This paper reexamines the game-theoretic bargaining theory from logic and Artificial Intelligence perspectives. We present an axiomatic characterization of the logical solutions to bargaining problems. A bargaining situation is described in propositional logic with numerical representation of bargainers’ preferences. A solution to the n-person bargaining problems is proposed based on the maxmin...

Note: This is a only a draft version, so there could be flaws. If you find any errors, please do send email to [email protected]. A more thorough version would be available soon in this space. The Nash bargaining problem represents one of the earliest and most influential results in cooperative game theory. Given two rational and intelligent players and a set of feasible allocations from a...

We consider a non-cooperative coalitional bargaining game with random proposers to bridge a gap between non-cooperative game theory and cooperative game theory. Theoretical results include the existence of a stationary subgame perfect equilibrium (SSPE) and the characterization of the grand-coalition SSPE as a generalized Nash bargaining solution, provided that it lies in the core. We also prov...

The theory of bargaining as formulated by Nash (1950, 1953) has developed along two routes. One is axiomatic (e.g., Nash 1950; Kalai and Smorodinsky 1975; Roemer 1988). Here, the negotiation process underlying the bargaining is only implicit. The idea is to try to characterize the negotiated outcome (the solution) through a set of axioms without formally modeling the process. The advantages of ...

Experiments with the ultimatum game—where one party can make a take-it-or-leave-it offer to a second party on how to split a pie—illustrate that conventional game theory has been wrong in its predictions regarding the simplest of bargaining settings: Even when one party has enormous bargaining power, she may be able to extract all the surplus from trade, because the second party will reject gro...

A new game theoretic analysis of finite horizon, complete information bargaining is advanced. The extensive form reflects an attempt to model unstructured negotiations, in which the negotiants can gain no artificial advantage from the details of the bargaining protocol. Conditions are identified under which the game is dominance solvable in the sense that iterative deletion of weakly dominated ...

Power indices suggest that adding new members to a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the original members may actually gain even if voters are bargaining over a fixed budget. We show that this phenomenon can occur as an equilibrium of a non-cooperative bargaining game based on the...

We present a new technique for analyzing the rate of convergence of local dynamics in bargaining networks. The technique reduces balancing in a bargaining network to optimal play in a randomturn game. We analyze this game using techniques from martingale and Markov chain theory. We obtain a tight polynomial bound on the rate of convergence for a nontrivial class of unweighted graphs (the previo...

Whereas orthodox game theory relies on the unrealistic assumption of (commonly known) perfect rationality, the participants in game-playing experiments are, at best, rational only within limits. This makes it necessary to supplement orthodox game theory with a behavioral theory of game playing. This contribution first points out that this applies also to (one person-) decision theory. After rev...