We construct and study the transition probability matrix of evolutionary games in which the number of players is finite (and relatively small) of such games. We use a simplified version of the population games studied by Sandholm. After laying out a general framework we concentrate on specific examples, involving the Iterated Prisoner's Dilemma, the Iterated Stag Hunt, and the Rock-Paper-Scissors game. Also we consider several revision protocols: Best Response, Pairwise Comparison, Pairwise Proportional Comparison etc. For each of these we explicitly construct the MC transition probability matrix and study its properties.

翻译：我们构建并研究了玩家数量有限（且相对较少）的演化博弈的转移概率矩阵。我们采用了Sandholm所研究的群体博弈的一个简化版本。在建立一般性框架后，我们专注于具体示例，包括迭代囚徒困境、迭代猎鹿博弈以及石头-剪刀-布博弈。同时，我们考虑了多种修订协议：最佳响应、成对比较、成对比例比较等。针对每一种情况，我们明确构建了马尔可夫链转移概率矩阵并研究了其性质。