Game Theory: Contract Enforcement Between Buyer and Seller in a Supply Chain

1. Contract Enforcement Between Buyer and Seller in a Supply Chain. Suppose that two rms, 1 and 2, must undergo a certain amount of investment so as to coordinate their efforts in order to enable the supplier to produce a good to be used as an input in the buyer's production process. Such investment may involve the costs incurred by both parties in the initial planning and design phase of the relationship and/or involve the rms in having to incur the associated costs of purchasing specialized equipment and developing certain production processes in order to satisfy the needs and specic requirements of both parties. In any case, suppose that the technology of the relationship and the structure of the underlying game are given by the following normal form representation of the game: Firm 2 Invest (I) Not Invest (N) Firm 1 Z]: Z; Y], X2 Invest (I) (41, 35) ( 32, 21) X1, Y2 Not Invest (N) (92, 42) (0, 0) Further suppose that the players contract in a setting of court-imposed breach remedies. The players can therefore write a formal contract specifying the strategy prole they intend to play; the court then observes their behavior in the underlying game and, if one or both of them cheated, impose a breach transfer. Note though of course, that the players wish to support the investment outcome (1, I). (l .a) Write out the resulting payoffs associated with the induced game under the assumption that the court imposes expectation damages. Can a contract specifying (I, I) be enforced? Explain your answer. (Hint: write out the formulas for expectation damages above the appropriate payoffs in the appropriate cells in the matrix below and just plug in the numbers)