Cooperative Game Theory Methods in the Analysis of Economic and Political Interaction at the International Level

The main attention is focused on the application of the methods of the theory of cooperative games to the analysis of the relationship between the leading actors in international politics, or, as they say, the centers of power. One of the speci c features of the modern world is the "triple type" of conflicts. Namely, at different levels of relationships, con ict situations with three participants (players) are often observed. Such situations are objectively characterized by the formation of possible paired coalitions, rejecting the third. The main idea of the proposed approach is the transition from cooperative games with deterministic values of characteristic functions to their counterparts with stochastic values. One of the possible concepts of solutions for stochastic cooperative games is associated with the extension of the ideas of the bargaining set to them. Problems of development and interpretation of this concept in the case of a triple conflict of international centers of power. An essential advantage of this approach is the possibility of meaningful interpretations of the significance level, at which the conditions for the rationality of the shares of the players should be ensured, taking into account the non-determinism of their utilities given by the characteristic function.

On the Core, Bargaining Set and the Set of Competitive Allocations of Fuzzy Exchange Economy with a Continuum of Agents

In this paper, we present a new model closer to the real-life — called the fuzzy exchange economy with a continuum of agents (FXE-CA) — that combines fuzzy consumption and fuzzy initial endowment with the agent’s fuzzy preference in the fuzzy consumption set. To characterize the fuzzy competitive allocations of the FXE-CA, we define the indifference fuzzy core of a FXE-CA as the set of all fuzzy allocations that cannot be dominated by any coalition of agents. We also propose the Mas-Colell indifference fuzzy bargaining set, in which no coalition has a justified objection at a fuzzy allocation against any other coalition. Finally, we verify that the indifference fuzzy core and the indifference fuzzy bargaining set of a FXE-CA coincide with the set of all fuzzy competitive allocations under some conditions, respectively. This indicates that the agents unanimously distribute the fuzzy competitive allocations of a FXE-CA.

Game Theory

Now in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reference for researchers.

Reactive and Semi-Reactive Bargaining Sets for Games with Restricted Cooperation

Generalizations of reactive and semi-reactive bargaining sets of TU games are defined for the case when objections and counter-objections are permitted not between singletons but between elements of a family of coalitions [Formula: see text] and can use coalitions from [Formula: see text]. Necessary and sufficient conditions on [Formula: see text], [Formula: see text] that ensure existence results for generalizations of the reactive bargaining set and of the semi-reactive barganing set at each TU game [Formula: see text] with nonnegative values are obtained. The existence conditions for the generalized reactive bargaining set do not coincide with existence conditions for the generalized kernel and coincide with conditions for the generalized semi-reactive bargaining set only if [Formula: see text] and [Formula: see text]. The conditions for the generalized semi-reactive bargaining set coincide with conditions for the generalized classical bargaining set that were described in the previous papers of the author. For monotonic [Formula: see text], the condition on [Formula: see text] for existence of the generalized semi-reactive bargaining sets on the class of games with nonnegative values is also necessary and sufficient on the class of simple games, but similar result for the generalized classical bargaining sets is proved only for [Formula: see text].