Consider the game T = (I, {S_1}, {u_i}) where I = {1,2}, S_1 = {1,..., 7}, S_2 =
ID: 1197039 • Letter: C
Question
Consider the game T = (I, {S_1}, {u_i}) where I = {1,2}, S_1 = {1,..., 7}, S_2 = {A,G}. The payoffs are given by the following matrix: What is the unique outcome that survives iterative deletion of strictly dominated strategies in T? What are the payoffs associated with this unique strategy profile? Is the unique outcome obtained in (1) a Nash equilibrium? Do you think that it is possible for a Nash equilibrium to be eliminated by the procedure of iterative deletion of strictly dominated strategies? Explain your intuition.Explanation / Answer
Looking at the above game clearly for player 1 strategies 1 and 4 are strictly dominated.Whereas for player2 strategies B , F and G are strictly dominated as both have higher pay offs in other strategies whatever the other player chooses.Thus eliminating the above strategies our game becomes
Clearly in the above game strategies 2 , 6 and 7 are strictly dominated as player1 gets higher pay offs in all other strategies with player2 playing any strategy.
Thus our new game becomes
Given the above game all other strategies rather than C ire strictly dominated for player2 as he gets a higher pay off in strategy C.
Thus our new game
Thus given the above game strategy 3 is strictly dominated by strategy 5 for player1 since he gets higher pay off in 5.Hence the unique outcome that survives elimination is strategy 5 for player1 and strategy C for player2.Pay offs associated with this strategy is (4,3) for player 1 and 2 respectively.
2)Yes the outcome is a nash equilibrium because given player2 plays C player1 plays 5 as it maximises his pay off similarly given player1 plays 5 , player 2 plays C as it gets maximum pay off by doing so.Thus none of them want to change their position hence its a nash equilibrium.
No its not possible that a nash equilibrium is eliminated by iterative deletion of strictly dominated strategies.Nash equilibrium is a position where both are maximising their pay offs and none wants to change its strategy.That is given what the other player does each one maximises its pay off.Under the deletion process we delete only those strategies that the player wont choose given other player chooses any strategy.Thus these deleted stategies cant comprise nash equilibrium.
A C D E 2 1,3 1,2 -2,4 -1,2 3 2.0 3,4 1,-0.5 2,3 5 2,-2 4,3 4,0 1,2 6 0,2 1,3 4,1 0,3 7 -1,5 2,3 4,2 0,3