Static Games * Article Outline Glossary and Notation

Player A participant in a game. Action set The set of actions that a player may choose. Action profile A list of actions, one for each player. Payoff The utility a player obtains from a given action profile. 1 Definition of the subject and its importance Game theory concerns the interaction of decision makers. This interaction is modeled by means of games. There are various approaches to constructing games. One approach is to focus on the possible outcomes of the decision-makers' interaction by abstracting from the actions or decisions that may lead to these outcomes. The main tool used to implement this approach is the cooperative game. Another approach is to focus on the actions that the decision-makers can take, the main tool being the non-cooperative game. Within this approach, strategic interactions are modeled in two ways. One is by means of dynamic, or extensive form games, and the other is by means of static, or strategic games. Dynamic games stress the sequentiality of the various decisions that agents can make. An essential component of a dynamic game is the description of who moves first, who moves second, etc. Static games, on the other hand, abstract from the sequentiality of the possible moves, and 2 model interactions as simultaneous decisions, where the decisions may well be complicated plans of actions that dictate different moves for different situations that may arise. All extensive form games can be modeled as static games, and all strategic form games can be modeled as extensive form games. But some situations may be more conveniently modeled as one or the other kind of game. This chapter reviews the main ideas and results related to static games, as well as some interesting relationships that connect equilibrium concepts with the idea of rationality. The objective is to introduce the reader to the area of static games and to stimulate his interest for further knowledge of game theory in general. For a comprehensive exposition of some results not covered in this chapter, the reader is referred to the many excellent textbooks available on game theory. Although the definition of a static game is a very simple one, static games are a very flexible model which allows us to analyze many different situations. In particular, one can use them to analyze strategic interactions that involve either common interests or diametrically opposed interests. Similarly, one can also use static games to …