Axioms concerning uncertain disagreement points in 2-person bargaining problems

We consider 2-person bargaining situations in which the feasible set is known, but the disagreement point is uncertain. We investigate the implications of various axioms concerning uncertain disagreement points and characterize the family of linear solutions, which includes the egalitarian, lexicographic egalitarian, Nash, and Kalai-Rosenthal solutions. We also show that how the important subfamilies (or members) of this family can be singled out by imposing additional axioms or strengthening the axioms used in the characterizations.

Risk aversion for losses and the Nash bargaining solution

We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses.

Forming the Bargaining Win-Win-Win Papakonstantinidis Tripartite Focal Points Analysis of the Bibliography

Focal points, in a period that people are reviewing their priorities, in a more social direction due to thepandemic, as a global threat and catastrophe, are examined in this work, under the prism of the win -win-winpapakonstantinidis perception, closer to the tripartite global concept. Identity, social justice, and the community spirit seem to be the new-day priorities in a “pandemic period”, under a win-win-win perception: the last one is analyzed through the sequence toward the limit ln2 =0,693 and the disagreement point in a bargain. Finally, its philosophical perspective is analyzed through the tripartite thesis. Research on pandemic “behavior” is provided at the end of this work.

A Perspective-Invariant Approach to Nash Bargaining

The Nash axioms lead to different results depending on whether the negotiation is framed in terms of gains relative to no agreement or in terms of sacrifices relative to an ideal. We look for a solution that leads to the same result from both perspectives. To do so, we restrict the application of Nash’s IIA axiom to bargaining sets where all options are individually rational and none exceed either party’s ideal point. If we normalize the bargaining set so that the disagreement point is (0, 0) and maximal gains are (1, 1), then any perspective-invariant bargaining solution must lie between the Utilitarian solution and the maximal equal-gain (minimal equal-sacrifice) solution. We show that a modified version of Nash’s symmetry axiom leads to the Utilitarian solution and that a reciprocity axiom leads to the equal-gain (equal-sacrifice) solution, both of which are perspective invariant. This paper was accepted by Joshua Gans, Business Strategy.

Bargaining Problem: Does Disagreement Point Result from Value Control or Value Deprivation? or, Does Value Control (or Value Deprivation) Result from Disagreement?- A Win-Win-Win Papakonstantinidis Approach

The article concerns the Convergence policy as a prospect for the future economic view, as it deals with the value deprivation. Value deprivation arises due to the lack of goods-values which are available to a higher economic class of consumers as a point of disagreement in a cause-effect relationship or even vice versa, within a huge bargain between 2 having opposing interests, as the result of value control. State of deprivation, Value destruction, and disagreement point are examined separately, and so is the methodological tool, called the “win-win-win Papakonstantinidis model” intended for investigating the impact of the value control to the disagreement point I. Value destruction can be turned into a Value creating opportunity. thus the disagreement point. The win-win-win Papakonstantinidis model is used as a methodological tool for examining the impact of the control value to the disagreement point. A strong correlation between disagreement and value control is found, through the research on 30 CEO’s all over Europe

Negotiating transfer pricing using the Nash bargaining solution

This paper analyzes and proposes a solution to the transfer pricing problem from the point of view of the Nash bargaining game theory approach. We consider a firm consisting of several divisions with sequential transfers, in which central management provides a transfer price decision that enables maximization of operating profits. Price transferring between divisions is negotiable throughout the bargaining approach. Initially, we consider a disagreement point (status quo) between the divisions of the firm, which plays the role of a deterrent. We propose a framework and a method based on the Nash equilibrium approach for computing the disagreement point. Then, we introduce a bargaining solution, which is a single-valued function that selects an outcome from the feasible pay-offs for each bargaining problem that is a result of cooperation of the divisions of the firm involved in the transfer pricing problem. The agreement reached by the divisions in the game is the most preferred alternative within the set of feasible outcomes, which produces a profit-maximizing allocation of the transfer price between divisions. For computing the bargaining solution, we propose an optimization method. An example illustrating the usefulness of the method is presented.

Intrinsic Comparative Statics of a Nash Bargaining Solution

A generalization of the class of bargaining problems examined by Engwerda and Douven [(2008) On the sensitivity matrix of the Nash bargaining solution, Int. J. Game Theory 37, 265–279] is studied. The generalized class consists of nonconvex bargaining problems in which the feasible set satisfies the requirement that the set of weak Pareto-optimal solutions can be described by a smooth function. The intrinsic comparative statics of the aforesaid class are derived and shown to be characterized by a symmetric and positive semidefinite matrix, and an upper bound to the rank of the matrix is established. A corollary to this basic result is that a Nash bargaining solution is intrinsically a locally nondecreasing function of its own disagreement point. Other heretofore unknown results are similarly deduced from the basic result.

Game-Theoretic Models for Cooperative Equilibrium Solutions of Interacting Engineering Sub-Systems

Although game-theoretical models to study social and economic problems have existed for a long time, they have been sparsely used for the design of engineering systems. This is due to the significant theoretical hurdles posed by game formulations for real engineering environments /problems. In this study we show our first attempt at adapting the frame-work of game-theoretical models for engineering problems, in particular the aero-mechanical optimization of a notional turbine blade. We pose the design problem as a series of games, starting with the determination of the Pareto front, the non-cooperative (disagreement) point and the optimal solution as the tangent intersection of the Pareto front and contours of the overall system objective. We present gradient-based algorithms that determine the Pareto front, the non-cooperative solution and the tangent solution. The solution to this series of games provides the basis of a new equilibrium concept namely, System Optimal Cooperative Solution (SOCS), which is the central theme of this paper. Finally we compare the SOCS solution against other cooperative solutions like Nash-Bargaining [1]. The results of this study show that in engineering environments previously known cooperative solutions like Nash-Bargaining and Kalai-Smordinsky [2] are not that important while the notion of a System Optimal Cooperative Solution, SOCS, is the equilibrium solution of relevance. For the particular example we consider, the SOCS is shown to be more favoring the aerodynamic performance when compared against the Nash-Bargaining equilibrium solution.