An axiomatization of the Euclidean compromise solution

The utopia point of a multicriteria optimization problem is the vector that specifies for each criterion the most favourable among the feasible values. The Euclidean compromise solution in multicriteria optimization is a solution concept that assigns to a feasible set the alternative with minimal Euclidean distance to the utopia point. The purpose of this paper is to provide a characterization of the Euclidean compromise solution. Consistency plays a crucial role in our approach.Consistency; Euclidean compromise solution; Multicriteria optimization

WPO, COV and IIA bargaining solutions

The class of bargaining solutions that are defined on the domain of finite sets of alternatives and satisfy Weak Pareto Optimality (WPO), Independence of Irrelevant Alternatives (IIA) and Covariance (COV), is characterized. These solutions select from the set of maximizers of a nonsymmetric Nash product -- i.e., from a nonsymmetric (multi-valued) Nash bargaining solution -- according to a specific decomposition of the indifference curves of this Nash product. We use this characterization in two ways. First, we derive consequences on this domain and on larger domains of compact (non-convex) bargaining problems, and show that most results in the literature are special cases and consequences of our central results -- in particular by adding continuity or symmetry axioms. Second, since the continuity axiom prevents nontrivial selections from the Nash bargaining solutions, we use the Axiom of choice to construct for example non-single-valued discontinuous WPO, IIA and COV bargaining solutions. It is conjectured that, in the case of two-person bargaining problems,the existence of such discontinuous bargaining solutions cannot be shown from the Zermelo-Fraenkel axioms for set theory without using the Axiom of Choice.mathematical economics;

Complaint, compromise and solution concepts for cooperative games

This thesis mainly focuses on solution concepts for cooperative games. We investigate the solution concepts concerning the complaints of players. Motivated by the work the procedural values, we study the formation of the grand coalition and define a new kind of complaint for individual players. We then reveal that the solutions for both models coincide with the ENSC value either based on the lexicographic criterion or the least square criterion. We propose the so called alpha-ENSC value by considering the egoism of players. We implement the alpha-ENSC value by means of optimization and also the satisfier of a set of properties. Following the similar idea, we propose two kinds of complaints for coalitions and define the optimal compromise values based on the lexicographic criterion. It turns out that the optimal compromise values coincides with the ENSC value and the CIS value under corresponding complaint. We show an application of the previous mentioned method. We introduce and axiomatize a class of cost sharing methods for polluted river sharing systems that consists of the convex combinations of the known Local Responsibility Sharing (LR) method and the Upstream Equal Sharing (UES) method. We also deals with the solution concepts based on the compromise between the ideal and minimal payoffs for players, which is inspired by the definition of the tau value but in a more general way. We reveal the relations between the general compromise value with several well known solution concepts. Furthermore, we investigate the solution concepts for cooperative games with stochastic payoffs. We focus on a subset of all allocations and introduce the stochastic complaint for players. Under the least square criterion, the most stable solutions and the fairest solutions are proposed. Moreover, the optimal solution stays the same whether the optimization model depends on the coalitions or individual players

A THEORY OF RATIONAL CHOICE UNDER COMPLETE IGNORANCE

This paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing ""limited information."" Specifically, we consider the limiting case of ""Complete Ignorance"" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. ""Rationality"" is conceptualized in terms of a ""Principle of Preference-Basedness,"" according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called ""Simultaneous Expected Utility Maximization"" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).

Potential Games and Interactive Decisions with Multiple Criteria.

Abstract: Game theory is a mathematical theory for analyzing strategic interaction between decision makers. This thesis covers two game-theoretic topics. The first part of this thesis deals with potential games: noncooperative games in which the information about the goals of the separate players that is required to determine equilibria, can be aggregated into a single function. The structure of different types of potential games is investigated. Congestion problems and the financing of public goods through voluntary contributions are studied in this framework. The second part of the thesis abandons the common assumption that each player is guided by a single goal. It takes into account players who are guided by several, possibly conflicting, objective functions.

Some analytical foundations of multidimensional scaling for ordinal data

"Ingwer Borg has contributed intensively and successfully to MDS, in theory and applications (e.g., Borg 1981a,b; Borg & Lingoes 1987; Roskam, Lingoes & Borg 1977). This paper offers some notes on the foundations of MDS, based on ranks of proximities. Two approaches are sketched, one working with contingencies of distance ranks, represented by boundaries in a dimensional space. The other approach uses the generalized betweenness relation, leading to configurations of object points. Details of the procedures and examples for both approaches are given for the one- and two-dimensional case. A procedure to find an optimal solution in a given dimensionality for data with random error is illustrated. The role of facet theory for theory testing by MDS is emphasized. Using the concepts of this paper will allow a fine-grained evaluation of a MDS solution for ordinal data." (author's abstract

Stability in shortest path problems

We study three remarkable cost sharing rules in the context of shortest path problems, where agents have demands that can only be supplied by a source in a network. The demander rule requires each demander to pay the cost of their cheapest connection to the source. The supplier rule charges to each demander the cost of the second-cheapest connection and splits the excess payment equally between her access suppliers. The alexia rule averages out the lexicographic allocations, each of which allows suppliers to extract rent in some pre-specified order. We show that all three rules are anonymous and demand-additive core selections. Moreover, with three or more agents, the demander rule is characterized by core selection and a specific version of cost additivity. Finally, convex combinations of the demander rule and the supplier rule are axiomatized using core selection, a second version of cost additivity and two additional axioms that ensure the fair compensation of intermediaries