Bargaining Model on the Plane (Algorithmic and Computational Theory in Algebra and Languages) (original) (raw)
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Non-coalition non-zero-sum game related with arbitration procedure is considered. Two players (firlns) propose backslashSOIiotaiotae\backslash SOI\iota\iota ebackslashSOIiotaiotae solutions on the plane. The arbtrator has his own solution which is inodelling by random variables in the circle on the plane. As a solution of the conflict we use here the final offer arbitration procedure (FOA). The objective is the construction of Nash equilibrium. For two cases of thc random solution of the arbitrator we found the equilibrium in pure stratcgics.
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Decision theory includes arbitration, bargaining and game theory, whose relationships to each other are not well-understood. This paper introduces a particular weighted arbitration operator and applies it to King Solomon’s dilemma and Nash’s original bargaining problem. These applications allow a more meaningful comparison of the three theories and show that arbitration provides a more natural, simpler and flexible solution than the previously proposed bargaining and game theory solutions.
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The present paper provides three different supporting results for the Nash bargaining solution of n-person bargaining games. First, for any bargaining game there is defined a non-cooperative game in strategic form, whose unique Nash equilibrium induces a payoff vector that ...
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show that the Nash (1950) solution emerges as a limit point of a two player alternating o¤ers bargaining game when the time di¤erence between o¤ers goes to zero. establish the same result in the n¡player cake sharing set up. argue that noncooperative bargaining behavior á la Krishna-Serrano can be compactly described by means of von Neumann-Morgenstern stable set. This paper analyses the general problem. We show that a stable set exists and converges to the Nash solution in any smooth, compact and convex problem. A connection to the generalized Krishna-Serrano game is also established.
On the implementation of the L-Nash bargaining solution in two-person bargaining games
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The "Nash program" initiated by Nash (1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky , the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein's alternative offer game (1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard's game (1992) also implements the L-Nash solution.
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Two parties who discount the future negotiate on the partition of a pie of size one. Each party may in turn either make a concession to the other on what has not been conceded yet or call the arbitrator. In case of arbitration, each party endures a¯xed cost c, and what has not been conceded yet is shared equally between the two parties. The negotiation stops when either there is nothing left to be conceded or there is arbitration. The game is dominance solvable, and its solution has the following properties: 1) The equilibrium concessions are gradual and cannot exceed 4c, which results in delays; 2) The strategic behavior of the parties may involve \wars of attrition" because at some point each party is willing not to be the¯rst to concede.
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The bargaining problem deals with the question of how far a negotiating agent should concede to its opponent. Classical solutions to this problem, such as the Nash bargaining solution (NBS), are based on the assumption that the set of possible negotiation outcomes forms a continuous space. Recently, however, we proposed a new solution to this problem for scenarios with finite offer spaces de Jonge and Zhang (Auton Agents Multi-Agent Syst 34(1):1–41, 2020). Our idea was to model the bargaining problem as a normal-form game, which we called the concession game, and then pick one of its Nash equilibria as the solution. Unfortunately, however, this game in general has multiple Nash equilibria and it was not clear which of them should be picked. In this paper we fill this gap by defining a new solution to the general problem of how to choose between multiple Nash equilibria, for arbitrary 2-player normal-form games. This solution is based on the assumption that the agent will play either...
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We present an alternative formulation of the two-person equal area bargaining solution based on a dynamical process describing the disagreement point set. This alternative formulation provides an interpretation of the idea of equal concessions. Furthermore, it leads to an axiomatic characterization of the solution.