Bilateral bargaining with multiple opportunities: knowing your opponent´s bargaining position

Negotiations have been extensively studied theoretically throughout the years. A well-known bilateral approach is the ultimatum game, where two agents negotiate on how to split a surplus or a "dollar"-the proposer makes an offer and responder can choose to accept or reject. In this paper a natural extension of the ultimatum game is presented, in which both agents can negotiate with other opponents in case of a disagreement. This way the basics of a competitive market are modeled, where, for instance, a buyer can try several sellers before making a purchase decision. The game is investigated using an evolutionary simulation. The outcomes appear to depend largely on the information available to the agents. We find that if the agents\´ number of remaining bargaining opportunities is commonly known, the proposer has the advantage. If this information is held private, however, the responder can obtain a larger share of the surplus. For the first case we also provide a game-theoretic analysis and compare the outcome with evolutionary results. Furthermore, the effects of search costs, uncertainty about future opportunities, and allowing multiple issues to be negotiated simultaneously are investigated