The concept of and search for the fair distribution in cooperative games

Well-known conflict equilibria are used to formulate the concept of fair distribution, and a technique is proposed to find it in an arbitrary cooperative game. Any cooperative game is shown to have only one fair distribution, which can always be found from the formulas of conflict equilibrium theory. The study was carried out in line with the OITVS RAN program (Project No. 1-3) and was sponsored by the Russian Foundation for Basic Research (Project No. 06-01-00821). Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 131–141, November–December 2008.     

New Theory of Cooperative Games

The paper proposes a new theory of cooperative games based on the notions of conflict equilibrium alone. In this theory, the solution always exists, and it is often unique. The study was sponsored by the Russian Fund for Basic Research, Project No. 03-01-00329, and according to the OITVS Program of the Russian Academy of Sciences, Project No. 1–3. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 156–167, September–October 2005.     

Extending the theory of conflict equilibria

New symmetric coalition conflict equilibria are proposed. Together with already known equilibria, they allow one to find the strongest equilibrium in the majority of static and dynamic conflict problems. The study is carried out according to the OITVS RAN program, Project No. 1.3. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 80–89, March–April 2007.     

Associativity in combination of belief functions; a derivation of minC combination

 The nature of a contradiction (conflict) between two belief functions is investigated. Alternative ways of distributing the contradiction among nonempty subsets of frame of discernment are studied. The paper employes a new approach to understanding contradictions and introduces an original notion of potential contradiction. A method of an associative combination of generalized belief functions – minC combination and its derivation – is presented as part of the new approach. A proportionalization of generalized results is suggested as well. RID="*" ID="*" Support by Grant No. 1030803 of the GA AV ČR is acknowledged. I am grateful to Philippe Smets for a fruitful discussion on the topic.     

Expansion of classical noncooperative equilibrium and program differential games

A generalization of the classical noncooperative equilibrium is proposed. The new equilibrium exists in a broader class of games and problems of accepting proposals than the classical equilibrium. Applications of this equilibrium to program differential games are considered. This study was supported by the Russian Fund for Basic Research, Projects Nos. 97-01-00123 and 97-01-00962. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 105–115, July–Ausust, 2000.     

A Generalized Stochastic Method for Estimating the Characteristics of Potential Conflicts of a Controlled Air Traffic

A generalized stochastic method is presented for evaluating conflict characteristics such as conflict probability, collision probability, integral estimate of conflict probability on the near-collision time interval, and mean time to a predicted conflict. Equations are obtained for finding these conflict characteristics with regard for the stochastic nature and time correlation of the deviation from a planned controlled-flight trajectory. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 81–93, May–June 2005.     

Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order

A general method for solving game problems of approach for dynamic Volterra-evolution systems is presented. This method is based on the method of resolving functions [5] and the techniques of the theory of multivalued mappings. Properties of resolving functions are studied in more detail. Cases are separated where resolving functions can be derived in an analytical form. The scheme proposed covers a wide range of functional-differential systems, in particular, integral, integro-differential, and differential-difference systems of equations that describe the dynamics of a conflict controlled process. Game problems for systems with fractional Riemann-Liouville derivatives and regularized Dzhrbashyan-Nersesyan derivatives are studied in more detail. We will call them fractal games. An important role in the presentation of solutions of such systems is played by the generalized Mittag-Leffler matrix functions, which are introduced here. The use of asymptotic representations of these functions within the framework of the scheme of the method allows us to establish sufficient conditions of resolvability of game problems. A formal definition of parallel approach is given and illustrated by game problems for systems with fractional derivatives. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–32, May–June, 2000.     

Sufficient condition of completion of a pursuit in a nonlinear differential game

The sufficient condition of pursuit completion is proved for a nonlinear differential game on a smooth manifold with integral constraints on the players’ controls. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 134–140, November–December, 1999.     

Individually-optimal equilibria of noncooperative games in preference relations

For a game specified on a set of situations by preference relations of players, the individual optimum principle is considered that is a generalization of Nash, Berge, and Pareto optimum principles. On this basis, different types of equilibria and stability of game problems are characterized and investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 171–179, January–February 2009.     

