Find the Nash equilibria in pure strategies in the following games.

Question

Payoffs on the left correspond to Player 1 and payoffs on the right correspond to Player 2—for instance, in (U, L), player 1 gets a payoff of 3 and player 2 gets a payoff of 4. Explain in detail why they are NE. enter image description here

So my thoughs are that in this game, both (U.L) and (D,L) are nash equilibria. I am NOT SURE if (D,L) is actually a nash equilibria in the above image. Can anyone help me?

I'm not sure what the trouble is, but do you realise that it is player 1 who chooses between U and D, and player 2 who chooses between L and R? — Řídící, Nov 09 '13 at 11:51
Yes, of course. Basically, if player 1 choses U he will get the payoff of 3, and the player 2 get 4 by playing L and 1 by playing R; if player 1 choses D he will get the payoff of 2 no matter what the player 2 choses. The player 2 in this case gets 3 by playing L and 2 by playing R. Right? — Dimoftie Cristina Diana, Nov 09 '13 at 12:15
The problem is that i am not sure if (D, L) is an equilibrium.It should be. I just wanted a second taught. — Dimoftie Cristina Diana, Nov 09 '13 at 12:16
becuase if player 2 choses L he will be better of than chosing R, because 3>2, in the case in which player 1 choses D. They don't have no incentive to move. I am not sure, that's why i am asking — Dimoftie Cristina Diana, Nov 09 '13 at 12:24
Well, yes it might have an incentive to go to U because he gets in that case 3. I am confused — Dimoftie Cristina Diana, Nov 09 '13 at 12:47

Kapoios · Answer 1 · 2015-02-01T17:14:39.563

Nash dynamics do not lead player 1 to choose D, as he will maximize his payoff by choosing U. His objective is to maximize his own payoff, not to restrict player's 2 actions. The only Nash Equilibrium here is (U,L), as both players maximize their payoffs and there are no better actions to take.

Edit: I recently rechecked my answer, just by curiosity, and I realized that I had forgot to mention that $R$ is a strongly dominated strategy for player 2. So, by eliminating this strategy, player 1 faces just the pure strategy $L$ of player 2. Thus, her strategy $D$ is strongly dominated by $U$. This induction justifies my answer.

Find the Nash equilibria in pure strategies in the following games.

1 Answers1