Chapter summary

In this chapter we present the model of strategic-form games. A game in strategic form consists of a set of players, a strategy set for each player, and an outcome to each vector of strategies, which is usually given by the vector of utilities the players enjoy from the outcome. The strategic-form description ignores dynamic aspects of the game, such as the order of the moves by the players, chance moves, and the informational structure of the game.

The goal of the theory is to suggest which strategies are more likely to be played by the players, or to recommend to players which strategy to implement (or not to implement). We present several concepts that allow one to achieve these goals. The first concept introduced is domination (strict or weak), which provides a partial ordering of strategies of the same player; it tells when one strategy is “better” than another strategy. Under the hypothesis that it is commonly known that “rational” players do not implement a dominated strategy we can then introduce the process of iterated elimination of dominated strategies, also called rationalizability. In this process, dominated strategies are successively eliminated from the game, thereby simplifying it. We go on to introduce the notion of stability, captured by the concept of Nash equilibrium, and the notion of security, captured by the concept of the maxmin value and maxmin strategies. The important class of two-player zero-sum games is introduced along with its solution called the value (or the minmax value).