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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. [ABSTRACT FROM AUTHOR]

This paper presents a special class of equilibria in finite strategy noncooperative games, which are extensions of the traditional Nash equilibrium solution. An underlying role in these equilibria play the assumed extended models of players' rationality principles which admit their non-myopic behaviour. The crucial idea is that players possessing some information about their opponents and the game itself can forecast the consequences of their choices by analyzing the ‘move-countermove’ possible sequences and accordingly predict the stability of game outcomes. The class of discussed equilibria besides the classical Nash equilibrium includes all the solutions considered in metagame and hypergame theories, and its determinants allow for a useful characterization of new potential equilibria concepts in modeled real-life conflicts. For specific equilibrium concepts, their individual properties are discussed and some analytical characterizations are provided. The paper concludes with the description of a computer-based procedure developed for calculating different kinds of generalized equilibrium points. Possible applications of this procedure within simulation and gaming are briefly discussed. [ABSTRACT FROM AUTHOR]

This paper deals with downgrading the 1-median, i.e., changing values of parameters within certain bounds such that the optimal objective value of the location problem with respect to the new values is maximized. We suggest a game-theoretic view at this problem which leads to a characterization of an optimal solution. This approach is demonstrated by means of the Downgrading 1-median problem in the plane with Manhattan metric and implies an $\mathcal {O}(n\log^{2}n)$ time algorithm for this problem. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced by Bilbao (Cooperative Games on Combinatorial Structures, ) , we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical Shapley value for cooperative games. The main result of the paper is an axiomatic characterization of this value. [ABSTRACT FROM AUTHOR]

The coordination of strategies in a cooperative game, when some players decide to act together, is the basis of the partnership notion. Nevertheless, in some situations, it may be more convenient to form an effective coalition or alliance. In this work, we consider the Banzhaf semivalue and use it to discuss the convenience to form either partnerships or alliances, especially in simple games. Throughout the paper, some mathematical properties of the Banzhaf semivalue, in relation with the partnership formation, are derived. [ABSTRACT FROM AUTHOR]

In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space. Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic cooperative games among others are particular cases of this general theory. [ABSTRACT FROM AUTHOR]

This paper considers a special class of sequencing situations with two parallel machines in which each agent has precisely two jobs to be processed, one on each machine. The costs of an agent depend linearly on the final completion time of his jobs. We describe a procedure that provides an optimal processing order of the jobs for some particular classes. Furthermore, we study cooperative games arising from these sequencing situations. Our main result will be on the balancedness of these games. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new coalitional value in the context of TU games with an a priori system of unions, which it is called the symmetric coalitional Banzhaf value. This value satisfies the property of symmetry in the quotient game, the quotient game property, and it is a coalitional value of Banzhaf. Several characterizations are provided and two political examples illustrate the differences with respect to the Owen value and the Banzhaf-Owen value. [ABSTRACT FROM AUTHOR]

In this paper we study how to distribute the cost caused by the delay of a project among the firms which are responsible for it. We present two rules, one based on serial cost sharing problems and the other, in game theory. Moreover, we introduce some desirable properties, inspired by well-known principles, and study which of them are satisfied by the rules. [ABSTRACT FROM AUTHOR]

Processes of iterated elimination of strategies that are not best responses are studied. Some suggestions are made about how rational players may use their mutual knowledge about game and behavior. [ABSTRACT FROM AUTHOR]

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results. [ABSTRACT FROM AUTHOR]

In this article, we generalize the position value, defined by Meessen (Master's thesis, ) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539-556, ). We provide two characterizations of this new allocation rule. Following in Slikker's (International Journal of Game Theory 33:505-514, ) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473-489, ) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. [ABSTRACT FROM AUTHOR]

When analyzing mathematically decision mechanisms ruled by voting it is sometimes convenient to include abstention as a possible alternative for the voters. In classical simple games, abstention, if considered, is formally equivalent to voting against the proposal. Simple games with alternatives are useful to study voting systems where abstention does not favour any of the options. In this work, we axiomatically characterize the Shapley–Shubik index for simple games with alternatives and apply it to an example taken from real life. [ABSTRACT FROM AUTHOR]

Two-person zero-sum stochastic games with finite state and action spaces are considered. The expected average payoff criterion is introduced. In the special case of single controller games it is shown that the optimal stationary policies and the value of the game can be obtained from the optimal solutions to a pair of dual programs. For multichain structures, a decomposition algorithm is given which produces such optimal stationary policies for both players. In the case of both players controlling the transitions, a generalized game is obtained, the solution of which gives the optimal policies. [ABSTRACT FROM AUTHOR]