Finite Extensive Form Games

Most games derived from economic or political situations have in common with most parlor games (like card games and board games) that they are not ‘one-shot’: players move sequentially, and one and the same player may move more often than once. Such games are best described by drawing a decision tree which tells us whose move it is and what a player’s information is when that player has to make a move.

In this chapter these so-called ‘games in extensive form’ are studied. Attention here is restricted to games with finitely many players (usually two), finitely many decision moments and finitely many moves. See Sect. 1.3.3 for a few examples. We also assume that each player has ‘complete information’, which – formally – boils down to either there being no chance move in the game or, if a chance move occurs, each player becoming informed about the outcome of that chance move. This excludes, for instance, the game of entry deterrence with incomplete information in Sect. 1.3.3: for the analysis of games with incomplete information see Chap. 5. Chapter 14 extends the analysis of the present and the next chapter.

The first section of this chapter introduces games in extensive form. In order to avoid a load of cumbersome notation the treatment will be somewhat informal but – hopefully – not imprecise. In Sect. 4.2 we define strategies and the ‘strategic form’ of a game: the definition of Nash equilibrium for extensive form games is then practically implied. The focus in this chapter is on pure Nash equilibrium.

In the third section the concept of Nash equilibrium is refined by considering subgame perfection (first introduced in [117] and [118]) and backward induction. A further important refinement, called ‘perfect Bayesian equilibrium’, is treated in the fourth section.