Game Theoretic Models for Strategic Bargaining

Bargaining is one of the most common negotiation situations in which agents must reach an agreement regarding how to distribute objects or a monetary amount. On the one side, each agent prefers to reach an agreement, rather than abstaining from doing so. On the other side, each agent prefers that agreement which most favors her interests. This problem has been widely studied in the game theory literature, under the assumption that agents are intelligent (i.e., able to collect all the information over the opponents) and rational (i.e., able to maximize their gain). The most satisfactory models represent a bargaining situation as a non–cooperative (strategic) game, where a solution is a strategy profile, specifying a strategy per agent, that is somehow in equilibrium. This chapter surveys the game theoretic strategic models for bargaining and the corresponding solving algorithms. Although the bargaining problem has been studied in the literature for almost 30 years, no algorithm able to solve a general bargaining problem with uncertainty is known. The critical issues behind the game theoretic approaches and some possible new research directions are also discussed.

Keywords: Game theory, Bilateral bargaining, Nash equilibrium, Rational agents, Non–cooperative negotiation, Uncertainty, Bayesian models, Alternating–offers protocol, Bargaining in markets, Self–confirming equilibrium.