Question

1. Professor Nash announces that he will auction off a $20 bill in a competition between two students, Jack and Jill at the beginning of their game theory lecture. Each student is to privately submit a bid on a piece of paper; whoever places the highest bid wins the $20 bill. In case of a tie, each student gets $10. Each student must pay whatever he or she bid, regardless of who wins the auction. Suppose that each student has only two $1 bills in their wallets, so that their available strategies each are to bid $0, $1, or $2;Complete the 3*3 payoff matrix of this game below.

Answer 1

The 3*3 matrix of this game is shown below

This is an all pay auction. As given, both get 10 if both bid nothing and get 10 each. if both bid 1 and get 10 each, it means net they get 9 each as they will have to pay 1. Same way they get 8 each if they both bid 2.

If Jill bids 0 but jack bids 1, Jack gets 20 and has to pay 1 so the payout is 19 to him and 0 to Jill.

This way we can see all the outcomes.