Rights and responsibilities of dissent: Cooperative conflict

Cooperative conflict research supports the value of the right to dissent and self-expression as contributing significantly to organizational effectiveness. Through conflict, problems are identified, and solutions created and accepted, and a sense of justice and fairness established. Research also proposes a corresponding responsibility that employees and employers should establish a strong cooperative context for managing conflict. Structuring a conflict-positive organization is a powerful way to capture the benefits of conflict and support the right of dissent.     

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. It turns out that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games. However, when considering an assignment game as a (communication) graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph where buyers (sellers) are connected with sellers (buyers) only, we show that Myerson’s component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.     

Implementation in generalized matching problems

We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market (Shapley and Scarf, Journal of Mathematical Economics, 1974, 1, 23–28) and marriage problems (Gale and Shapley, American Mathematical Monthly, 1962, 69, 9–15). We show that the core correspondence is implementable. We show, furthermore, that any solution that is Pareto efficient, individually rational, and implementable is a supersolution of the core correspondence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corollary of independent interest in the context of the housing market is that the core correspondence is the only single-valued solution that is Pareto efficient, individually rational, and implementable.     

The link between the Shapley value and the beta factor

In this article, we provide a link between the Shapley value in cooperative game theory and the capital asset pricing model (CAPM) in finance. In particular, the Shapley value of a suitably defined cooperative game is closely related to the beta factor in the CAPM. The beta factor for any given security may be interpreted as the asset’s fairly allocated share of the market risk or as the asset’s average marginal contribution to the market risk, respectively. Other fairness properties and axioms of the Shapley value may be reinterpreted in this context to attain a deeper understanding of the beta factor and the connotation of systematic risk. Our game theoretic approach further allows for a generalisation of the CAPM with respect to arbitrary risk measures other than variance. Last but not least, we discuss the volatility of an asset’s theoretical fair assessment of risk and of its systematic risk, respectively. This result lends itself to face the challenge of an empirical investigation on real stock markets.     

基于改进Shapley值法的动态物流联盟利益分配

为建立公平合理的利益分配及激励机制,在传统Shapley值法的基础上,考虑风险成本、品牌信任度、联盟忠诚度,引入综合修正因子,建立了基于改进Shapley值法的动态物流联盟利益分配模型,使利益分配更公平合理化,减少联盟中利益分配冲突,稳固联盟,为其提供理论借鉴与参考。     

Implementation of solutions to the problem of fair division when preferences are single-peaked

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We address the issue of (Nash)-implementability of solutions to this problem. As the lack of monotonicity of preferences often causes solutions to violate no veto power, the classic Maskin-type theorems cannot be invoked. Instead, we show that more powerful theorems due to Danilov-Yamato and Sjöström can help settle implementation questions for most of the central fairness concepts, generally in the positive.     

Internalized social norms in conflicts: an evolutionary approach

An individual with an internalized norm prefers to comply with the norm as long as the opponents also comply. This paper studies the evolution of such norms in a conflict. Individuals play with the same opponent for a number of rounds, during which they adapt their behavior according to a myopic best response dynamic. The payoffs earned during this equilibration period enter into the cultural evolutionary process that determines which norms that survive. It is found that if agents play against the same opponent for sufficiently many times, then only norms that reduce conflict relative to the Nash equilibrium survive. If instead agents meet the same opponent only once, then only agents that play the Nash equilibrium survive. By way of example it is also shown that in the intermediate case the outcome of evolution can be either that conflict reducing norms or Nash behavior dominates. These results indicate that the common practice of disregarding equilibration in models of preference evolution is not without a cost.     

Lindahl's solution and values for a public-goods example

An example of an economy with a public good is presented with a non-atomic measure space of agents and money (transferable utility medium). Three solutions are computed: the Lindahl solution, the Shapley value, and the Harsanyi-Selten value. The three are found to differ significantly in their assignment of the societal benefits attributable to the presence of the public good.     

A strategic analysis of network reliability

Abstract. We consider a non-cooperative model of information networks where communication is costly and not fully reliable. We examine the nature of Nash networks and efficient networks. We find that if the society is large, and link formation costs are moderate, Nash networks as well as efficient networks will be ‘super-connected’ i.e. every link is redundant in the sense that the network remains connected even after the link is deleted. This contrasts with the properties of a deterministic model of information decay, where Nash networks typically involve unique paths between agents. We also find that if costs are very low or very high, or if links are highly reliable then there is virtually no conflict between efficiency and stability. However, for intermediate values of costs and link reliability, Nash networks may be underconnected relative to the social optimum.     

