# Battle of the sexes online quizzes

### Battle of the sexes online quizzes

The players will miscoordinate with probability 13/25, leaving each player with an expected return of 6/5 (less than the return one would receive from constantly going to one's less favored event).

These four probabilities are: ) is the probability of each event multiplied by the payoff if it happens.

The equilibria may be found by a generic Nash equilibrium solver such as the Lemke-Howson algorithm.

But Bo S solutions are also simple enough to be found though a few steps of simple algebra.

The column player observes whether or not the row player burns and then chooses either to play Opera or Football.

If one iteratively deletes weakly dominated strategies then one arrives at a unique solution where the row player does not burn the money and plays Opera and where the column player plays Opera.

For example, the Probability that the man goes to football and the Woman goes to football multiplied by the Expected payoff to the man if that happens ( if the woman always goes to the opera and the man chooses randomly with probabilities based on the expected outcome, due to the symmetry in the value table.

But if both players always do the same thing (both have simple strategies), the payoff is just 1 for both, from the table above.The two pure strategy Nash equilibria are unfair; one player consistently does better than the other.The mixed strategy Nash equilibrium (when it exists) is inefficient.Given the above, how should players choose which of the three Nash equilibria to actually play in practice?One (contested) solution concept is that if they are both identical then they must arrive at the same rational answer, if one exists, and the only way to do this is to choose the mixed strategy equilibrium because it is symmetric. Interesting strategic changes can take place in this game if one allows one player the option of "burning money" – that is, allowing that player to destroy some of her utility.Consider the version of Battle of the Sexes pictured here (called Unburned).