Consider a piece-rate-tournament experiment like in the Niederle and Vesterlund paper but with groups of 2: 1 man and 1 woman, both of whom maximize expected value. Both men and women believe that men will solve 1 problem the time and 4 problems the time, while women will solve 2 problems the time and 3 problems the time. Piece-rate pays $1 per problem solved. Tournaments pay $2 per problem if you have the most correct, otherwise $0.
1. Calculate the expected value payoffs from piece-rate and from tournament pay for men and women. Show your math, and explain who will compete.
2. Suppose that one gender is more risk averse than the other. Explain how this might change your conclusion above, and which gender would have to be more risk averse.