分销供应链中竞争零售商联盟的稳定性

针对由单一供应商和三个相互竞争零售商组成的两层分销供应链系统,在三种不同的博弈框架下,采用合作博弈论中短视的Nash稳定性概念与远视的最大一致集(LCS)概念研究了供应商与不同零售商联盟间的定价博弈,分别讨论了不同类型零售商联盟的稳定性。发现不论是在供应商处于领导地位,还是在零售商处于领导地位的市场中,当竞争强度较弱时,大联盟不是短视零售商联盟的稳定结构,却有可能是远视零售商联盟的稳定结构;当竞争强度较强时,则无论是短视零售商还是远视零售商都以大联盟为稳定结构,但是,在供应商处于领导地位的市场中,远视零售商形成大联盟的阈值较高;在供应商和零售商地位相同的市场中,大联盟则是远视零售商和短视零售商共同的稳定结构。     

Response time and vendor–assembler relationship in a supply chain

Relationships between an assembler and a vendor in a supply chain are investigated in two-period models when the assembler wants to reduce response time by incentive systems. The assembler may offer myopic or farsighted incentive contracts to the vendor, under short-term or long-term relationships. Incentive schemes, effort levels, and expected payoffs under different perspectives and relationships are examined. We find that a farsighted assembler provides the vendor with a higher incentive than a myopic assembler in the first period. A long (short)-term relationship is preferred if the value of farsightedness under a long-term relationship is greater (less) than the switching option value under a short-term relationship. We propose several sufficient conditions regarding which perspectives and relationships are preferred.     

Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

We investigate farsighted stable sets in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players’ payoffs for any given strategies chosen by these other players. We particularly investigate a special class of farsighted stable sets, each of which consists of strategy profiles yielding a single payoff vector. We call such a farsighted stable set as a single-payoff farsighted stable set. We propose a concept called an inclusive set that completely characterizes single-payoff farsighted stable sets in strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by single-payoff farsighted stable sets is closely related to the strict \(\alpha \)-core in a strategic game. Furthermore, we apply the results to strategic games where each player has two strategies and strategic games associated with some market models.     

Noncooperative farsighted stable set in an <Emphasis Type="Italic">n</Emphasis>-player prisoners’ dilemma

We examine an n-player prisoners’ dilemma game in which only individual deviations are allowed, while coalitional deviations (even non-binding ones) are not, and every player is assumed to be sufficiently farsighted to understand not only the direct outcome of his own deviation but also the ultimate outcome resulting from a chain of subsequent deviations by other players. We show that there exists a unique, noncooperative farsighted stable set (NFSS) and that it supports at least one (partially and/or fully) cooperative outcome, which is individually rational and Pareto-efficient. We provide a sufficient condition for full cooperation. Further, we discuss the relationship between NFSS and other “stable set” concepts such as the (myopic) von Neumann–Morgenstern stable set, Harsanyi (1974)’s strictly stable set, Chwe (1994)’s largest consistent set, and the cooperative farsighted stable set examined by Suzuki and Muto (2005). The author is very grateful to Professor Eiichi Miyagawa, the editor and the associate editor of this journal for their insightful comments and suggestions. He also acknowledges the financial support of Japan Society for the Promotion of Science [Grant-in-Aid for Scientific Research (C), No. 18530175].     

THE SIZE OF FARSIGHTED STABLE COALITIONS IN A GAME OF POLLUTION ABATEMENT

Abstract The game theoretical analysis of international environmental problems has received increasing attention in recent years. Major issues are as follows. Under which conditions will an international environmental agreement (IEA) be signed? Will the agreement be stable? Game theory has given different answers to these questions; in particular, it is possible to show that if countries are myopic then only small stable coalitions occur, but if they are farsighted then both large and small stable coalitions exist. This paper studies the size of a farsighted stable IEA by considering a quadratic cost function in a pollution abatement model. Following Rubio and Ulph [2006] , we consider both the case of non‐negative emissions as well as the case of unrestricted ones.     

