Suppose that Toyota and GM are considering entering a new market for electric automobiles and that their profits (in millions of dollars) from entering or staying out of the market are included a van Gogh, a Cézanne, and an early Picasso

(Vogel, Carol, “Rock, Paper, Payoff,” New York Times, April 29, 2005, A1, A24). He resolved the issue by having the two auction houses’ representatives compete in the playground game of rock-paperscissors. A rock (fist) breaks scissors (two extended fingers), scissors cut paper (flat hand), and paper smothers rock. At stake were several million dollars in commissions. Christie’s won: scissors cut paper.

a. Show the profit or payoff matrix for this rockpaper-scissors game. (Hint: You may assume that the payoff is -1 if you lose, 0 if you tie, and 1 if you win.)

b. Sotheby’s expert in Impressionist and modern art said, “[T]his is a game of chance, so we didn’t really give it much thought. We had no strategy in mind.” In contrast, the president of Christie’s in Japan researched the psychology of the game and consulted with the 11-year-old twin daughters of the director of the Impressionist and modern art department. One of these girls said, “Everybody knows you always start with scissors. Rock is way too obvious, and scissors beats paper.” The other opined, “Since they were beginners, scissors was definitely the safest.” Evaluate these comments on strategy. What strategy would you recommend if you knew that your rival was consulting with 11-year-old girls?

In general, what pure or mixed strategy would you have recommended, and why? M