B.* In the text, we indicated that mixed strategy equilibria in complete information games can be interpreted as pure strategy equilibria in a related incomplete information game. We will illustrate this here. Suppose that you and your partner know each other’s ordinal preferences over opera and football, but you are not quite sure just how much the other values the most preferred outcome. In particular, your partner knows your payoff from both showing up at the football game is 5, but he thinks your payoff from both showing up at the opera is 110 1 a2 with some uncertainty about what exactly a is. Similarly, you know your partner gets a payoff of 5 if both of you show up at the opera, but you think his/her payoff from both showing up at the football game is 110 1 b2, with you unsure of what exact value b takes. We will assume that both a and b are equally likely to take any value in the interval from 0 to x; that is, a and b are drawn randomly from a uniform distribution on 30 , x]. We have thus turned the initial complete information game into a related incomplete information game in which your type is defined by the randomly drawn value of a and your partner’s type is defined by the randomly drawn value of

b, with 30 , x] defining the set of possible types for both of you.