Solutions Sample Games 1

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Solutions Sample Games 1 Find the saddle point for the game having the following payoff table. Use the minimax criteria to find the best strategy for each player. Does this game have a saddle point? Is it a stable game? Soln: Shown below. The maximum of the minimums is strategy 3 for player 1 and the maximum of the minimums is strategy 2 for player 2. Payoff for the game is -1 which is the same element for each player. This is the saddle point for the game. Game is stable. If we were to do an LP formulation for this game x*=(0,0,1) and y*=(0,1,0,0).

Solutions Sample Games 2 Consider the game having the following payoff table. We note the minimum of the maximums and the maximum of the minimums do not translate to the same elements; game is not stable. Consequently, we must formulate and solve through some other means. For Player 1, For Player 2

Solutions Sample Games 3 Consider the game having the following payoff table. For Player 1,

Solutions Sample Games 4 Consider the game having the following payoff table. For Player 2

Solutions Sample Games 5 Consider the game having the following payoff table: Use the graphical procedure to determine the value of the game and the optimal mixed strategy for each player.

Solutions Sample Games 6 At minimax point then,

Solutions Sample Games 7 At minimax point then, Solving for y*, at x1=0,