The market for food trucks in Hamsterville is a duopoly. Both firms are planning their menus for the year: Mike's Munchies must choose between serving loaded tater tots and fried chicken, and Frida's foods must choose between serving stuffed churros and fajita fries.

The profits for each food truck in different scenarios are given in the payoff matrix shown here, given in thousands of dollars. The first entry represents Mike's payoff and the second entry represents Frida's payoff. The two trucks have agreed to collude.

What happens to industry profits if Mike violates the agreement and chooses his best response, but Frida does not?

Choose 1 answer:
(A) Industry profits are unchanged
(B) Industry profits decrease by $\$ 50,000$.
(C) Industry profits increase by $\$ 10,000$.
(D) Industry profits fall by $\$ 30,000$.
(E) Industry profits decrease by $\$ 10,000$

Question

The market for food trucks in Hamsterville is a duopoly. Both firms are planning their menus for the year: Mike's Munchies must choose between serving loaded tater tots and fried chicken, and Frida's foods must choose between serving stuffed churros and fajita fries.

The profits for each food truck in different scenarios are given in the payoff matrix shown here, given in thousands of dollars. The first entry represents Mike's payoff and the second entry represents Frida's payoff. The two trucks have agreed to collude.

What happens to industry profits if Mike violates the agreement and chooses his best response, but Frida does not?

Choose 1 answer:
(A) Industry profits are unchanged
(B) Industry profits decrease by $\$ 50,000$.
(C) Industry profits increase by $\$ 10,000$.
(D) Industry profits fall by $\$ 30,000$.
(E) Industry profits decrease by $\$ 10,000$

Accepted Answer

∻Solution∻ ‖ a ⋮ Identify the Payoff Matrix: The given payoff matrix shows the profits for Mike and Frida in different scenarios. Let's denote the strategies as follows: - Mike's strategies: Loaded Tots (LT) and Fried Chicken (FC) - Frida's strategies: Stuffed Churros (SC) and Fajita Fries (FF) The payoff matrix is: $$ \begin{array}{c|c|c} & \text{SC} & \text{FF} \ \hline \text{LT} & (50, 50) & (30, 60) \ \hline \text{FC} & (60, 30) & (40, 40) \ \end{array} $$ ‖ ‖ b ⋮ Determine the Best Response: To find Mike's best response, we need to look at his payoffs for each of Frida's strategies: - If Frida chooses SC, Mike's payoffs are 50 (LT) and 60 (FC). Mike's best response is FC. - If Frida chooses FF, Mike's payoffs are 30 (LT) and 40 (FC). Mike's best response is FC. Thus, Mike's best response is to choose FC regardless of Frida's choice. ‖ ‖ c ⋮ Calculate Industry Profits: If Mike violates the agreement and chooses his best response (FC), while Frida does not change her strategy, we need to compare the industry profits in the collusion scenario and the new scenario: - Collusion scenario: Both firms agree to a strategy that maximizes joint profits. Let's assume they choose (LT, SC) with profits (50, 50), so total industry profit is $50,000 + $50,000 = $100,000. - New scenario: Mike chooses FC, and Frida sticks to SC. The new profits are (60, 30), so total industry profit is $60,000 + $30,000 = $90,000. The change in industry profits is $100,000 - $90,000 = $10,000. ‖ ∻Answer∻ ⚹ (E) Industry profits decrease by $10,000 ⚹ ∻Key Concept∻ ⚹ Best Response in Game Theory ⚹ ∻Explanation∻ ⚹ In game theory, a player's best response is the strategy that maximizes their payoff given the other player's strategy. When Mike chooses his best response (FC) while Frida does not change her strategy (SC), the total industry profits decrease by $10,000. ⚹◊What would be the impact on the Nash equilibrium if Mike violates the agreement and chooses his best response⍭ Generate me a similar question◊

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