Robustness of Intermediate Agreements for the Discrete Raiffa Solution (original) (raw)
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Axiomatization of the Discrete Raiffa Solution
This article provides an axiomatic characterization of the discrete Raiffa solution for two-person bargaining games. The extension to n > 2 players is straightforward. This solution had been introduced as one of four "arbitration schemes" by Raiffa (Arbitration schemes for generalized-two person games, 1951; Ann Math Stud 28: 1953). The axiomatization expresses a consistency property by which the standard midpoint solution for TU-bargaining games can be extended to general NTU-bargaining games. The underlying linear approximation from inside captures a dual view to the linear approximation from outside that underlies Nash's (Econometrica 18:155-162, 1950) axiomatization of his Nash solution that is also embodied in Shapley's (Utility comparison and the theory of games. In La Décision, pp. 251-263, 1969) λ-transfer principle and, even earlier, in a lemma by Harsanyi (Contributions to the theory of games IV, pp 325-355, 1959). Finally, the present axiomatization is compared with other ones in the literature that are motivated by Kalai (Econometrica 45:1623-1630 axiom of step-by-step negotiation.
Games and Economic Behavior, 2011
We define a family of solutions for n-person bargaining problems which generalizes the discrete Raiffa solution and approaches the continuous Raiffa solution. Each member of this family is a stepwise solution, which is a pair of functions: a step-function that determines a new disagreement point for a given bargaining problem, and a solution function that assigns the solution to the problem. We axiomatically characterize stepwise solutions of the family of generalized Raiffa solutions, using standard axioms of bargaining theory.
Two characterizations of the Raiffa solution
Economics Letters, 1980
It is shown when and how the two-person bargaining solution proposed by Raiffa can be generalized to the n-person case. Two characterizations are proposed involving the familiar axioms of Pareto-optimality, Symmetry, and Invariance, as well as two new Monotonicity axioms.
An axiomatization of the sequential Raiffa solution
Economics, 2009
IMW · Bielefeld University Postfach 100131 33501 Bielefeld · Germany email: imw@wiwi.uni-bielefeld.de http://www.wiwi.uni-bielefeld.de/imw/Papers/showpaper.php?425 ISSN: 0931-6558 ... An Axiomatization of the Sequential Raiffa Solution
A non-cooperative foundation for the continuous Raiffa solution
International Journal of Game Theory
This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl-Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player's opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes.
Robustness of Intermediate Agreements and Bargaining Solutions
2009
Most real-life bargaining is resolved gradually. During this process parties reach intermediate agreements. These intermediate agreements serve as disagreement points in subsequent rounds. We identify robustness criteria which are satisfied by three prominent bargaining solutions, the Nash, Proportional (and as a special case to the Egalitarian solution) and Discrete Raiffa solutions. We show that the "robustness of intermediate agreements" plus additional well-known and plausible axioms, provide novel axiomatizations of the above-mentioned solutions. Hence, we provide a unified framework for comparing these solutions' bargaining theories.
Three additive solutions of cooperative games with a priori unions
Applicationes Mathematicae, 2003
We analyze axiomatic properties of three types of additive solutions of cooperative games with a priori unions structure. One of these is the Banzhaf value with a priori unions introduced by G. Owen (1981), which has not been axiomatically characterized as yet. Generalizing Owen's approach and the constructions discussed by J. Deegan and E. W. Packel (1979) and L. M. Ruiz, F. Valenciano and J. M. Zarzuelo (1996) we define and study two other solutions. These are the Deegan-Packel value with a priori unions and the least square prenucleolus with a priori unions. Each of known cooperative game solutions is usually constructed by means of different methods with specific assumptions. In this paper we investigate a modification of three types of such solutions. The first of these solutions, the Banzhaf value of a player, was introduced by J. F. Banzhaf III (1965). It describes the average profit for a coalition after co-opting the player. Numerous applications of this concept are now known in the social and economic practice, because the relevant formulas represent a good instrument to investigate the power of participants in collective decision processes. In 1981 G. Owen constructed a modification of this notion-the Banzhaf value with a priori unions. The main assumption of this model is a partition of the set of players into nonempty disjoint subsets called a priori unions or precoalitions. The Banzhaf value with a priori unions was constructed on the basis of the "normal" Banzhaf value. E. Lehrer (1988) suggested the first axiomatization of the Banzhaf value. It is the unique solution with the following properties: dummy player, equal treatment, amalgamation and additivity. An axiomatization theorem for the
Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions
Social Choice and Welfare, 2015
We reconsider the class of weighted Kalai-Smorodinsky solutions of Dubra (2001), and using methods of Imai (1983), extend their characterization to the domain of multilateral bargaining problems. Aside from standard axioms in the literature, this result involves a new property that weakens the axiom Bilateral Consistency (Lensberg, 1988), by making the notion of consistency dependent on how ideal values in a reduced problem change relative to the original problem.