Lech Kruś

The role of multi-objective optimization in negotiation and mediation support

The paper reviews the methodology of multi-objective modeling and optimization used in decision support based on computerized analytical models (as opposed to logical models used in expert systems) that represent expert knowledge in a given field. The essential aspects of this methodology relate to its flexibility: modeling and optimization methods are treated not as goals in themselves but as tools that help a sovereign user (an analyst or a decision maker) to interact with the model, to generate and analyze various decision options, to learn about possible outcomes of these decisions. Although the applications of such methods in negotiation and mediation support is scarce yet, their flexibility increases essentially the chances of such applications. Various aspects of negotiation and mediation methods related to multi-objective optimization and game theory are also reviewed. A possible application of the MCBARG system for supporting negotiation related to the acid rain problem is briefly summarized.

Some New Results in Interactive Approach to Multicriteria Bargaining

A growing interest in methodology and applications of multiperson decision support systems is observed. In particular, approaches based on multicriteria optimization in group decision problems are subject of the papers by Korhonen, Moskowitz, Wallenius, Zionts (1986), Jarke, Jelassi, Shakun (1987), Kersten (1988), DeSanctis, Gallupe (1987), Korhonen and Wallenius (1989) and others. On the other hand there exists the developed theory of bargaining problem started by Nash (1950), continued by Raiffa (1953), Harsanyi, Selten (1972), Kalai, Smorodinsky (1975), Roth (1979), Thomson (1980), Imai (1983) and others. It seems to be reasonable to construct systems supporting negotiations combining the multicriteria optimization approach, and achievements of the theory and the practical experience in bargaining. However in this case new theoretical problems arise related to a generalization of the solution concepts and their axiomatization, a construction of interactive processes making easier the decision analysis of the bargaining situation and supporting the negotiation.

Multicriteria Decision Support in Bargaining, a Problem of Players’ Manipulations

The paper relates to construction of computer based systems for decision support in negotiations. A special case of distributed decision making — a class of bargaining situations is considered. DSS (decision support systems) utilizing mathematical model of decision situation can serve as a tool supporting unilateral and multilateral analysis made by negotiating sides (players). A problem of players’ manipulations is discussed. What does it mean fairness? How can players manipulate using DSS? Can we minimize the players’ manipulations applying game theoretical solution concepts in DSS? How can interactive procedures be constructed? This sort of questions is discussed in the paper.

On n-person noncooperative multicriteria games described in strategic form

This paper undertakes the problem of multicriteria decision support in conflict situations described as a noncooperative game. Construction of such a decision support requires the development of the noncooperative game theory to be generalized for the multicriteria case. New theoretical results in this case are presented. Features of the multicriteria noncooperative games are shown with use of a duopoly model in case of two goods and two criteria of each player. Concepts of the decision support are discussed.

Fiscal-Monetary Game Analyzed with Use of a Dynamic Macroeconomic Model

The paper deals with the fiscal-monetary game. In the game the fiscal and the monetary authorities take decisions on the choice of the optimum strategy from the point of view of realization of their respective economic objectives. A macroeconomic model has been constructed and used to represent the interrelations between, on the one hand, the instruments of fiscal policy and of the monetary policy, and, on the other hand – the economic effects resulting from their application. The best response strategies of the authorities and the Nash equilibrium state are analyzed. The simulation results obtained indicate that in a general case the Nash equilibrium is not Pareto optimal. It means that the policies should be coordinated and that respective negotiations leading to a Pareto-optimal consensus are needed.

Solution concepts in multicriteria cooperative games without side payments

The paper presents a study of n-person cooperative games without side payments in the case of vector payoffs of players. Recently, much attention has focused on problems with vector payoffs in the field of game theory, since multicriteria models can better apply to real-world situations. In the paper, solution concepts are formulated and analysed. A nucleolus concept is proposed which is invariant on affine transformation of criteria and coincides with the Schmeidler nucleolus in case of unicriteria games with payments and with Raiffa-Kalai-Smorodinsky solution in case of unicriteria bargaining problem.

Selecting the Efficient Market Indicators in the Trading System on the Forex Market

A concept of the trading system is proposed in which only selected market indicators generating the most beneficial recommendations for traders are included. The proposal can be implemented as an additional module included in the existing trading systems. We present a procedure, in which for a given initially considered indicators, only the selected ones being the most beneficial for a trader for a given time window are derived. In the procedure, an efficiency of initially considered indicators is verified in each time window on the basis of their past performance. Using the verification results the ranking and selection of the best ones is made.

On Computer-Based Support in Noncooperative Multicriteria Games

The paper deals with noncooperative games in which each player has some number of criteria measuring his payoff. A decision support system is considered as a computer-based tool that allows the players to make an analysis of the conflict situation, taking into account their preferences. The analysis can be done using an interactive, learning procedure utilizing methods of multicriteria optimization. An algorithm supporting analysis of payoffs in the multicriteria game and derivation of the best response strategies satisfying preferences of the players is proposed. The reference point approach with application of the respected achievement function is used in the interactive procedure in which payoffs of players are calculated closely to their preferences. The algorithm utilizes new theoretical results of the theory of noncooperative games. The results presented in the form of theorems include parametric characterization of the multicriteria gains representing preferences of the players and show relations among equilibria in the multicriteria games and the respective classical games.

Supporting Cooperative Decisions with a Multicriteria Generalization of the Nash Solution

A decision situation is considered in which two decision makers negotiate cooperation conditions to realize a joint project. Each decision maker has his own set of criteria measuring results of the cooperation. The situation is modeled as the multicriteria bargaining problem. A special multiround mediation procedure is presented which can be implemented in a computer-based system. According to the procedure the system supports multicriteria analysis made by the decision makers and generates mediation proposals. The mediation proposals are derived on the basis of the original solution to the multicriteria problem, presented in the paper. The solution expresses preferences of the decision makers. It generalizes the classic Nash solution concept on the multicriteria case.

An Interactive Method for Decision Support in a Two-Person Game with an Example from Regional Planning

The basic idea of our interactive method was proposed by Wierzbicki (1982). The method was implemented and several modifications tested by Fortuna and Kruś (1983). A number of experiments based on this method have been carried out for a regional planning problem. This paper presents the results of one such experiment. A general outline of the method is also given.