# Nash Equilibrium and IESDS

1. Aug 8, 2015

### Issam2204

Hello everyone!

Applying the Iterated Elimination of Strictly Dominated Strategies (IESDS) to a game resulted with the solution of the Nash Equilibrium.

Actually that specific "quadrant" of the matrix is the:

* Pareto optimal
* Nash Equilibrium
* Dominant strategies (through IESDS).

This is a Matrix that shows what I'm talking about:

Quadrant (1, 1) is a Nash Equilibrium, the solution of IESDS, and the Pareto optimum scenario.

What I'm trying to ask is: are my results wrong or this can actually happen? Did I come up correctly with the Nash Equilibrium? Is the IESDS solution really the quadrant (1, 1)?

Cheers!

2. Aug 8, 2015

### Mirero

Well, if a finite game can be solved by IESDS, the the solution is going to be the unique Nash Equilibrium.

As for Pareto optimality, Quadrant (1,1) is the best outcome for both players anyway, so there doesn't exist another strategy one could switch into to take advantage of. So your answer is right.

However, you are correct in your suspicion that Nash Equilibrium and Pareto Optimality don't necessarily coincide. For example, in the typical example of the Prisoner's Dilemma, the Nash Equilibrium of the game is when both players confess, while the Pareto Optimal strategy is when both players remain silent.

3. Aug 8, 2015

### Issam2204

Thank you very much!