertainty
论文作者
论文摘要
我们研究了两人连续时间的非零和停止游戏的通用家族，该游戏模拟了一场消耗战争，其中依赖于同质线性扩散的对称信息和随机收益。我们首先表明，任何对玩家$ i $的马尔可夫混合策略都可以由一对$（μ^i，s^i）$表示，其中$μ^i $是代表播放器$ i $停止强度的状态空间的措施，而$ s^i $是player $ i $ i $ coperable afterbigaligation $ 1 $ $ 1 $ $ $ $ $ $ $ $ $ $ $ $ $。然后，我们证明，如果玩家是不对称的，那么，在所有混合策略马尔可夫完美的平衡中，这些度量$μ^i $必须基本上是离散的，并且我们通过玩家的平衡价值功能所满足的各种系统来表征任何此类均衡。该结果与文献相反，文献侧重于纯净的平衡，或者在对称参与者的情况下，在混合策略均衡方面，绝对连续停止强度。我们通过在不确定性下重新审视双向垄断中的退出模型来说明这一结果，并在均衡路径上表现出混合构成平衡，尽管公司具有不同的清算值。
We study a generic family of two-player continuous-time nonzero-sum stopping games modeling a war of attrition with symmetric information and stochastic payoffs that depend on an homogeneous linear diffusion. We first show that any Markovian mixed strategy for player $i$ can be represented by a pair $(μ^i,S^i)$, where $μ^i$ is a measure over the state space representing player $i$'s stopping intensity, and $S^i$ is a subset of the state space over which player $i$ stops with probability $1$. We then prove that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, the measures $μ^i$ have to be essentially discrete, and we characterize any such equilibrium through a variational system satisfied by the players' equilibrium value functions. This result contrasts with the literature, which focuses on pure-strategy equilibria, or, in the case of symmetric players, on mixed-strategy equilibria with absolutely continuous stopping intensities. We illustrate this result by revisiting the model of exit in a duopoly under uncertainty, and exhibit a mixed-strategy equilibrium in which attrition takes place on the equilibrium path though firms have different liquidation values.
