An axiomatization of the sequential 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.
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.
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.
A synthetic theory of sequential domains
Annals of Pure and Applied Logic, 2012
Synthetic Domain Theory (SDT) was originally suggested by Dana Scott as a uniform and logic based account of domain theory. In SDT the domain structure is intrinsic to a chosen class of sets with ''good'' properties. General SDT has a lot of different models which differ w.r.t. the ambient logic but also w.r.t. the PCF hierarchy, i.e. the finite type hierarchy over the partial natural numbers. From the early days of SDT we know satisfactory axiomatizations of SDT à la Scott which enforce the existence of ''parallel or''. A realizability model for SDT where the PCF hierarchy coincides with the strongly stable model of Bucciarelli and Ehrhard has been found independently by van Oosten (1999) [24] and Longley (2002) [13]. Their model is based on the typed partial combinatory algebra SA of concrete data structures and sequential algorithms. In this paper, we try to axiomatize this kind of Sequential SDT for the first time. Our approach is based on replacing SA by OSA, the observably sequential algorithms, as suggested by Cartwright et al. (1994) [3]. The axioms are inspired by the realizability model over OSA and its type O of observations with two global elements standing for nontermination and termination with error, respectively. Unlike in traditional domain theory this type is not a dominance because binary infimum is not available as an operation. This forces us to adapt some of the basic machinery of SDT.
Specifications Involving Initial Values (AB71)
F13.38> is called #@pre ). Its usefulness lies in the fact that it shortens specifications by doing away with the need for most specification variables, without having to drag in the full apparatus of the relational calculus. The extent to which this simple expedient cleans up formulae becomes clear if we observe that the classical criterion for repetition termination [2, (9, 28)] ### ## ## # # # # # ## # ## # #### # can now be shortened to ## # ## # ## # ### # # # (2) As suggested by these examples, the intention may be captured by considering # # as a specification variable and implicitly extending the precondition with a conjunct # # # # .In other word
Principles of iterational calculus
This is my translation from the Polish original of a series of papers by Lucjan Emil Boettcher (1872-1937), a Polish mathematician. The current file corresponds to Zasady rachunku iteracyjnego (cz\c e\'s\'c pierwsza i cz\c e\'s\'c druga) [Principles of iterational calculus (part one and two)], Prace Matematyczno Fizyczne, vol. X (1899 1900), pp. 65-86, 86-101 Zasady rachunku iteracyjnego (cz\c e\'s\'c III) [Principles of iterational calculus (part III)], Prace Matematyczno Fizyczne, v. XII(1901), p. 95-111 The electronic copies of the original Polish papers can be found Polish Digital Mathematics Library (DML-PL) http://matwbn.icm.edu.pl/ksiazki/pmf/pmf10/pmf1016.pdf http://matwbn.icm.edu.pl/ksiazki/pmf/pmf12/pmf1213.pdf
An equational axiomatization for multi-exit iteration
Information and Computation, 1997
This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the form X1=P1.X_1+Q1 ... Xn=Pn.Xn+Qn, where n is a positive integer and the Pi and the Qi are process terms. The addition of multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA*). As a consequence, the proof of completeness of the proposed equational axiomatization for this language, although standard in its general structure, is much more involved than that for BPA*. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke, and Ponse is also offered.