Maximal nash subsets for bimatrix games

In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.     

Constant risk aversion in stochastic contests with exponential completion times

This article analyzes a class of stochastic contests among multiple players under risk‐averse exponential utility. In these contests, players compete over the completion of a task by simultaneously deciding on their investment, which determines how fast they complete the task. The completion time of the task for each player is assumed to be an exponentially distributed random variable with rate linear in the player's investment and the completion times of different players are assumed to be stochastically independent. The player that completes the task first earns a prize whereas the remaining players earn nothing. The article establishes a one‐to‐one correspondence between the Nash equilibrium of this contest with respect to risk‐averse exponential utilities and the nonnegative solution of a nonlinear equation. Using the properties of the latter, it proves the existence and the uniqueness of the Nash equilibrium, and provides an efficient method to compute it. It exploits the resulting representation of the equilibrium investments to determine the effects of risk aversion and the differences between the outcome of the Nash equilibrium and that of a centralized version.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:4–14, 2019     

基于三方动态博弈模型的网络生存防御策略优化配置

针对网络攻防环境中防御方以提高系统生存能力为目的所进行的最优生存防御策略的选取问题,提出了一种基于完全信息动态博弈理论的生存防御策略优化配置算法。将恶意攻击方、故障意外事件及防御方作为博弈的参与人,提出了一种混合战略模式下的三方动态博弈模型,对博弈的主要信息要素进行了说明,以混合战略纳什均衡理论为基础,将原纳什均衡条件式的表达式转化为可计算数值结果的表达式,并据此增加了近似的概念,最后,将提出的模型和近似纳什均衡求解算法应用到一个网络实例中,结果证明了模型和算法的可行性和有效性。     

Evolutionary determinants of war

This paper considers evolutionarily stable decisions about whether to initiate violent conflict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically confined area, we use the concept of evolutionary stability in finite populations. We find that players’ evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent conflict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are reflected in the equilibrium set of peaceful resource allocations.     

军事虚拟仓库组织结构的博弈分析

简要介绍了军事虚拟仓库及其组织结构形式．以及博弈论的相关知识。结合军事后勤系统的特点,采用完全信息静态博弈纳什均衡的方法分析了军事虚拟仓库的组织结构模式,在假设的合理的条件下模拟3种组织形式的博弈过程。通过各个模型的最终纳什均衡,指出了3种组织结构形式运作的结果和其积极因素、消极因素、噪声构成．结合我军现有的后勤保障体制,提出现行保障体制的合理与不合理的地方,并给出了改进方案,对优化全军后方仓库布局及管理和战备物资储备及应急保障有着重要意义,可以为总部决策提供咨询建议。     

Purchase and retrieval competition for seasonal produce

We study the competition problem of purchase and multiretrieval of perishable seasonal produce, where wholesalers purchase and stock their products in the first period, and then retrieve and sell them in subsequent periods. We first consider the duopoly case and assume that the prices are exogenous and fluctuate. In each period, after the price realization, the wholesalers retrieve some stock from their warehouses to satisfy their demands. One wholesaler's unsatisfied customers can switch to another and be satisfied by its left retrieved products. Any unsold retrieved stock has no salvage value and any unsatisfied demand is lost. The unretrieved stock is carried to the next period at a perishable rate. The wholesalers compete for the substitute demand by determining their own purchase and retrieval quantities. We show the existence and uniqueness of a pure-strategy Nash equilibrium, and that the Nash equilibrium strategy has the simple “sell-down-to” structure. We also consider the general N-person game and show the existence of the Nash equilibrium, and characterize the structure of the equilibrium strategy for the symmetric case. In addition, we consider the case with endogenous prices, and show that the problem reduces to a repeated newsvendor game with price and inventory competition. We derive the conditions under which a unique Nash equilibrium exists and characterize the equilibrium strategy. Finally, we conduct numerical studies to examine the impacts of the model parameters on the equilibrium outcomes and to generate managerial insights.     

The incentive effect of acceptance sampling plans in a supply chain with endogenous product quality

This article studies a firm that procures a product from a supplier. The quality of each product unit is measured by a continuous variable that follows a normal distribution and is correlated within a batch. The firm conducts an inspection and pays the supplier only if the product batch passes the inspection. The inspection not only serves the purpose of preventing a bad batch from reaching customers but also offers the supplier an incentive to improve product quality. The firm determines the acceptance sampling plan, and the supplier determines the quality effort level in either a simultaneous game or a Stackelberg leadership game, in which both parties share inspection cost and recall loss caused by low product quality. In the simultaneous game, we identify the Nash equilibrium form, provide sufficient conditions that guarantee the existence of a pure strategy Nash equilibrium, and find parameter settings under which the decentralized and centralized supply chains achieve the same outcome. By numerical experiments, we show that the firm's acceptance sampling plan and the supplier's quality effort level are sensitive to both the recall loss sharing ratio and the game format (i.e., the precommitment assumption of the inspection policy). © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

两类新的Nash平衡点的精选

本文从系统的观点出发,对n-人非合作对策的解点作了探讨,提出了两类新的Nash平衡点的精选,并证明了其存在性。这两种Nash平衡点分别称之为第一类Nash平衡点和第二类Nash平衡点。第一类Nash平衡点具有冒险性,第二类Nash平衡点具有保守性,二者都满足整体上的最优性。     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Stability in a general oligopoly model

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.     

