Ingrid and Jeff would like to use Saturday night together but have dissimilar tastes in entertainment. Jeff would like to go to the opera but Ingrid would prefer to see soccer. As the following payoff matrix shows, Jeff would most favour to go to the opera with Ingrid, but prefers watching soccer with Ingrid to going to the opera alone, and likewise for Ingrid.
Verify the Nash equilibria of this game, suppose that Ingrid and Jeff do not randomize over actions.
Strategies in which a player makes a specific choice or takes a specific action will not always result in a Nash equilibrium. In some cases, players can make a random choice among two or more possible actions, based on a set of chosen probabilities. A strategy like this is called a mixed strategy.