The monoclus of a coalitional game

The analysis of single-valued solution concepts, providing payoffs to players for the grand coalition only, has a long tradition. Opposed to most of this literature we analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce several closely related allocation scheme rules, each resulting in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game with transferable utilities has a PMAS. Monotonicities, which measure the payoff difference for a player between two nested coalitions, are the driving force. These monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Variants are obtained by considering different domains and/or different collections of monotonicities. We deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues.     

Production-inventory games: A new class of totally balanced combinatorial optimization games

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.     

Noncooperative foundations of the nucleolus in majority games

This paper studies coalition formation, payoff division and expected payoffs in a “divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses a weak version of Kohlberg's [SIAM J. Appl. Math. 20 (1971) 62] balancedness result reinterpreting the balancing weights as probabilities in a mixed strategy equilibrium.     

Stable governments and the semistrict core

We consider the class of proper monotonic simple games and study coalition formation when an exogenous weight vector and a solution concept are combined to guide the distribution of power within winning coalitions. These distributions induce players' preferences over coalitions in a hedonic game. We formalize the notion of semistrict core stability, which is stronger than the standard core concept but weaker than the strict core notion and derive two characterization results for the semistrict core, depending on conditions we impose on the solution concept. A bounded power condition, which connects exogenous weights and the solution, turns out to be crucial. It generalizes a condition termed “absence of the paradox of smaller coalitions” that was previously used to derive core existence results.     

Extendable Cooperative Games

A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core. Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof.     

Achieving efficiency with manipulative bargainers

Two agents bargain over the allocation of a bundle of divisible commodities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a family that includes the Nash and the Raiffa–Kalai–Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent's features to virtually implement the Nash bargaining solution.     

Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games

The axiom of balanced collective contributions is introduced as a collective variant of the axiom of balanced contributions proposed by Myerson. It requires the identical average impact of the withdrawal of any agent from a game on the remaining population. It turns out that the axiom of balanced collective contributions and the classical axiom of efficiency characterize the equal allocation of nonseparable costs, an allocation rule that is extensively used in cost allocation problems and in accounting. In particular, the equal allocation of nonseparable costs coincides with the nucleolus on the class of data games within the European REACH legislation. While our result does not hold on data games, extra axioms enable provision of comparable characterizations of the equal allocation of nonseparable costs and the Shapley value on this class of games.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

Economies with Land—A Game Theoretical Approach

With an economy with land (an economy of Debreu-type in which land is the unique commodity) we associate a cooperative game with transferable utility v . The set of all TU-games of type v is investigated and the set of equilibrium payoffs (in the TU-sense) of the economy is described as a subset of the core of v . We prove that equilibrium payoffs can be extended to population monotonic allocation schemes in the sense of Sprumont.     

Maskin's Theorem with limited veto power

We weaken the no-veto power condition of Maskin [Maskin, E.,1999. Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38] to limited veto power, and prove that any monotonic social choice rule is Nash implementable if it satisfies this weaker condition. The result is obtained by using the canonical Maskin mechanism without modification. An immediate corollary is that the weak core is Nash implementable in any coalitional game environment. An example is given to show that the strong core need not be implementable, even when it is monotonic.     

Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack

The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. However many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studies the allocation problem confronting a defender who must decide how to distribute limited resources across multiple sites before an attacker chooses where to strike. Unlike many Blotto games which only have very complicated mixed-strategy equilibria, the sequential, nonzero-sum “Blotto” game always has a very simple pure-strategy subgame perfect equilibrium. Further, the defender always plays the same pure strategy in any equilibrium, and the attacker's equilibrium response is generically unique and entails no mixing. The defender minmaxes the attacker in equilibrium even though the game is nonzero-sum, and the attacker strikes the site among its best replies that minimizes the defender's expected losses.     

Nash consistent representation of effectivity functions through lottery models

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model—i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries—which has a Nash consistent representation. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries. No additional condition on the original effectivity function is needed.     

