Original or Fake — A Bargaining Game with Incomplete Information

Summary

We consider a special class of noncooperative bargaining games with incomplete information and two agents who bargain about the price of a given object. The object can be either of high value or of low value. Whereas the seller knows the real value, the buyer is not completely informed in that respect. With probability w he expects that the object is of low value and with the probability 1-w that it is of high value. The parameter w is common knowledge. One can therefore distinguish two types of the seller, namely the one who tries to sell an object of low value and the one who offers the more valuable object. To have something specific in mind, the commodity is assumed to be a work of art which can be either a fake or an original. The two types of the seller are accordingly called fake seller and honest seller. The buyer is of a unique type. Bargaining is supposed to proceed in form of a unanimity game, i.e., the players simultaneously determine their price offers. A contract results only if a seller and the buyer have chosen the same prices. As it is typical for bargaining games, the game has many equilibrium points. We apply the equilibrium selection theory of Harsanyi and Selten to determine a unique solution point for each of the bargaining games.