直觉模糊支付合作对策的核仁解

本文主要研究支付值为直觉模糊集的合作对策问题及其模糊核仁解.首先定义了直觉模糊集的得分函数和精确函数,并给出其排序方法,得到基于直觉模糊集的合作对策模型和适合这种模型的相应定义,同时提出了直觉模糊核仁解的概念;其次运用新的排序方法将求核仁解的问题转化为求解双目标非线性规划问题;最后通过实例分析验证了该方法的可行性和有效性。     

Loss aversion equilibrium

The Nash equilibrium solution concept for games is based on the assumption of expected utility maximization. Reference dependent utility functions (in which utility is determined not only by an outcome, but also by the relationship of the outcome to a reference point) are a better predictor of behavior than expected utility. In particular, loss aversion is an important element of such utility functions.  We extend games to include loss aversion characteristics of the players. We define two types of loss-aversion equilibrium, a solution concept endogenizing reference points. The two types reflect different procedures of updating reference points during the game. Reference points emerge as expressions of anticipation which are fulfilled.  We show existence of myopic loss-aversion equilibrium for any extended game, and compare it to Nash equilibrium. Comparative statics show that an increase in loss aversion of one player can affect her and other players' payoffs in different directions. Received August 1998/Revised version February 2000     

基于区间与模糊Shapley值的合作收益分配策略

将经典Shapley值三条公理进行拓广,提出具有模糊支付合作对策的Shapley值公理体系。研究一种特殊的模糊支付合作对策,即具有区间支付的合作对策,并且给出了该区间Shapley值形式。根据模糊数和区间数的对应关系,提出模糊支付合作对策的Shapley值,指出该模糊Shapley值是区间支付模糊合作对策的自然模糊延拓。结果表明:对于任意给定置信水平α,若α=1,则模糊Shapley值对应经典合作对策的Shapley值,否则对应具有区间支付合作对策的区间Shapley值。通过模糊数的排序,给出了最优的分配策略。由于对具有模糊支付的合作对策进行比较系统的研究,从而为如何求解局中人参与联盟程度模糊化、支付函数模糊化的合作对策,奠定了一定的基础。     

Farsighted coalitional stability in TU-games

We study farsighted coalitional stability in the context of TU-games. We show that every TU-game has a nonempty largest consistent set and that each TU-game has a von Neumann–Morgenstern farsighted stable set. We characterize the collection of von Neumann–Morgenstern farsighted stable sets. We also show that the farsighted core is either empty or equal to the set of imputations of the game. In the last section, we explore the stability of the Shapley value. The Shapley value of a superadditive game is a stable imputation: it is a core imputation or it constitutes a von Neumann–Morgenstern farsighted stable set. A necessary and sufficient condition for a superadditive game to have the Shapley value in the largest consistent set is given.     

Zones of cooperation in demographic prisoner's dilemma

The emergence of cooperation in prisoner's dilemma (PD) games is generally assumed to require repeated play (and strategies such as Tit for Tat, involving memory of previous interactions) or features (“tags”) permitting cooperators and defectors to distinguish one another. In the demographic PD, neither assumption is made: Agents with finite vision move to random sites on a lattice and play a fixed culturally-inherited zero-memory strategy of cooperate (C) or defect (D) against neighbors. Agents are indistinguishable to one another—they are “tagless.” Positive payoffs accrue to agents playing C against C, or D against C. Negative payoffs accrue to agents playing C against D, or D against D. Payoffs accumulate. If accumulated payoffs exceed some threshold, agents clone offspring of the same strategy onto neighboring sites and continue play. If accumulated payoffs are negative, agents die and are removed. Spatial zones of cooperation emerge. © 1998 John Wiley & Sons, Inc.     

模糊支付合作博弈的可信性准核仁

合作博弈是处理局中人之间协同行为的数学理论。有诸如核心、稳定集、沙普利值、准核仁和核仁等不同的解概念。在很多情形,除了借助专家经验和主观直觉,没有恰当的方式来确定支付函数,由此产生了具有模糊支付的合作博弈模型。准核仁是一种重要的解概念,在模糊支付合作博弈中如何恰当定义准核仁是个重要的问题。本文在可信性理论的框架下研究了这个问题,定义了两类可信性准核仁概念并证明了它们的存在性和唯一性,同时研究了可信性核心、可信性核仁与它们之间的关系。     

博弈联盟模糊收益的分配

提出了联盟模糊收益合理分配的一种新方法.首先,在模糊收益α截集上定义了α合理分配集,分析了该分配集与模糊收益Shapley值的关系.接着,给出了模糊收益的α合理Shapley分配函数,对其性质进行了讨论.然后,构造了模糊合理Shapley分配,证明其连续性,得到了联盟模糊收益与模糊合理Shapley分配具有包含关系的结论.     

