Some games have Nash equilibria both in pure
strategies and in mixed strategies. An example is “The Battle of the Sexes,” a
game that you might find familiar. It goes like this. Jim and Joan would like to
spend Saturday night together but have different tastes in entertainment. Jim
would like to go to the opera, but Joan prefers mud wrestling. As the payoff
matrix in Table 13.7 shows, Jim would most prefer to go to the opera with Joan,
but prefers watching mud wrestling with Joan to going to the opera alone, and
similarly for JoanSome games have Nash equilibria both in pure
strategies and in mixed strategies. An example is “The Battle of the Sexes,” a
game that you might find familiar. It goes like this. Jim and Joan would like to
spend Saturday night together but have different tastes in entertainment. Jim
would like to go to the opera, but Joan prefers mud wrestling. As the payoff
matrix in Table 13.7 shows, Jim would most prefer to go to the opera with Joan,
but prefers watching mud wrestling with Joan to going to the opera alone, and
similarly for Joan