Games,Kernels, and Antitone Operations

In this note we want to point out the usefulness of antitone operations in the study of games on graphs. We demonstrate this by proving, among others, the generalizations from games to antitone operations of theorems stated by Fraenkel. This perspective makes also clear the general nature of some problems by separating what is general and what is particular.     

半马尔可夫对策

本文考虑半马尔可夫随机对策.在一定条件下,我们证明随机对策有值函数,两个局中人相对于折扣报酬都有最优策略.     

Convergence in almost periodic cooperative systems with a first integral

This paper is to investigate the asymptotic dynamics in almost periodic cooperative systems with a first integral. By appealing to the theory of skew-product semiflows we establish the asymptotic almost periodicity of bounded solutions to such systems, which extends the existing convergence results for time independent and periodic cooperative systems with a first integral and proves a conjecture of B. Tang, Y. Kuang and H. Smith in SIAM J. Math. Anal., 24 (1993), 1331-1339.

     

The Böhm–Bawerk horse market: a cooperative analysis

Single–valued solutions for the case of two-sided market games without product differentiation, also known as Böhm–Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the τ value, and is thus the midpoint of the core. The Shapley value is in the core only if the game is a square glove market, and in this case also coincides with the two aforementioned solutions.Institutional support from research grants BEC 2002-00642, FEDER and SGR2001-0029 is gratefully acknowledged     

Pricing Behaviors on Networks: Some General Results for Two-way Networks

In this paper, we study monopolistic pricing behaviors within a two-way network. In this symbiotic production system, independent decision centers carry out an activity which concurs to the production of different system goods. The players are assumed to know the whole network. Due to this rationality, they try to capture a share of the profit of the firms who sell the system goods to the consumers. These double marginalization behaviors are studied within very general networks. Conditions with ensure existence and uniqueness are discussed. We even provided a complete characterization of an equilibrium. Potential applications are also discussed     

Terror and Counterterror Operations: Differential Game with Cyclical Nash Solution

The purpose of this paper is to study efficient measures to combat terror. To choose efficient actions against terror organizations, the response of terrorists has to be taken into consideration. Thus, an appropriate framework to study the intertemporal strategic interactions of Western governments and terror organizations is dynamic game theory. Using the open-loop Nash solution concept, it turns out that the system may exhibit long-run persistent oscillations. However, transitory behavior is nonunique.     

Relaxation in cooperative systems: Use of mixture virial coefficients

The coefficients in power series in the variable time that describe relaxation in a cooperative system can be calculated using a combinatorial approach where one considers how many ways one can introduce a given number of properly defined events in a system. The coefficients obtained in this manner can be related to the equilibrium virial coefficients for a mixture. If one assumes rapid internal equilibration, the relaxation process can be expressed completely in terms of the viral coefficients for a mixture with at most one solute particle, or, in some cases, just the virial coefficients for a single-component system. Thus, equilibrium virial coefficients can give useful information about the time evolution of processes in cooperative systems.     

Economical tight examples for the biased Erd?s-Selfridge theorem

A positional game is essentially a generalization of tic-tac-toe played on a hypergraph (V,F). A pivotal result in the study of positional games is the Erd?s-Selfridge theorem, which gives simple criteria for the existence of a Breaker's winning strategy on a hypergraph F. It has been shown that the Erd?s-Selfridge theorem can be tight and that numerous extremal systems exist for that theorem. We focus on a generalization of the Erd?s-Selfridge theorem proven by Beck for biased (p:q) games, which we call the (p:q)-Erd?s-Selfridge theorem. We show that for pn-uniform hypergraphs there is a unique extremal system for the (p:q)-Erd?s-Selfridge theorem (q?2) when Maker must win in exactly n turns (i.e., as quickly as possible).     

Alliances, partnerships and the Banzhaf semivalue

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.