矩阵对策的公平性研究

众所周知，零和二人有限对策也称为矩阵对策。设做一个矩阵对策的两个局中人都希望对策结果尽可能公平。当两个局中人使用对策解中的策略进行对策时，如果对策结果最公平，那么这个对策解称为最优的。本文证明了最优对策解集的一些性质，然后给出矩阵对策公平度的概念并证明了它的一些有趣的性质。     

一类多步矩阵对策上的计策问题

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.     

一般化两人零和模糊对策的模糊规划法

本文在充分考虑局中人的策略集是模糊子集的基础上,给出更一般化的具有模糊支付与模糊赢得的两人零和模糊对策的模糊规划模型。利用模糊数的序方法,得到了此对策求解问题可以转化为带有模糊参数的两个经典规划的求解问题。文末给出算例予以说明。     

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.     

具有风险因素的多联盟部分合作对策

多联盟部分合作对策是指对策中的局中人通过引入合作函数,彼此合作或采取单独行动来对非合作对策规则进行更改,形成具有多联盟结构的扩展型部分合作对策.本文克服多联盟部分合作对策中不同局中人联盟单调递增约束,局中人加入联盟后可以退出加入到其他联盟中;同时考虑风险因素的影响,采用专家打分法和网络分析法(ANP)重新确定联盟局中人各自所占的权重,对多联盟部分合作对策中构造的合作子对策的联盟收益分配方式进行改进,从而建立具有风险因素的多联盟部分合作对策模型,并利用逆推归纳法得到对策解的算法.最后通过实例说明所建模型及结论的合理性,体现实际经济管理过程中结盟的变化和风险的影响.     

B矩阵对策

提出了一类局中人都设定有得失控制值的二人零和有限对策,即B矩阵对策.引入了稳妥策略、弱稳妥策略等概念.给出了B矩阵对策的数学模型、有关理论和求解方法.最后,还给了一个计算例子.     

基于Selectope解集和局中人最大满意度的合作对策解的研究

针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。     

拟阵上合作对策的Banzhaf函数

本文结合文[1,2]中关于拟阵上静态结构和动态结构合作对策Shapley函数的描述,探讨了两类拟阵上的Banzhaf函数.通过给出相应的公理体系,论述了两类拟阵上Banzhaf函数的存在性和唯一性,拓展了拟阵上分配指标的研究范围.同时讨论了两类合作对策上Banzhaf函数的有关性质.最后通过算例来说明局中人在此类合作对策中的Banzhaf指标.     

考虑公平性的两阶段系统固定成本分摊DEA模型

针对两阶段系统固定成本分摊问题,已有研究大多是基于效率不变性或构造满意度指标等提出不同方法,少有考虑固定成本分摊方案的公平性。本文首先通过非自利原则得到系统整体与各阶段的成本分摊上限,针对具有群组式组织结构的两阶段系统,提出新的固定成本分摊模型,所得分摊结果更为公平,最后通过实际算例验证了本文模型的可行性和有效性。     

决策支持下的不完全偏好信息多目标对策

针对多目标对策的不完全偏好信息,将理性策略概念和偏好规划理论引入到多目标对策研究中,把两人的多目标对策考虑为两个局中人同时面临的两个多目标决策问题,偏好信息用可行权重限定集合进行建模.多目标对策模型分为对策模型和决策模型两部分.在对策模型中,利用理性和偏好的共同知识,获得理性策略集.在决策模型中,局中人将策略选择作为使用私人偏好信息的多目标决策问题.最后,通过实例验算表明所提方法的有效性.     

Perturbation theory for games in normal form and stochastic games

In this paper, the effect on values and optimal strategies of perturbations of game parameters (payoff function, transition probability function, and discount factor) is studied for the class of zero-sum games in normal form and for the class of stationary, discounted, two-person, zero-sum stochastic games.A main result is that, under certain conditions, the value depends on these parameters in a pointwise Lipschitz continuous way and that the sets of -optimal strategies for both players are upper semicontinuous multifunctions of the game parameters.Extensions to general-sum games and nonstationary stochastic games are also indicated.     

On the role of chance moves and information in two-person games

The value of information has been the subject of many studies in a strategic context. The central question in these studies is how valuable the information hidden in the chance moves of a game is for one or more of the players. Generally speaking, only the extra possibilities that are beneficial for the players have been considered so far. In this note we study the value of information for a special class of two-person games. For these games we also investigate how “badly” the players can do, both with and without knowing the result of the chance move. In this way one can determine to what extent the players are restricted in their possibilities by the fact that some information is hidden in the chance moves of the games. This allows for a comparison of the influence of the chance move to the control that the players have over the game result.     

Computation of equilibria and the price of anarchy in bottleneck congestion games

We study Nash and strong equilibria in weighted and unweighted bottleneck games. In such a game every (weighted) player chooses a subset of a given set of resources as her strategy. The cost of a resource depends on the total weight of players choosing it and the personal cost every player tries to minimize is the cost of the most expensive resource in her strategy, the bottleneck value. To derive efficient algorithms for finding equilibria in unweighted games, we generalize a transformation of a bottleneck game into a congestion game with exponential cost functions introduced by Caragiannis et al. (2005). For weighted routing games we show that Greedy methods give Nash equilibria in extension-parallel and series-parallel graphs. Furthermore, we show that the strong Price of Anarchy can be arbitrarily high for special cases and give tight bounds depending on the topology of the graph, the number and weights of the users and the degree of the polynomial latency functions. Additionally we investigate the existence of equilibria in generalized bottleneck games, where players aim to minimize not only the bottleneck value, but also the second most expensive resource in their strategy and so on.     

Games with a permission structure - A survey on generalizations and applications

In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize existing solutions for TU-games. In this survey, we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies is that of games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms.     

Discounted,positive, and noncooperative stochastic games

In this paper, we consider the stochastic games ofShapley and prove under certain conditions the stochastic game has a value and both players have optimal strategies. We also prove a similar result for noncooperative stochastic games.     

Two Game Models for Cooperation with Implicit Noncooperation

We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University.     

Efficient Winning Strategies in Random‐Turn Maker–Breaker Games

We consider random‐turn positional games, introduced by Peres, Schramm, Sheffield, and Wilson in 2007. A p‐random‐turn positional game is a two‐player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p ). We analyze the random‐turn version of several classical Maker–Breaker games such as the game Box (introduced by Chvátal and Erd?s in 1987), the Hamilton cycle game and the k‐vertex‐connectivity game (both played on the edge set of ). For each of these games we provide each of the players with a (randomized) efficient strategy that typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players.     

Computing the value of information of quadratic decision problems and its non-negativity conditions

Abstract

There are many examples in the literature of non-cooperative games in which players prefer not to have additional information in order to improve their payoff. We present a general quadratic game in which, if one of the players improves his payoff upon obtaining more information, the other player’s payoff worsens in such a way that there is a net social loss due to having more information. How can we ensure this does not occur? The results of this paper are (1) the mathematical expression of the (social) value of information in a quadratic non-cooperative game, and (2) the conditions that ensure the social value of information is non-negative.     

Deposit games with reinvestment

In a deposit game coalitions are formed by players combining their capital. The proceeds of their investments then have to be divided among those players. The current model extends earlier work on capital deposits by allowing reinvestment of returns. Two specific subclasses of deposit games are introduced. These subclasses provide insight in two extreme cases. It is seen that each term dependent deposit game possesses a core element. Capital dependent deposit games are also shown to have a core element and even a population monotonic allocation scheme if the revenue function exhibits increasing returns to scale. Furthermore, it is shown that all superadditive games are deposit games if one allows for debt.