Property rights out of anarchy? The Demsetz hypothesis in a game of conflict

The Demsetz hypothesis states that secure claims to property arise when the value of creating those rights is sufficiently high. This paper examines the conditions under which this holds in an anarchy equilibrium in which players may allocate labor to production, to conflict, or to the public good of secure claims to property protection. In a simultaneous choice Nash equilibrium, no secure claims to property are created. However, if players play a sequential choice game in which secure claims to property protection occurs in the first stage, then the strategic benefit of reducing others’ subsequent conflict allocation causes secure claims to property to arise. Secure claims to property in a social contract are imperfect, but for sufficiently high productivity of resources, the social contract welfare dominates autocracy.     

Reject and renegotiate: The Shapley value in multilateral bargaining

This paper investigates three distinctive and intuitive renegotiation bargaining protocols that all yield the Shapley value as the unique subgame perfect equilibrium outcome. These protocols, built on the multi-bidding procedure of Pérez-Castrillo and Wettstein (2001), allow more freedom in multilateral bargaining where rejected players can further negotiate and form coalitions. The self-duality of the Shapley value plays a key role in the second and third results. Moreover, these renegotiation protocols allow an actual play along the equilibrium path to restore the Shapley value in case of a ‘mistake’ made before.     

Duality and anti-duality in TU games applied to solutions,axioms, and axiomatizations

In this paper, for each solution for TU games, we define its “dual” and “anti-dual”. Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta–Ray solution.     

Value capture in hierarchically organized value chains

We study how the structure of negotiations in a value chain affects the distribution of value among its members. To this end, we generalize the Shapley value and the core to hierarchical bargaining situations. While the core yields no concrete predictions, the Shapley value analysis suggests that positions most conducive to value capture are those that allow to realize large complementarity gains. If the game exhibits “supercomplementarity,” then it is advantageous if a firm's negotiation partners are grouped into clusters. Using examples from the aircraft and white goods industries, we assess whether the firms’ actions are consistent with model predictions.     

On Maskin monotonicity of solution based social choice rules

Howard (J Econ Theory 56:142–159, 1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by defining a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even sufficient for Nash implementability.     

Nash bargaining in ordinal environments

We analyze the implications of Nash’s (Econometrica 18:155–162, 1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (J Econ Theory 16:247–251, 1977), we introduce a weaker independence of irrelevant alternatives (IIA) axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley–Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker IIA axiom. We also analyze the implications of other independence axioms.     

Null players,solidarity, and the egalitarian Shapley values

The Shapley value probably is the most eminent single-point solution concept for TU-games. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players non-negative payoffs whenever the grand coalition’s worth is non-negative. Second, the equal treatment property is strengthened into desirability. This way, we obtain a new characterization of the class of egalitarian Shapley values, i.e., of convex combinations of the Shapley value and the equal division solution. Within this characterization, additivity and desirability can be replaced by strong differential monotonicity, which translates higher productivity differentials into higher payoff differentials.     

基于Shapley值的供应链信息共享收益分配研究

研究当供应链信息共享时,产生的经济收益及其分配问题。提出将Shapley值法应用于解决信息共享活动中各成员收益分配问题,同时运用Shapley值法构建供应链企业间收益分配模型,并给出算例。     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

Fiscal and monetary policy co-ordination: A differential game approach

In this paper the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behaviour. Differential games are used in the framework of a continuous-time econometric model of the Italian economy. The Nash and the Stackelberg non-cooperative equilibrium solutions are computed, and the case for cooperation is analysed by considering the Nash and the Kalai-Smorodinsky bargaining models. It is shown that, in the Italian case, the government has a stronger bargaining position than the central bank. A comparison is then made between the different solutions to show that the drawbacks that emerge from non-cooperation are not simply those depending on the players' payoffs. Other features are in fact considered which constitute a further argument for policy co-ordination.     

主制造商-供应商模式下民用飞机研制供应链努力程度协调模型

民用飞机越来越多地采用主制造商供应商模式。供应商的努力程度在很大程度上决定了飞机的研制水平。因而作为供应链利益的集成者和分配者的主制造商,就会利用其自身的信息优势和主导地位,对供应商的努力程度进行统一协调。本文主要采用Nash均衡和Shapley值等方法构建了基于供应商努力程度的供应链协调模型,重点研究在主制造商的统一协调下实现供应链整体利益和各成员利益最优的,问题。研究结果表明,主制造商统一安排各供应商的努力程度使整个供应链的利益最大化,而主制造商对利益的合理分配则能增加供应链各成员的利益,实现整个供应链的有效协调。