Abstract
Drawing a diagram can make people find Nash equilibria of two-players strategic form games. The diagram consists of nodes, directed edges, and undirected edges. Nodes represent outcomes of a game, and edges represent responses of players against strategies of their opponents. Pure Nash equilibria are represented as nodes without outgoing directed edges. A mixed Nash equilibrium is represented as a node on an intersection of two undirected edges that are synthesized from directed edges. In this article, I describe a way to find such equilibria by using the diagram. Since games are represented by directed edges, games can be specified by pairwise comparisons. Then the preference of strategies may not be any longer a total order. I also provide two games in which there are cycles of preference in a player’s choices. One game has a mixed Nash equilibrium, and another does not have.
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