Several extensions of the Abian–Brown Fixed Point Theorem and their applications to extended and generalized Nash equilibria on chain-complete posets

In this paper, we provide several extensions of the Abian–Brown Fixed Point Theorem from single-valued mappings to set-valued mappings on chain-complete posets. Then we examine some non-monetized, non-cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets. By applying the extensions of the Abian–Brown Fixed Point Theorem and by applying the order-preserving property of mappings, we prove some existence theorems of extended and generalized Nash equilibria for non-monetized, non-cooperative games on chain-complete posets.     

Determination of Stackelberg–Nash equilibria using a sensitivity based approach

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating the RRS are compared on three example problems to find Nash and Stackelberg solutions. For the examples presented, it is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) has the ability to find multiple Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate nonlinear RRS, and (v) on one example problem, found a Nash solution better than the one reported in the literature.     

Joint optimization of product family configuration and scaling design by Stackelberg game

Product family design is generally characterized by two types of approaches: module-based and scale-based. While the former aims to enable product variety based on module configuration, the latter is to variegate product design by scaling up or down certain design parameters. The prevailing practice is to treat module configuration and scaling design as separate decisions or aggregate two design problems as a single-level, all-in-one optimization problem. In practice, optimization of scaling variables is always enacted within a specific modular platform; and meanwhile an optimal module configuration depends on how design parameters are to be scaled. The key challenge is how to deal with explicitly the coupling of these two design optimization problems.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches

We demonstrate how the problem of determining the ask price for electricity swing options can be considered as a stochastic bilevel program with asymmetric information. Unlike as for financial options, there is no way for basing the pricing method on no-arbitrage arguments. Two main situations are analyzed: if the seller has strong market power he/she might be able to maximize his/her utility, while in fully competitive situations he/she will just look for a price which makes profit and has acceptable risk. In both cases the seller has to consider the decision problem of a potential buyer – the valuation problem of determining a fair value for a specific option contract – and anticipate the buyer’s optimal reaction to any proposed strike price. We also discuss some methods for finding numerical solutions of stochastic bilevel problems with a special emphasis on using duality gap penalizations.     

On the impact of advertising initiatives in supply chains

Advertising plays an important role in affecting consumer demand. Socially responsible firms are expected to use advertising judiciously, limiting advertising of “bad” products. An example is the advertising initiative adopted by several major food manufacturers to limit the advertising of unhealthy food categories to children. Such initiatives are based on the belief that less advertising will lead to less consumption of these unhealthy food categories. However, food manufacturers usually distribute products to consumers through retailers whose advertising is not restricted by those initiative programs. In this paper, we examine the effectiveness of such advertising initiative in a leader–follower supply chain with one manufacturer and one retailer. We assume that both the manufacturer and the retailer can choose to participate in the advertising initiative by reducing their advertising levels. The problem is formulated as a Stackelberg game. We show that the effectiveness of the advertising initiative critically depends on the leader’s participation in the initiative. If the leader is willing to reduce the advertising level below a threshold, the market coverage of the product can drop significantly. On the other hand, if only the follower participates in the initiative, the market coverage is likely to expand in the majority of cases. Managerial implications of this research are also discussed.     

On characterization of the core of lane covering games via dual solutions

The lane covering game (LCG) is a cooperative game where players cooperate to reduce the cost of cycles that cover their required lanes on a network. We discuss the possibilities/impossibilities of a complete characterization of the core via dual solutions in LCGs played among a collection of shippers, each with a number of service requirements along some lanes, and show that such a complete characterization is possible if each shipper has at most one service requirement.     

Bifurcations and chaos in a nonlinear discrete time Cournot duopoly game

A nonlinear discrete time Cournot duopoly game is investigated in this paper. The conditions of existence for saddle-node bifurcation, transcritical bifurcation and flip bifurcation are derived using the center manifold theorem and the bifurcation theory. We prove that there exists chaotic behavior in the sense of Marotto＇s definition of chaos. The numerical simulations not only show the consistence with our theoretical analysis, but also exhibit the complex but interesting dynamical behaviors of the model. The computation of maximum Lyapunov exponents confirms the theoretical analysis of the dynamical behaviors of the system.     

组织惯例演化的博弈分析

随着全球经济系统的日趋复杂和快速变化,持续性变革已经成为企业生存和发展的内在需要.组织惯例作为组织行为的基本要素和组织能力的载体,可以反映企业内在的深层变革.运用生物学隐喻,深入剖析了企业演化的机制;并在此基础上,运用演化博弈模型对组织惯例演化的路径选择进行了模拟分析;最后探讨了组织惯例演化的主要影响因素,并通过案例研究,对演化博弈模型进行了例证.     

基于远期合约的电力市场博弈分析

通过建立零售商与发电厂商之间的远期合约博弈模型,分析在发电和售电分开的电力市场模式下,零售商与发电厂商之间的远期合约在抑制发电厂商寡头垄断方面的作用.研究表明:在零售竞争的市场中,零售商采用激励策略主动与发电厂商签订远期合约,从而实现零售商自身利润最优化的目标,并在一定程度上减少了发电厂商的垄断利润,同时零售商的这种主动策略行为还能促进社会福利最大化的实现.这些分析为今后我国电力市场改革和电力金融衍生产品的创新提供了理论参考.