Inducing coordination in supply chains through linear reward schemes

Decentralized decision‐making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision‐making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi‐agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

STRATEGIC DEFENSE AND ATTACK FOR SERIES AND PARALLEL RELIABILITY SYSTEMS: COMMENT

The contest-theoretic literature on the attack and defense of networks of targets focuses primarily on pure-strategy Nash equilibria. Hausken's 2008 European Journal of Operational Research article typifies this approach, and many of the models in this literature either build upon this model or utilize similar techniques. We show that Hausken's characterization of Nash equilibrium is invalid for much of the parameter space examined and provides necessary conditions for his solution to hold. The complete characterization of mixed-strategy equilibria remains an open problem, although there exist solutions in the literature for special prominent cases.     

非对称Colonel Blotto博弈模型下的多信道功率分配抗干扰

针对智能干扰条件下传输速率固定的通信系统多信道功率分配问题,建立了非对称Colonel Blotto博弈模型。在完全信息条件下,推导出了各种功率预算约束下通信方和干扰方的等效单信道最优功率分配策略,进而证明了通信方和干扰方存在唯一混合纳什均衡策略,并求得了纳什均衡收益。基于等效单信道最优功率分布,提出了一种多重扫描直接列元素交换算法,可以快速构建多信道混合功率分配矩阵,且相比于线性规划方法,可适应更多的信道数和更广的功率分布范围。通过数值仿真,验证了所提多信道混合功率分配矩阵构造算法的有效性及多信道功率分配策略的最优性。     

A search game with a protector

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval [1, n] in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λ_ix_i)) exp (−μ_iy_i) when the searcher and protector allocate resources x_i and y_i respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000     

Inventory control under substitutable demand: A stochastic game application

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018     

Technical note: Find a hidden “treasure”

This paper deals with a two searchers game and it investigates the problem of how the possibility of finding a hidden object simultaneously by players influences their behavior. Namely, we consider the following two‐sided allocation non‐zero‐sum game on an integer interval [1,n]. Two teams (Player 1 and 2) want to find an immobile object (say, a treasure) hidden at one of n points. Each point i ∈ [1,n] is characterized by a detection parameter λ_i (μ_i) for Player 1 (Player 2) such that p_i(1 ? exp(?λ_ix_i)) (p_i(1 ? exp(?μ_iy_i))) is the probability that Player 1 (Player 2) discovers the hidden object with amount of search effort x_i (y_i) applied at point i where p_i ∈ (0,1) is the probability that the object is hidden at point i. Player 1 (Player 2) undertakes the search by allocating the total amount of effort X(Y). The payoff for Player 1 (Player 2) is 1 if he detects the object but his opponent does not. If both players detect the object they can share it proportionally and even can pay some share to an umpire who takes care that the players do not cheat each other, namely Player 1 gets q₁ and Player 2 gets q₂ where q₁ + q₂ ≤ 1. The Nash equilibrium of this game is found and numerical examples are given. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Group support for political violence: The role of emotions and expressive choice in creating conflict or providing peace

This paper provides a rationale for group support for political violence which does not provide a material benefit. Rabin’s (1993) theory of fairness is adopted to demonstrate that although group violence may not be a Nash equilibrium it may be a fairness equilibrium in a game containing psychological payoffs. For this to happen the material stakes must be perceived as low and psychological payoffs are expressive. Although the material stakes are actually high, members of each group may choose expressively to support the use of violence because the probability of being decisive is low. The paper also considers the possibility of peace emerging as a fairness equilibrium. This can only happen if each group perceives the other as making some sacrifice in choosing peace.     

Strategic Defense And Attack For Series And Parallel Reliability Systems: Rejoinder

In our original comment, we showed that Hausken's characterization of Nash equilibrium is invalid for much of the parameter space examined and provided necessary conditions for his solution to hold. Most of the comments in his reply are either tangential or irrelevant. However, several of the claims made in the reply reveal continuing misunderstandings and gaps in his understanding. In this rejoinder, we briefly clarify the fundamental issues.     

Jihad Against Palestinians? The Herostratos Syndrome and the Paradox of Targeting European Jews

Abstract

This paper addresses the waves of mass killings recently perpetrated by individuals with a weak or nonexistent ideological motivation, whose acts either appear to contradict their purported political cause or are admittedly driven by a quest for notoriety. Examples range from killers who have been waging jihad against European Jews to unattached mass killers such as the Germanwings pilot to the perpetrators of mass school shootings in America and worldwide. We argue that these phenomena can be understood as instances of the Herostratos syndrome, which has been known for thousands of years as characterizing the behavior of people who seek to survive in the collective memory by excelling in their infamous acts. We provide a model of hybrid killers which accommodates the Herostratic motive alongside a political motive and characterize a well-behaved Nash equilibrium where Herostratic killers are competing with one another with a view to make a name for themselves in infamy. The policy implications point towards reducing the publicity the killers enjoy, thus frustrating their quest for notoriety.     

A rent‐seeking model of international competition and alliances∗

This paper presents an alternative approach for analyzing international competition and alliances as rent‐seeking contests that are able to capture the impure public good nature of defense spending. Two‐country Cournot and Stackelberg games are considered and comparative static results derived. A three‐country model is investigated, and alliance behavior is explored in the context of this rent‐seeking model. The conjecture that an alliance may become less effective if the allies’ interests become more closely aligned is verified. Finally, the model is generalized, and a Nash‐Cournot equilibrium is computed.