1, (33%) Two firms compete in a local market. The market size (total avail- able

Question

1, (33%) Two firms compete in a local market. The market size (total avail- able profits) is $6 million per year. Each firm can choose to advertise on local television. If a firm chooses to advertise in a given year, it costs that firm $1 million. If one firm advertises and the other doesn't, then the firm that advertises captures the whole market. If both firms advertise, they split the market 50-50. If both firms choose not to advertise, they also split the market 50-50. (a) Suppose the two firms know they will compete for just one year. Write down the payoff matrix for this game and find the Nash equi- librium strategies. pete for 3 years. forever, and assume that future profits are discounted with an in- (b) Describe the Nash equilibrium if the firms know that they will com- (c) Now suppose that the firms expect to play this game repeatedly terest rate of 10% per year (r-0.1). i. Is there a Nash equilibrium in which both firms advertise every year? Explain. i. Is there a Nash equilibrium in which the firms do not advertise? Explain

Explanation / Answer

The Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash Equilibria or none at all.

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