The Tire Factory (TTF) is a regional automotive repair chain that provides quick service for simple repairs, such as oil changes, tire rotation, and other minor automotive maintenance services. They are considering entering into the body repair business. For this purpose, they are considering two potential body shops, Best Auto Body (BAB) and Reliable Body & Paint (RB&P). The two body shops have a similar reputation for quality. The Tire Factory is planning to earn profit by marking up the repair price it pays. Collision repair costs consist of labor and material, which are specific to each repair, and body shops make their profit by marking up those costs (so the customers pay two markups?one by the body shop and the second by TTF). The Tire Factory explained to the managers of the two body shops that it will sign an exclusive contract with the provider who agrees to charge the smallest mark-up, and invited them to propose either a 20% or a 30% mark-up. If both body shops propose the same-mark-up, the TTF will split the business between the two suppliers.

If one supplier wins the auction, this supplier will make a profit of 40 (thousand dollars), and the losing supplier gets zero. If there is a tie, the suppliers will make a profit of 30 (thousand dollars) each in a case they both bid 30%, and 20 (thousand dollars) each in a case they both bid 20%

TFF just got a call from the manager of Best Auto Body asking the name of the second body shop TFF is considering. Analyze this problem and make a recommendation on whether TFF should disclose the identity of the second bidder.

Let's represent this game in a normal form. Recall that it means to specify players, strategies available to each of them, and the payoffs corresponding to each combination of strategies. It is convenient to represent it in a form of a matrix, like I did in the slides. l have entered the players and the strategies into the table. Fill the values for the payoffs. The first value in each cell is for BAB, and the second value is for FIB&P. Enter just the number of thousands; for instance, if the payoff is 40 thousand dollars, enter 40. RB&P Bid 20% Bid 30% Does this game have dominant strategies? 0 Yes, for BAB (but not for FIB&P) bidding 30% is a dominant strategy 0 Yes, for both suppliers bidding 30% is a dominant strategy 0 Yes, for both suppliers bidding 20% is a dominant strategy 0 There are no dominant strategies in this game What are the Nash equilibria in this game? O Both suppliers bid 30% Both suppliers bid 20% There are two Nash equilibria: BAB bids 20% and RB&P bids 30%, and vice versa O This game has no Nash equilibrium in pure strategies (that is, the suppliers will randomize their bids)