Numerical techniques for finding equilibrium in von Neumann’s model

Numerical methods for finding an equilibrium position in von Neumann’s multisector economy model are proposed. They can be implemented using computers with floating-point arithmetic. The proposed methods are based on reducing the problem to solving the corresponding matrix games.     

Axiomatizations of the core on the universal domain and other natural domains

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse reduced game property, and the reconfirmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games. Received September 1999/Final version December 2000     

Coordination mechanisms for inventory control in three-echelon serial and distribution systems

This paper is concerned with the coordination of inventory control in three-echelon serial and distribution systems under decentralized control. All installations in these supply chains track echelon inventories. Under decentralized control the installations will decide upon base stock levels that minimize their own inventory costs. In general these levels do not coincide with the optimal base stock levels in the global optimum of the chain under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. To remove this cost inefficiency, two simple coordination mechanisms are presented: one for serial systems and one for distribution systems. Both mechanisms are initiated by the most downstream installation(s). The upstream installation increases its base stock level while the downstream installation compensates the upstream one for the increase of costs and provides it with a part of its gain from coordination. It is shown that both coordination mechanisms result in the global optimum of the chain being the unique Nash equilibrium of the corresponding strategic game. Furthermore, all installations agree upon the use of these mechanisms because they result in lower costs per installation. The practical implementation of these mechanisms is discussed.     

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.     

舰艇对抗微分对策建模研究

编队舰艇对抗攻击瞬时运动状态过程的完整描述是一个尚未很好解决的技术难点，本就驱逐舰对多艘导弹快挺对抗攻击建模问题进行了研究，建立了攻击时间尽可能短的定量微分对策模型，并给出了具体实现方法，中模型和方法可为实时舰艇作战指挥系统的研制、开发提供技术支持及理论依据。     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

An algorithm of evolutionarily stable strategies for the single-population evolutionary game

In this paper, we study the single-population evolutionary game and construct an algorithm to find evolutionarily stable strategies. Finally, by an example, we illuminate the computing process of algorithm.     

The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. Communicated by A. Zhou.     

Efficiency of Classical and Quantum Games Equilibria

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied.     

Failure prediction of hybrid composite using Arcan's device and Drucker-Prager model

Hybrid composites are promising materials due the possibility of combining the properties of different fiber types with those of the polymeric matrix. The higher number of phases involved in this kind of material and the hydrostatic component of polymer behavior make it unfeasible to use classic models for failure prediction, like the Von Mises or Treska models. In this study, a modified Arcan's device was applied for mechanical characterization of a polymeric blend matrix composite reinforced with randomly oriented continuous fibers (a clutch disc) to generate combined loading conditions. Experimental results were applied in the Von Mises and Drucker-Prager theoretical models for failure prediction. Additionally, scanning electron microscopy (SEM) was applied to analyze the fracture surface. The failure envelope provided by the Drucker-Prager model fit the experimental results, making it a promising tool for predicting the behavior of this type of hybrid composite.