1. (4 points, modified based on Holt-Chapter 26 Q1 & Q2 in the hard copy version

Question

1. (4 points, modified based on Holt-Chapter 26 Q1 & Q2 in the hard copy version or Chapter 12 Q1 & Q2 in the soft version) Consider the game in the following table. Player 2 A (26%) B (6%) C(68%) D (0%) | 200, 50 | 0, 45 | 10, 30 | 20.-250 Bottom (32%) 250T10.-100 | 30, 30 | 50, 40 Player l Top (68%) (a) (2 points) Find all Nash equilibria in pure strategies. (b) (2 points) In this table, the number in the parenthesis after each strategy shows the percentage of people who chose that strategy when the game was played only once (Goeree and Holt (2001)). Conjecture why Option C was selected so frequently by those who played the role as Player 2

Explanation / Answer

Consider the following game, here there are 2 players, “P1” have 2 strategies and “P2” have 4 strategies.

So, let’s say if “P1” will play “TOP”, then optimum strategy for “P2” is to play “A”, since 50 > 45, 30, -250. Now, if “P2” will choose to play “A”, then the optimum choice for “P1” is to play “TOP”, since 200 > 0. So, (TOP, A) = (200,50), be the NE here.

So, let’s say if “P1” will play “BOTTOM”, then optimum strategy for “P2” is to play “D”, since 40 > 30, -100, -250. Now, if “P2” will choose to play “D”, then the optimum choice for “P1” is to play “BOTTOM”, since 50 > 20. So, (BOTTOM, D) = (50, 40), be the NE here.

So, there are 2 NE in this given game, these are (TOP, A) and (BOTTOM, D).

b).

We can see in the table that 68% players have selected “C” as a “P2”, since if someone choose then it doesn’t matter what the “P1” will play, in each and every possibility “P2” will get “30” as a payoff.

But in other cases, “P2” there is a possibility that the “P2” may get negative payoff.

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