Question

In: Economics

Consider the situation below where two players are engaged in a game of chicken. In this...

Consider the situation below where two players are engaged in a game of chicken. In this game, both players drive their cars at each other and each player can choose to either drive straight, or swerve. If both cars drive straight, they will crash in to one another, causing damage to both vehicles. If one car goes straight, while the other swerves, the player that swerves is a "chicken" while the other player is respected for their bravery. If both players swerve, they are both considered "chickens". The players

are depicted below:

                                    Player 2

                                    Straight Swerve

Player 1 Straight     -5,-5         5,-2

                 Swerve     -2,5          -1,-1

a) Would a player rather crash their car into the other player (Both players choose

straight) or swerve and be branded as a "chicken"? How do you know this?

b) Find all Nash equilibria of the simultaneous move game

For Parts (c)-(e), suppose now that Player 1 could choose to drive straight or swerve, ,then Player 2 could respond to Player 1.s action.

1

c) Depict the extensive form of the sequential game.

d) Find all subgame perfect Nash equilibria of the sequential move game.

e) Compare your results in parts (b) and (d). Why do they differ?

Solutions

Expert Solution

e)

In this case the difference between (b) and (d) results is in (d) any one player got to move first. Then he takes his moves judging the moves of other player and choosing optimal payoff. Thus, the player moves first get highest payoff and the game has one NE. In case of (b) both of them move simultaneously and end up playing some probable moves of both and the game turn towards mixed strategy equilibrium.

Rahul Sunny answered 2 years ago
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