Answer 2a) no strictly dominant strategy for p1, but strategy D for P1 is strict
ID: 1148252 • Letter: A
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2a) no strictly dominant strategy for p1, but strategy D for P1 is strictly dominated by strategy M and strategy U. P1 has 2 weakly dominated strategies
I need help understanding why, with detailed explanation!
Q2. Examine the following normal foom games. P2 P2 Payoff table 1 Payoff table 2 5,1 6,0 P1 P1 -3, 2 4,4 (a) Determine if any player has a »ea*j or a stricty dominated strategy. Explain yonc answer nsing payoff from the table. Note: there is a strictly DOMINATED strategies for Pi if there exists another strategy xi e Xi snch that for ALL other players x-i e X-1 (where-i means ALL players other than ui(xi.x-i) > uj(Xi,X-i) (b) Using yon answer in a) find the Nash equiibninm of the game. PROVE THAT THE STATHE EQUILIBRIUM(A)ARE INDEED NASH EQUILIBRIUM(A) Remember that stating the Nash equilibrinm is different from proving that a pair of strategies is a Nash equiibcia. In all cases nse payoffs to jnstify yonc answerExplanation / Answer
In Payoff table 1, if consider the pay off for P1 only, it is as follows:
Now, A strategy is strictly dominant if, regardless of what any other players do, the strategy earns a player a strictly higher payoff than any other. Hence, a strategy is strictly dominant if it is always strictly better than any other strategy, for any profile of other players' actions. If a player has a strictly dominant strategy, than he or she will always play it in equilibrium. Also, if one strategy is strictly dominant, than all others are dominated.
Now if we analyse the payoff for player 1, we can see that player 1 will be better off by playing U(1,-1) rather than playing D(-2,-3) for both strategies of player 2. Again, player 1 will be better off by playing M(-1,1) rather than playing D(-2,-3) for both strategies of player 2. So, it is clearly seen than both U and M is strictly dominant over D.
In Payoff table 2, if consider the pay off for P1 only, it is as follows:
A strategy is weakly dominant if, regardless of what any other players do, the strategy earns a player a payoff at least as high as any other strategy, and, the strategy earns a strictly higher payoff for some profile of other players' strategies. Hence, a strategy is weakly dominant if it is always at least as good as any other strategy, for any profile of other players' actions, and is strictly better for some profile of others' strategies. If a player has a weakly dominant strategy, than all others are weakly dominated.
Now, Now if we analyse the payoff for player 1, we can see that player 1 will be better off by playing D over U, when player 2 plays L, but when player 2 plays R, the payoff of player 1 is same for playing both U and D ,i.e 4. Again, the payoff for player 1, we can see that player 1 will be better off by playing D over M, when player 2 plays R, but when player 2 plays L, the payoff of player 1 is same for playing both M and D ,i.e 6.
So, it is clearly seen than both U and M is weakly dominated.
P2 P2 L R P1 U 1 -1 P1 M -1 1 P1 D -2 -3