In this paper we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc indicating the preferred option for that player. Response graphs, and particularly their sink strongly connected components, play an important role in modern techniques in evolutionary game theory and multi-agent learning. We show that the response graph is a simple and well-motivated model of strategic interaction which captures many non-trivial properties of a game, despite not depending on cardinal payoffs. We characterise the games which share a response graph with a zero-sum or potential game respectively, and demonstrate a duality between these sets. This allows us to understand the influence of these properties on the response graph. The response graphs of Matching Pennies and Coordination are shown to play a key role in all two-player games: every non-iteratively-dominated strategy takes part in a subgame with these graph structures. As a corollary, any game sharing a response graph with both a zero-sum game and potential game must be dominance-solvable. Finally, we demonstrate our results on some larger games.

翻译：本文通过响应图分析两人博弈。响应图的节点为策略组合，若两个策略组合仅在一个博弈方的策略上不同，且弧线方向表示该博弈方的偏好选择，则两者之间存在弧线。响应图，特别是其汇强连通分量，在现代演化博弈论和多智能体学习中扮演重要角色。我们证明：响应图是一种简洁且动机明确的策略互动模型，虽不依赖基数收益，却能捕捉博弈的许多非平凡性质。我们刻画了分别与零和博弈或势博弈共享响应图的博弈类别，并展示这两类集合之间的对偶性，从而理解这些性质对响应图的影响。研究表明，匹配铜币博弈与协调博弈的响应图在所有两人博弈中起关键作用：每个非迭代占优策略都参与具有这些图结构的子博弈。作为推论，任何同时与零和博弈及势博弈共享响应图的博弈必为占优可解博弈。最后，我们在一些较大博弈中验证了所得结论。