Types of Nash Equilibria: After considering dominance and best responses in the previous section, this section tackles the critical concept of a Nash equilibrium.  By presenting the best response discussion as a series of ‘what if’ questions it is possible to identify full best response functions for each player rather quickly.  A pure strategy Nash equilibrium can then be explained as an outcome in which there is coincidence of these best responses for each player.

 

An alternative mechanism for identifying Nash equilibria is to engage in cell-by-cell inspection to test each outcome for regret on the part of any of the players.  Since regret, a desire to make a different choice once the outcome is known, cannot be part of a best response, identifying points of regret allows one to rule out various outcomes as candidates for being Nash equilibria.  It is important to point out to students that all that is necessary to eliminate an outcome from the list of possible Nash equilibria is to identify regret by one player.

 

This section also considers mixed-strategy Nash equilibria and it is important to take the time to walk students through the details using a couple of examples.  Details are included in the appendix and when walking through an example students often find the intuition easier to understand if the optimal probability is described as the value that keeps your opponent guessing.  The key part of the strategy is to make sure that your opponent cannot exploit any part of your choice by choosing a pure strategy in response to your mixed one.