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.
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?
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.