Two salespeople make identical trips in their cars. They both cross five bridges

Problem 2. The Traveler's Dilemma

Two salespeople make identical trips in their cars. They both cross five bridges. Some of the bridges have a $1.00 toll. The manager knows that two of the bridges have one dollar tolls, but she does not know whether the others have $1.00 tolls or are free. She askes each salesperson to separately report their bridge expenses (which will be an integer between 2 and 5). As an incentive to report accurately, the manager makes the following rule

: • If both salespeople report the same amount, both are reimbursed that amount.

• If they report different amounts, then she will assume the lower amount is correct.

– The salesperson who reported the lower amount is reimbursed that amount plus a $2 bonus.

– The salesperson whwo reported the higher amount is reimbursed the lower amount minus a $2 penalty.

1. Using the strategy spaces Si = {2,3,4,5}, write the normal form for this game showing all payoffs.

2. Use iterated elimination of weakly dominated strategies to find a dominant strategy equilibrium.