Consider the two-person,zero-sum game having the following payoff table. Determine the optimal strategy and payoff for each player by successively eliminating dominated strategies.Show your reasoning and the order in which you eliminated strategies.

Question

Consider the two-person,zero-sum game having the following payoff table.  Determine the optimal strategy and payoff for each player by successively eliminating dominated strategies.Show your reasoning and the order in which you eliminated strategies.

Quizplus · Accepted Answer

The Answer is Since

but with

,strategy 1 of player 2 is dominated by strategy 3,so this strategy 1 is eliminated.Next,[-2 -1] < [3 1] and [-2 -1] < [4 0] ,so strategy 2 for player 1 is dominated by both strategy 1 and strategy 3,so this strategy 2 is eliminated.Next,

,so strategy 2 for player 2 is dominated by strategy 3,so this strategy 2 is eliminated.Finally,1 > 0,so strategy 3 for player 1 is dominated by strategy 1,so this strategy 3 is eliminated.Therefore,player 1 will choose strategy 1 and player 2 will choose strategy 3,resulting in a payoff of 1 to player 1 and a payoff of -1 to player 2.

Consider the Two-Person,zero-Sum Game Having the Following Payoff Table