(10 points) There are two movie theaters in town. They agree to charge $9 per ti
ID: 1173988 • Letter: #
Question
(10 points) There are two movie theaters in town. They agree to charge $9 per ticket in order to maximize joint profits. However, each theater must decide 6. whether or not to "cheat" on the agreement and offer a "2 for 1" ticket price to its customers. Consider the payoff matrix below, depicting their payoffs in a game played once. Note the payoffs are (Firm 1, Firm 2) FIRM 2 charge $9 offer 2 for 1 rge $9 (40004000) (1000,6000) offer 2 for 1 (6000,1000) (3000,3000) 1 Determine if either theater has a dominant strategy. Solve for the Nash Equilibrium of the gameExplanation / Answer
If Firm 2 charges $9 per ticket then Firm 1 gets profit of $4,000 if it also charges $9 per ticket and a profit of $6,000 if it offers '2 for 1' ticket price.
Since, pay-off for Firm 1 is greater in case of '2 for 1' ticket price, Firm 1 will offer '2 for 1' ticket price, if Firm 2 charges $9 per ticket.
If Firm 2 offers '2 for 1' ticket price then Firm 1 gets profit of $1,000 if it charges $9 per ticket and a profit of $3,000 if it offers '2 for 1' ticket price.
Since, pay-off for Firm 1 is greater in case of '2 for 1' ticket price, Firm 1 will offer '2 for 1' ticket price, if Firm 2 offers '2 for 1' ticket price.
It can be seen that Firm 1 will prefer to offer '2 for 1' ticket price irrespective of the strategy adopted by the Firm 2.
This indicates that Firm 1 has dominant strategy of offer '2 for 1' ticket price.
If Firm 1 charges $9 per ticket then Firm 2 gets profit of $4,000 if it also charges $9 per ticket and a profit of $6,000 if it offers '2 for 1' ticket price.
Since, pay-off for Firm 2 is greater in case of '2 for 1' ticket price, Firm 2 will offer '2 for 1' ticket price, if Firm 1 charges $9 per ticket.
If Firm 1 offers '2 for 1' ticket price then Firm 2 gets profit of $1,000 if it charges $9 per ticket and a profit of $3,000 if it offers '2 for 1' ticket price.
Since, pay-off for Firm 2 is greater in case of '2 for 1' ticket price, Firm 2 will offer '2 for 1' ticket price, if Firm 1 offers '2 for 1' ticket price.
It can be seen that Firm 2 will prefer to offer '2 for 1' ticket price irrespective of the strategy adopted by the Firm 1.
This indicates that Firm 2 has dominant strategy of offer '2 for 1' ticket price.
Combination of dominant strategies is the nash equilibrium.
So,
Nash equilibrium of this game is Firm 1 will offer '2 for 1' ticket price and Firm 2 will offer '2 for 1' ticket price.
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