Question

Two companies are interdependent.

When Beta Company acts, it affects Gamma Industries.

Beta has two actions, A and B.

Gamma has two actions D and E.

The payoffs:

Beta | |||
---|---|---|---|

A | B | ||

Gamma | D | $30/ $10 | $16 / $20 |

E | $20/ $25 | $15/ $22 |

If Beta chooses A and Gamma chooses D then Beta gets $10 and Gamma gets $30.

If Beta chooses A and Gamma chooses E then Beta gets $25 and Gamma gets $20.

The other cells can be interpreted similarly.

Beta and Gamma are rational and Beta can reasonably foresee Gamma's decisions because these payoffs are common knowledge.

Required:

If the firms are independent and Beta moves first, what actions will they take?

a. Beta chooses A and Gamma chooses E.

b. Beta chooses A and Gamma chooses D.

c. Beta chooses B and Gamma chooses D.

d. Beta chooses B and Gamma chooses E.

Answer #1

Beta | |||

A | B | ||

Gamma | D | $30/ $10 | $16 / $20 |

E | $20/ $25 | $15/ $22 |

**c. Beta chooses B and Gamma chooses D**

This option is correct.

If beta chooses A expecting its payoff to be $25, then it would be a mistake as Gamma would then choose D (because of higher payoff for Gamma for D/A combination than E/A ). This would decrease A's payoff to $10.

Hence Beta selects B (expecting Gamma would choose D and hence Beta's payoff would be $20), after which Gamma selects D to maximize its payoff to $16

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