Game Theory Solutions 1 Find the saddle point for the game having the following payoff table. Use the minimax criterion to find the best strategy for.

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Presentation transcript:

Game Theory Solutions 1 Find the saddle point for the game having the following payoff table. Use the minimax criterion to find the best strategy for each player. Does this game have a saddle point? Is it a stable game? Player 2 Strategy 1 2 3 Player 1 2 -1 -2 Soln: Maximin pt. Player 1, strategy 3 Minimax pt. Player 2, strategy 2 Saddle pt.

Game Theory Solutions 3 Soln: We can check this with LP formulation. For player 1, Player 1, strategy 3

Game Theory Solutions 3 Soln: We can check this with LP formulation. For player 2, Player 2, strategy 2

Game Theory Solutions 4 Alternatively, we could consider payoff matrix for player 2. Soln: Maximin pt. Player 2, strategy 2 Minimax pt. Player 1, strategy 3 Saddle pt. Player 2 payoff is negative of player 1 payoff

Game Theory Solutions 5 For 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 according to the minimax criterion. Player 2 Strategy 1 2 3 Player 1 2 4

Game Theory Solutions 6 Soln: maximin

Game Theory Solutions 7 Soln: maximin

Game Theory Solutions 8 Soln: Check by LP

Game Theory Solutions 9 Soln: Check by LP