The existence of budget-constrained pareto-efficient allocations

The existence of a budget constrained Pareto efficient allocation is proved. Preferences are assumed to be strongly monotonic and continuous pre-orderings. In addition, it is assumed that the set of Pareto efficient allocations, corresponding to a utility distribution, is a convex set. The mathematical tool is Brouwer's (or Kakutani's) fixed point theorem.     

Overcoming free riding in multi-party computations—The anonymous case

This paper addresses the question of multi-party computation in a model with asymmetric information. Each agent has a private value (secret), but in contrast to standard models, the agent incurs a cost when retrieving the secret. There is a social choice function the agents would like to compute and implement. All agents would like to perform a joint computation, which input is their vector of secrets. However, agents would like to free-ride on others' contribution.A mechanism which elicits players' secrets and performs the desired computation defines a game. A mechanism is ‘appropriate’ if it (weakly) implements the social choice function for all secret vectors. namely, if there exists an equilibrium in which it is able to elicit (sufficiently many) agents' secrets and perform the computation, for all possible secret vectors. We show that ‘appropriate’ mechanisms approach agents sequentially and that they have low communication complexity.     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

基于区间数二级收敛的风险型方案的择优

区间数多属性择优问题是多属性决策研究中的重要内容.为解决成本与效益型混合的多属性风险型方案择优问题,在分析区间数的定义及其在方案属性集中应用的基础上,本文运用区间数的二级收敛思想,给出了多属性风险型方案的择优过程:首先规范决策矩阵并将各备选方案属性权重的区间数收敛为点值;其次计算各备选方案综合属性值的区间数并建立可能度矩阵再将各备选方案综合属性值的区间数收敛为点值;最后运用综合属性排序向量计算各备选方案的综合属性点值并进行排序.本文实例印证了该择优过程的实用性和有效性.本文研究成果可丰富多属性决策研究内容并有助于风险投资者科学高效地选择最佳投资方案,因而具有较高的理论意义及实践价值.     

京津冀协同发展背景下文化产业资源配置效率评价与对策

为提高京津冀协同发展战略实施效率,利用DEA方法,对京津冀地区文化产业资源配置效率进行了评价。结果表明,京津冀地区文化产业发展不均衡。其中,北京文化产业资源配置效率最高,天津资源配置效率有所波动,而河北省资源配置效率不佳;京津冀整体相比于长三角地区在资源配置效率方面还存在一定差距。在此基础上,提出京津冀协同发展文化产业资源配置目标调整和改进方案。最后,提出了提高京津冀协同发展文化产业资源配置效率的对策建议。     

The existence of core allocations in a one sector model of capital accumulation

The existence of core allocations in a one sector model of capital accumulation with heterogeneous households is demonstrated. The result follows as an application of Scarf's Theorem on the core of a balanced game.     

Representation of constitutions under incomplete information

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizens are private information. We investigate whether there exist decision schemes (i.e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: (i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and (ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties.     

Anonymous monotonic social welfare functions

This paper presents two results about preference domain conditions that deepen our understanding of anonymous and monotonic Arrovian social welfare functions (ASWFs). We characterize the class of anonymous and monotonic ASWFs on domains without Condorcet triples. This extends and generalizes an earlier characterization (as Generalized Majority Rules) by Moulin (Axioms of Cooperative Decision Making, Cambridge University Press, New York, 1988) for single-peaked domains. We also describe a domain where anonymous and monotonic ASWFs exist only when there are an odd number of agents. This is a counter-example to a claim by Muller (Int. Econ. Rev. 23 (1982) 609), who asserted that the existence of 3-person anonymous and monotonic ASWFs guaranteed the existence of n-person anonymous and monotonic ASWFs for any n>3. Both results build upon the integer programming approach to the study of ASWFs introduced in Sethuraman et al. (Math. Oper. Res. 28 (2003) 309).