Autonomous Agents and Multi-Agent Systems
Computing sequential equilibria for two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Alternating-offers bargaining with one-sided uncertain deadlines: an efficient algorithm
Artificial Intelligence
Simple search methods for finding a Nash equilibrium
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
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Bilateral bargaining has received a lot of attention in the multi--agent literature and has been studied with different approaches. According to the strategic approach, bargaining is modeled as a non--cooperative game with uncertain information and infinite actions. Its resolution is a long--standing open problem and no algorithm addressing uncertainty over multiple parameters is known. In this paper, we provide an algorithm to solve bargaining with any kind of one--sided uncertainty. Our algorithm reduces a bargaining problem to a finite game, solves this last game, and then maps its strategies with the original continuous game. We prove that with multiple types the problem is hard and only small settings can be solved in exact way. In the other cases, we need to resort to concepts of approximate equilibrium and to abstractions for reducing the size of the game tree.