A set optimization approach to zero-sum matrix games with multi-dimensional payoffs

A new solution concept for two-player zero-sum matrix games with multi-dimensional payoffs is introduced. It is based on extensions of the vector order in \(\mathbb {R}^d\) to order relations in the power set of \(\mathbb {R}^d\), so-called set relations, and strictly motivated by the interpretation of the payoff as multi-dimensional loss for one and gain for the other player. The new concept provides coherent worst case estimates for games with multi-dimensional payoffs. It is shown that–in contrast to games with one-dimensional payoffs–the corresponding strategies are different from equilibrium strategies for games with multi-dimensional payoffs. The two concepts are combined into new equilibrium notions for which existence theorems are given. Relationships of the new concepts to existing ones such as Shapley and vector equilibria, vector minimax and maximin solutions as well as Pareto optimal security strategies are clarified.     

Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points

Equilibrium points in mixed strategies seem to be unstable, because any player can deviate without penalty from his equilibrium strategy even if he expects all other players to stick to theirs. This paper proposes a model under which most mixed-strategy equilibrium points have full stability. It is argued that for any gameΓ the players' uncertainty about the other players' exact payoffs can be modeled as a disturbed gameΓ ^*, i.e., as a game with small random fluctuations in the payoffs. Any equilibrium point inΓ, whether it is in pure or in mixed strategies, can “almost always” be obtained as a limit of a pure-strategy equilibrium point in the corresponding disturbed gameΓ ^* when all disturbances go to zero. Accordingly, mixed-strategy equilibrium points are stable — even though the players may make no deliberate effort to use their pure strategies with the probability weights prescribed by their mixed equilibrium strategies — because the random fluctuations in their payoffs willmake them use their pure strategies approximately with the prescribed probabilities.     

Incentives and the needham paradox: An agent-based perspective

This article discusses how restructured incentives could have inhibited innovation in ancient China and explain the Needham paradox. Agents in a genetic algorithmic game maximize their payoffs by choosing between innovating and studying the Classics. By restructuring incentives toward studying the Classics, initial spurts of innovation are smothered, resulting in a population with all agents studying the Classics. The incentive structure has a statistically and quantitatively significant impact on the expected average payoffs and the strategy profile of the population: the average payoffs for a regime which rewards innovation fluctuate more but are always higher and the strategy profile is varied. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Independent mistakes in large games

Economic models usually assume that agents play precise best responses to others' actions. It is sometimes argued that this is a good approximation when there are many agents in the game, because if their mistakes are independent, aggregate uncertainty is small. We study a class of games in which players' payoffs depend solely on their individual actions and on the aggregate of all players' actions. We investigate whether their equilibria are affected by mistakes when the number of players becomes large. Indeed, in generic games with continuous payoff functions, independent mistakes wash out in the limit. This may not be the case if payoffs are discontinuous. As a counter-example we present the n players Nash bargaining game, as well as a large class of “free-rider games.” Received: November 1997/Final version: December 1999     

Scarcity,competition, and value

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.     

Transfers,contracts and strategic games

This paper analyses the role of transfer payments and strategic contracting within two-person strategic form games with monetary payoffs. First, it introduces the notion of transfer equilibrium as a strategy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail.     

STABILITY OF THE PRICE REACTION FUNCTION WHEN THE CONSUMERS ANTICIPATE FUTURE PRICES

The hypothesis of the price reaction function-prices change in dependence of capacity utilization-is frequently applied to model OPEC's response to world oil market conditions. These studies assume implicitly myopic consumer behavior, or more bluntly, only the “experts” know this model but not the consumers. This paper extends the analysis to rational expectations (more precisely, perfect foresight due to a deterministic framework) and proves the (saddlepoint) stability of the equilibrium. Numerical examples highlight the differences of the two hypotheses, myopic versus rational consumer expectations. In particular, damped oscillations result for the empirical application (larger and more persistent for myopic consumers), which explains past volatility.     

Farsighted Stability in an n-Person Prisoner’s Dilemma

Farsighted stability is examined in an n-person prisoner’s dilemma. It is shown that any individually rational and Pareto efficient outcome is a farsighted stable set and no other farsighted stable set exists; it is further shown that the largest consistent set consists of all individually rational outcomes.