Game approach problems for dynamic processes with impulse controls

This paper deals with game problems with impulse and geometric constraints on the players' controls. To analyze conflict-controlled processes with discontinuous trajectories, the method of resolving functions is used. This makes it possible to derive sufficient conditions of the game termination in a finite guaranteed time. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 135–156, January–February 2009.     

Realization of a bounded feedback in a nonlinear control problem

We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 108–116, January–February 2009.     

Generalized Cournot-Stackelberg-Nash equilibrium

The concept of the Cournot-Stackelberg-Nash equilibrium is proposed in which the leader’s payoff is no less than its payoff in the case of the Cournot-Nash equilibrium and the follower’s payoff is no less than its payoff in the case of the Stackelberg-Nash equilibrium. The generalized equilibrium coincides with the Cournot-Nash and Stackelberg-Nash equilibria for extreme values of a parameter. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 3–9, January–February 2006.     

Investigating equilibria stability on the basis of individual optimum principle

The so-called individual optimum principle is considered that is a generalization of the Nash and Pareto optimality principles. Based on it, the stability of various types of equilibria in game problems is characterized and investigated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 162–169, July–August 2007.     

General pattern of global system conflicts and global threats of the 21st century

Data on global conflicts took place from 750 B.C. up to now are analyzed and their general pattern is revealed. An attempt is made to foresee the next global conflict called the conflict of the 21st century. Its nature and main characteristics are analyzed. Main global threats are listed, and their impact on five groups of countries is determined using cluster analysis. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 87–99, September–October 2007.     

Macroeconomic governmental regulation and self-regulation of market equilibrium

Conditions for the gross domestic product (GDP) growth are established based on the developed mathematical model of market equilibrium regulation. Governmental regulation measures necessary to ensure GDP growth without overproduction crises are identified. The Ukrainian economy is used as an example to analyze market equilibrium regulation. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 106–121, September–October 2006.     

Game problems for systems with discontinuous dynamics

Differential games with discontinuous dynamics and a fixed termination time are considered. The operators describing the structure of a game are determined under certain conditions. The results obtained are illustrated by a model example. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 183–187, July–August, 2000.     

A linear differential game with a fixed termination time and restrictions on resources

A linear game with a fixed termination time and integral restrictions on player controls is considered. The pursuer constructs his control with knowledge of the control of the evader, and the evader uses information on all previous actions of his opponent at each instant of time. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 178–183, July–August, 2000.     

Antagonistic games with interval parameters

Antagonistic (matrix) games with payoff matrices given to within an interval are considered. The necessan and sufficient conditions of existence of solutions of such games are established. It is shown that the basic theorem of the Von Neumann theory is not valid for such games. The method of solution of an internal game by reducing it to two boundary exact games is proposed. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 149–160, July–August, 1999.     

The Cooperative Work of Gaming: Orchestrating a Mobile SMS Game

This paper focuses on orchestration work in the first iteration of a mobile game called Day Of The Figurines, which explores the potential to exploit text messaging as a means of creating an engaging gaming experience. By focusing on orchestration we are especially concerned with the ‘cooperative work that makes the game work’. While the assemblage or family of orchestration practices uncovered by our ethnographic study are specific to the game – including the ways in which behind the scenes staff make sense of messages, craft appropriate responses, and manage and track the production of gameplay narratives as the game unfolds – orchestration work is of general significance to our understanding of new gaming experiences. The focus on orchestration work reveals that behind the scenes staff are co-producers of the game and that the playing of games is, therefore, inseparably intertwined with their orchestration. Furthermore, orchestration work is ‘ordinary’ work that relies upon the taken for granted skills and competences of behind the scenes staff; ‘operators’ and ‘authors’ in this case. While we remain focused on the specifics of this game, explication of the ordinary work of orchestration highlights challenges and opportunities for the continued development of gaming experiences more generally. Indeed, understanding the specificities of orchestration work might be said to be a key ingredient of future development.     

Multivalued mappings and their selectors in the theory of conflict-controlled processes

Conflict-controlled processes with a cylindrical terminal set are considered. The method of resolving functions is used to obtain sufficient conditions of game termination in a guaranteed time in a class of stroboscopic strategies. These conditions are expressed as star-shapedness in certain cones or convex-valuedness of special multivalued mappings. A functional form of first direct Pontryagin method is derived. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 129–144, September–October 2007.