Question

Game Theory: There are two games below. Players are American and United with planes with 96 seats or 64 seats. Solve both the simultaneous and sequential versions of the game. Explain how you got your answer.

American 96 4.1

Answer 1

A. Simultaneous game nash equilibrium= (UA,AMERICAN)= (64,64).

Reason- When UA chooses 96, American chooses 64. As (2>0)

When UA chooses 64, American chooses 64. As (4.1>3.1)

When American chooses 96, UA chooses 64. As (2>0)

When American chooses 64, UA chooses 64. As (4.1>3.1)

So the dominant strategy for both the parties is to choose 64. Hence nash equilibrium is (64,64)

Sequential game nash equilibrium =(64,64)

Reason-

Solve is using backward induction

Start from player UA's decision node.

Use subgame perfect nash equilibrium

UA prefers 64 seats in both Cases as payoff is higher (3.1>0) and (4.1>2)

So optimal payoff for UA are (2,3.1) & (4.1,4.1)

Out of the two choices, AA prefers (4.1,4.1) due to higher payoff.

So the path of play is AA selects 64 and UA selects 64.

So nash equilibrium is (64,64)