econ7340_HW3_FS10[1] - Game Theory Problem Set#3 Mixed...

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Game Theory Problem Set #3: Mixed Strategies and Nash Equilibria Due: Beginning of class , Tuesday, September 28, 2010 Problem 1 (Find NE 1) Find all of the Nash equilibria of the game in Table 1. (Hint: start by removing all dominated strategies. Some strategies may be dominated by mixed strategies.) E F G H A 1,2 0,0 2,1 3,1 B 0,0 3,1 -1,0 0,-1 C 0,2 1,1 0,3 6,1 D -1,2 2,5 -2,-1 4,1 Table 1: Game for problem 1 Problem 2 (Chasing and Escaping) Recall the “Chasing and Escap- ing” game from class and from the experimental sets: Player 1 and Player 2 each have to choose a number in the interval [0 , 100]. Player 1 wants to be as close as possible to Player 2 while Player 2 wants to be as far as possible from Player 1. Payoff functions are: u 1 ( s 1 , s 2 ) = -| s 1 - s 2 | u 2 ( s 1 , s 2 ) = | s 1 - s 2 | where | x | is the absolute value of x , and ( s 1 , s 2 ) are the numbers chosen by Players 1 and 2, respectively. 1. Show that in equilibrium Player 2 will never play a pure strategy, and explain why.
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