Algorithms for non-convexS n -games

We considerS-games in which the setS is the parametric curve{(p ₁ (t),, p _n(t)): t [0, 1]} and thep _i(t) are real polynomials. These games will be referred to asS _n -games. Two iterative algorithms are given in the case ofn = 2. One gives linear convergence to an optimal of player I, and the other gives monotone convergence. In the case of arbitraryn we give an algorithm of the cutting plane family converging to the value. The principal features of this algorithm are that the hyperplanes arise intrinsically as tangents to an associated concave function which is not in general differentiable, and the linear subproblems arise as matrix games. Because of the latter property inactive constraints are in principle automatically dropped. We give a game theoretic convergence proof. This algorithm may be used multiply for bounding optimals of player I.     

强场下的Li-like氖复合机制X光激光的数值模拟

论述了隧道电离和阈上电离加热过程。并把此二过程加到一个non-LTE平均原子模型,用此模型来研究强场下光致电离类锂氖复合机制X射线激光。计算结果表明,当驱动激光脉冲为100fs、波长为0.248μm、功率密度为2×10¹⁷Wcm^-2,氖气的密度为10^-3gcm^-3时,类锂氖精细结构跃迁3d_5/2→2p_3/2(λ=98Å)的最大增益系数约为100cm^-1,其维持时间约为1.5ps。     

Coordination in decentralized assembly systems with uncertain component yields

The literature on assembly systems with random component yields has focused on centralized systems, where a single decision maker chooses all components’ production quantities and incurs all the costs. We consider a decentralized setting where the component suppliers choose their production quantities based solely on their own cost/reward structure, and the assembly firm makes ordering decisions based on its own cost/reward structure. When the suppliers control their inputs but the outputs exhibit random yields, coordination in such systems becomes quite complex. In such situations, incentive alignment control mechanisms are needed so that the suppliers will choose production quantities as in the centralized system case. One such mechanism is to penalize the supplier with the worse delivery performance. We analyze the conditions under which system coordination is achieved while respecting participation constraints. Further, we determine the optimal component ordering policy for the assembly firm and derive the optimal coordinating penalties.     

On extremal pure Nash equilibria for mixed extensions of normal-form games

In this paper we derive conditions under which mixed extensions of normal-form games have least and greatest Nash equilibria in pure strategies, and either of them gives best utilities among all mixed Nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings, and the values of utility functions are in separable ordered Banach spaces. The obtained results are applied to supermodular normal-form games whose strategy spaces are multidimensional.     

Relational dominant strategy equilibrium as a generalization of dominant strategy equilibrium in terms of a social psychological aspect of decision making

In this paper, incorporating a social psychological aspect of decision making, called attitudes, into analysis of games in normal form, the author proposes a new equilibrium concept, called relational dominant strategy equilibrium (RDSE). The author also analyzes relationships between RDSE and dominant strategy equilibrium (DSE), and shows the following fact: RDSE coincides with DSE under a condition on attitudes of players. The story of “The Gift of the Magi” by Henry is analyzed and given a convincing interpretation using the proposed equilibrium concept.     

A duopoly model with heterogeneous congestion-sensitive customers

This paper analyzes a model with two firms (providers), and two classes of customers. These customers classes are characterized by their attitude towards ‘congestion’ (caused by other customers using the same resources); a firm is selected on the basis of both the prices charged by the firms, and the ‘congestion levels’. The model can be represented by a two-stage game: in the first providers set their prices, whereas in the second the customers choose the provider (or to not use any service at all) for given prices. We explicitly allow the providers to split their resources, in order to serve more than just one market segment. This enables us to further analyze the Paris metro pricing (Pmp) proposal for service differentiation in the Internet.     

Depreciation games

The main aim of this paper is to show how Game Theory can be used in the day-to-day running of a company. No precedent, as far as we know, in the literature of the application of Cooperative Game Theory in order to obtain new depreciation methods for a fixed asset which is owned by a company. To this end, we will first illustrate the usual depreciation methods employed in accountancy. Then, with the objective of finding new depreciation methods, we will establish the relationship between Game Theory and Accountancy. On the basis of this relationship we introduce some new depreciation methods. Finally, a family of solutions is defined which improves the properties of traditional and previously introduced methods. Financial support from the Generalitat Valenciana through project GV05/077 is gratefully acknowledged by J. Aparicio. Financial support from the Generalitat Valenciana through project GRUPOS04/79 and from the Ministerio de Educación y Ciencia through project HI2002/0032 are gratefully acknowledged by J. Sánchez-Soriano.     

An equitable solution for multicriteria bargaining games

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

Quantitative agent-based firm dynamics simulation with parameters estimated by financial and transaction data analysis

Firm dynamics on a transaction network is considered from the standpoint of econophysics, agent-based simulations, and game theory. In this model, interacting firms rationally invest in a production facility to maximize net present value. We estimate parameters used in the model through empirical analysis of financial and transaction data. We propose two different methods (analytical method and regression method) to obtain an interaction matrix of firms. On a subset of a real transaction network, we simulate firm's revenue, cost, and fixed asset, which is the accumulated investment for the production facility. The simulation reproduces the quantitative behavior of past revenues and costs within a standard error when we use the interaction matrix estimated by the regression method, in which only transaction pairs are taken into account. Furthermore, the simulation qualitatively reproduces past data of fixed assets.