Scenario: Miguel and Stephanie are competitors who sell tacos out of their food trucks by the same beach. For each taco they sell, they get a profit of $1.00. Each morning they must decide at which of the three legally permitted locations, A, B, or C, they should park their trucks. The picture below shows the three locations.

In each of the three locations, there are 100 customers per day, and each customer buys a taco from the nearest vendor. If the two trucks are in the same location, then each vendor gets half of the customers. So, for example, if Miguel's truck is in location A, and Stephanie's is also in location A, then half of customers from locations A, B, and C will buy from Miguel's and the other half will buy from Stephanie's, so that each gets a profit of $150. If Miguel's truck is in location A and Stephanie's is in location B, then everyone in location A will buy from Miguel and everyone from locations B and C will buy from Stephanie, so that Miguel's profit is $100 while Stephanie's is $200. If Miguel's truck is in location A and Stephanie's is in location C, then everyone in A plus a half from B will buy from Miguel, and everyone in C plus half from B will buy from Stephanie so that each vendor gets a profit of $150, and so on. The table below is the payoff matrix for this game. The first number in each cell is Miguel's profit, and the second number is Stephanie's profit.

-Refer to the scenario above.What,if any,is a Nash equilibrium for this game?

Question

Scenario: Miguel and Stephanie are competitors who sell tacos out of their food trucks by the same beach. For each taco they sell, they get a profit of $1.00. Each morning they must decide at which of the three legally permitted locations, A, B, or C, they should park their trucks. The picture below shows the three locations.
  
In each of the three locations, there are 100 customers per day, and each customer buys a taco from the nearest vendor. If the two trucks are in the same location, then each vendor gets half of the customers. So, for example, if Miguel's truck is in location A, and Stephanie's is also in location A, then half of customers from locations A, B, and C will buy from Miguel's and the other half will buy from Stephanie's, so that each gets a profit of $150. If Miguel's truck is in location A and Stephanie's is in location B, then everyone in location A will buy from Miguel and everyone from locations B and C will buy from Stephanie, so that Miguel's profit is $100 while Stephanie's is $200. If Miguel's truck is in location A and Stephanie's is in location C, then everyone in A plus a half from B will buy from Miguel, and everyone in C plus half from B will buy from Stephanie so that each vendor gets a profit of $150, and so on. The table below is the payoff matrix for this game. The first number in each cell is Miguel's profit, and the second number is Stephanie's profit.
 
-Refer to the scenario above.What,if any,is a Nash equilibrium for this game?

Quizplus · Accepted Answer

A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy. If both Miguel and Stephanie choose B, neither has an incentive to deviate unilaterally, making it a Nash equilibrium.

Scenario: Miguel and Stephanie Are Competitors Who Sell Tacos Out