47. Consider a situation in which you and a friend both must choose a number from the two numbers 1 and 2. The relevant payoffs are as follows:

If you choose 1 and he chooses 1, If you choose 1 and he chooses 2, If you choose 2 and he chooses 1, If you choose 2 and he chooses 2, you both win $10 he wins $15 and you win $0 you win $15 and he wins $0 you both win $5.

(a) How would you go about assigning probabilities to his two actions?

(b) On the basis of the probabilities assigned in (a), what is your optimal action?

(c) Could you have determined that this was your optimal action without using any probabilities? Why?

(d) Would you expect your action to be different if you could get together with your friend and make a bargain with him before the game is played? Explain.