3. Consider the following two-player simultaneous-move game. Player A chooses ei

Question

3. Consider the following two-player simultaneous-move game. Player A chooses either up (u) or 'down' (d). Player B chooses between 'left' () and 'right' (). The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the first number. There are payoffs provided for three versions of this simple game. For each of the three games express the payoff information in the normal form as presented in class. Determine all of the pure strategy Nash equilibria for each of the following three games. Explain your work. (20 pts) Game 1 Game 2 Game 3 u,l 1,1 1,5 3,7 u, r 5,0 10,10 8,2 d, 0,5 2,2 9,1 d,r 4,4. 5,1 5,6

Explanation / Answer

For Game 1

(U,L) is a PSNE (Pure Strategy Nash Equillibrium) as no player has profitable deviation if they choose other strategy than this one in Game 1

Game 2 & Game 3 has no Pure Strategy Nash Equillibrium

In game 2 As (U,R) & (D,L) both are Nash Equillibrium which are not dominated by available strategies.

In Game 3 (U.L) & ( D,R) both are Nash Equillibrium which are not dominated by available strategies

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