A systematic process for evaluating structured perfect Bayesian equilibria in dynamic games with asymmetric information
A systematic process for evaluating structured perfect Bayesian equilibria in dynamic games with asymmetric information
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DOI：
10.1109/acc.2016.7525439
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
Deepanshu Vasal;A. Anastasopoulos
中科院分区：
文献类型：
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作者：
Deepanshu Vasal;A. Anastasopoulos
我们考虑一个有限时域动态博弈，N个自私的玩家私下观察他们的类型，并采取行动，这是公开观察。参与者的类型演化为条件独立的马尔可夫过程，条件是他们当前的行动。他们的行为和类型共同决定了他们的即时回报。由于每个参与者都有不同的信息集，这就形成了一个信息不对称的动态博弈，目前还没有已知的方法来找到这种博弈的完美贝叶斯均衡（PBE）。在本文中，我们提供了一个两步向前向后递归算法，找到一类PBE使用的信念状态的基础上共同的信息的球员。我们将这种均衡称为结构化贝叶斯完美均衡（SPBE）。该算法的后向递归部分定义了一个平衡生成函数。在向后递归的每个阶段涉及解决一个不动点方程的概率单形空间的每一个可能的信念类型。使用这个函数，均衡策略和信念是通过向前递归定义的。我们提供了一个公共产品的例子来证明的方法。
We consider a finite horizon dynamic game with N selfish players who observe their types privately and take actions, which are publicly observed. Players' types evolve as conditionally independent Markov processes, conditioned on their current actions. Their actions and types jointly determine their instantaneous rewards. Since each player has a different information set, this forms a dynamic game with asymmetric information and there is no known methodology to find perfect Bayesian equilibria (PBE) for such games in general. In this paper, we provide a two-step backward-forward recursive algorithm to find a class of PBE using a belief state based on common information of the players. We refer to such equilibria as structured Bayesian perfect equilibria (SPBE). The backward recursive part of this algorithm defines an equilibrium generating function. Each period in the backward recursion involves solving a fixed point equation on the space of probability simplexes for every possible belief on types. Using this function, equilibrium strategies and beliefs are defined through a forward recursion. We provide a public goods example to demonstrate the methodology.