Principles of Game Theory

Abstract

Consider the following sequential game (Fig. 11.1).

Player 1 has the strategies {No entry, Entry}, while player 2 has the strategies {Fight, Concede}.

• 1. (No entry, Fight) is a Nash equilibrium.

• 2. (No entry, Concede) is a Nash equilibrium.

• 3. (Entry, Fight) is a Nash equilibrium.

• 4. (Entry, Concede) is a Nash equilibrium.

Consider the following game in normal form (Table 11.1).

• 1. Strategy U is dominant for player 1.

• 2. $(D,R)$ is a Nash equilibrium in this game.

• 3. $(U,L)$ is a Nash equilibrium in this game.

• 4. $(D,R)$ is an equilibrium in dominant strategies in this game.

Consider the following game in extensive form (Fig. 11.2).

• 1. The strategy sets of the players are $S_{1}=\{Y,X\}$ for player 1 and $S_{2}=\{O,U\}$ for player 2.

• 2. In order to maximize his utility, player 2 will never choose O.

• 3. This is a simultaneous-move game.

• 4. The following game in normal form (Table 11.2) has the same Nash equilibrium/equilibria as the former extensive-form game.