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In this chapter we consider games of the following simple form: first the players simultaneously choose actions; then the players receive payoffs that depend on the combination of actions just chosen. Within the class of such static (or simultaneous–move) games, we restrict attention to games of complete information.
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That is, each player’s payoff function (the function that determines the player’s payoff from the combination of actions chosen by the players) is common knowledge among all the players. We consider dynamic (or sequential-move) games in Chapters 2 and 4, and games of incomplete information (games in which some player is…
In this chapter we introduce dynamic games. We again restrict attention to games with complete information (i.e., games in which the players’ payoff functions are common knowledge); see Chapter 3 for the introduction to games of incomplete information. In Section 2.1 we analyze dynamic games that have not only complete but also perfect information, by which we mean that at each move in the game the player with the move knows the full history of the play of the game thus far. In Sections 2.2 through 2.4 we consider games of complete but imperfect information: at some move the player…
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This chapter begins our study of games of incomplete information, also called Bayesian games. Recall that in a game of complete information the players’ payoff functions are common knowledge. In a game of incomplete information, in contrast, at least one player is uncertain about another player’s payoff function. One common example of a static game of incomplete information is a sealed–bid auction: each bidder knows his or her own valuation for the good being sold but does not know any other bidder’s valuation; bids are submitted in sealed envelopes, so the players’ moves can be thought of as simultaneous….
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In this chapter we introduce yet another equilibrium concept—perfect Bayesian equilibrium. This makes four equilibrium concepts in four chapters: Nash equilibrium in static games of complete information, subgame–perfect Nash equilibrium in dynamic games of complete information, Bayesian Nash equilibrium in static games of incomplete information, and perfect Bayesian equilibrium in dynamic games of incomplete information. It may seem that we invent a brand new equilibrium concept for each class of games we study, but in fact these equilibrium concepts are closely related. As we consider progressively richer games, we progressively strengthen the equilibrium concept, in order to rule…
