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In: Economics

Q1. There are ten customers and two cafes A and B. Customers want to purchase from...

Q1. There are ten customers and two cafes A and B. Customers want to purchase from the cafe with fewer customers. A customer’s payoff when purchasing from cafe A is −mA, where mA is the number of customers excluding herself purchasing from A. A customer’s payoff when purchasing from cafe B is −mB, where mB is the number of customers excluding herself purchasing from B. a. Find a pure-strategy Nash equilibrium of this game. Prove that it is a Nash equilib- rium. b. Suppose each player chooses cafe A with probability 1/2 and cafe B with probability 1/2. Show that this is a (mixed-strategy) Nash equilibrium. c. Compare the expected number of customers for each cafe in the pure-strategy and mixed-strategy Nash equilibria. (Remember to show all working)

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