# Nash equilibrium and game theory construction

Kodak & Fuji produce photographic film. Suppose that there are no other significant producers, so that Kodak and Fuji constitute a duopoly (oligopoly). Suppose that the firms can produce 500 or 750 rolls of film for a given market in a given quarter. Assume (1) that firms face the same cost structure; (2) that if both produce 500, then each will profit $16 per day; (3) that if Fuji produces 500 and Kodak 750, then Fuji earns $14 and Kodak earns $21; (4) that if both produce 750 rolls then each will profit $15. The remaining combination is implicit.

(a) Construct a game matrix for this scenario.

(b) Is there a Nash Equilibrium for this game? Why or why not.

(c) Suppose that Fuji & Kodak decide to collude. What level of output would be chosen? Why?

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#### Solution Preview

Please refer to the attachment.

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<br>(a) Construct a game matrix for this scenario.

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<br>This is a typical "Prisoner's Dilemma" game.

<br>Production Fuji

<br>Game Matrix 500 750

<br>Kodak 500 16, 16 14, 21

<br> 750 21, 14 15, 15

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<br>(b) Is there a Nash Equilibrium for this game? Why or why not.

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<br>Nash equilibrium is the combination iff while keeping the strategies of the other agents fixed, no single agent Ai could unilaterally increase the utility (or, in cases involving mixed strategies, ...

#### Solution Summary

Construct a game matrix for this scenario.