Workbook for Principles of Microeconomics pp 173-195 | Cite as

# Principles of Game Theory

## Abstract

Consider the following sequential game (Fig. 11.1).

- 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.