Question

Two firms referred to as buyer and seller are engaged in a long term business relationship. The buyer moves first and decides whether or not to make an investment of V which if prices do not change, will increase her profits by P > V (representing a net saving of P -V). If the investment is made, the supplier then moves second and decides whether to raise her price by R or keep it the same. If the supplier raises her price, the buyer is third to move and decides whether to keep the same supplier or change to a dierent supplier. Payoffs represent utility and are 0 to both buyer and supplier if the investment is not made. If the buyer makes the investment, the payoffs are P - V to the buyer and 0 to the supplier, provided the supplier does not raise prices. If the supplier raises prices by R, the payoffs are now P - V - R to the buyer and R to the supplier, provided the buyer does not change suppliers. If the buyer changes suppliers, the payoffs are -V to the buyer (equating to the loss of the original investment) and -B to the supplier (a penalty reflecting loss of business). a. Draw the game tree. b. Determine the conditions on P; V and R such that the buyer will invest under the rollback solution outcome.

Answer 1

Let as consider buyer as player1 and supplier as player2.