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.     

On the core of cooperative queueing games

We consider a class of cooperative games for managing several canonical queueing systems. When cooperating parties invest optimally in common capacity or choose the optimal amount of demand to serve, cooperation leads to “single-attribute” games whose characteristic function is embedded in a one-dimensional function. We show that when and only when the latter function is elastic will all embedded games have a non-empty core, and the core contains a population monotonic allocation. We present sufficient conditions for this property to be satisfied. Our analysis reveals that in most Erlang B and Erlang C queueing systems, the games under our consideration have a non-empty core, but there are exceptions, which we illustrate through a counterexample.     

Population Monotonic Allocation Schemes in Bankruptcy Games

The USA Bankruptcy Code legislates the bankruptcy of firms. Any allocation mechanism that is legal according to the Bankruptcy Code is necessarily population monotonic. Bankruptcy rules yielding a population monotonic allocation scheme in the associated bankruptcy game are characterized by efficiency, reasonability (each claimant receives a nonnegative amount not exceeding his claim), and the thieve property. The thieve property for bankruptcy problems entails that if a claimant manages to escape with his claim, the amount allocated to each remaining claimant is not larger than his share in the original problem. Many bankruptcy rules studied in the literature are efficient, reasonable, self-consistent, and monotonic. Rules satisfying these axioms are shown to yield population monotonic allocation schemes.     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

A characterization of convex games by means of bargaining sets

The aim of the paper is to characterize the classical convexity notion for cooperative TU games by means of the Mas-Colell and the Davis–Maschler bargaining sets. A new set of payoff vectors is introduced and analyzed: the max-Weber set. This set is defined as the convex hull of the max-marginal worth vectors. The characterizations of convexity are reached by comparing the classical Weber set, the max-Weber set and a selected bargaining set.     

Connection problems in mountains and monotonic allocation schemes

Directed minimum cost spanning tree problems of a special kind are studied, namely those which show up in considering the problem of connecting units (houses) in mountains with a purifier. For such problems an easy method is described to obtain a minimum cost spanning tree. The related cost sharing problem is tackled by considering the corresponding cooperative cost game with the units as players and also the related connection games, for each unit one. The cores of the connection games have a simple structure and each core element can be extended to a population monotonic allocation scheme (pmas) and also to a bi-monotonic allocation scheme. These pmas-es for the connection games result in pmas-es for the cost game.     

Minimal large sets for cooperative games

We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma. Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA.     

Dynamic cost allocation for economic lot sizing games

We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this game, i.e. an allocation over time that exactly distributes costs and is stable against coalitional defections at every period of the time horizon.     

Dominating set games

In this paper, we study cooperative cost games arising from domination problems on graphs. We introduce three games to model the cost allocation problem and we derive a necessary and sufficient condition for the balancedness of all three games.     

具有区间支付的宗派对策

在区间不确定环境下,针对具有否决权的成员与其他成员之间的合作,建立了具有区间支付的宗派对策。在区间核心中,非宗派成员得到的区间分配不能超过他对大联盟的边际贡献。给出了完全区间宗派对策的等价条件。当相应的区间减法可行时,完全区间宗派对策的区间核心中的分配可以通过两种单调区间分配方案扩张得到。算例验证了模型的有效性。     

Regular population monotonic allocation schemes

The paper introduces a refinement of the notion of population monotonic allocation scheme, called regular population monotonic allocation scheme (regularpmas). This refinement is based on economic situations in which players may have to select new partners from a set of potential players and in which there exist certain capacity constraints. A sufficient condition for the existence of a regularpmas is given. For the class of games with regularpmas, we prove that the core coincides with the Davis and Maschler and the Mas-Colell bargaining sets.     

Inventory games with permissible delay in payments

Meca et al. (2004) studied a class of inventory games which arise when a group of retailers who observe demand for a common item decide to cooperate and make joint orders with the EOQ policy. In this paper, we extend their model to the situation where retailer’s delay in payments is permitted by the supplier. We introduce the corresponding inventory game with permissible delay in payments, and prove that its core is nonempty. Then, a core allocation rule is proposed which can be reached through population monotonic allocation scheme. Under this allocation rule, the grand coalition is shown to be stable from a farsighted point of view.     

The selectope for cooperative games

The selectope of a cooperative transferable utility game is the convex hull of the payoff vectors obtained by assigning the Harsanyi dividends of the coalitions to members determined by so-called selectors. The selectope is studied from a set-theoretic point of view, as superset of the core and of the Weber set; and from a value-theoretic point of view, as containing weighted Shapley values, random order values, and sharing values. Received May 1997/Revised version September 1999     

Vertical integration with endogenous contract leadership: Stability and fair profit allocation

This paper studies vertical integration in serial supply chains with a wholesale price contract. We consider a business environment where the contracting leader may be endogenously changed before and after forming the integration. A cooperative game is formulated to normatively analyze the stable and fair profit allocations under the grand coalition in such an environment. Our main result demonstrates that vertical integration is stable when all members are pessimistic in the sense that they are sure that they will not become the contracting leader if they deviate from the grand coalition. We find that in this case, the grand coalition’s profit must be allocated more to the retailer and the members with higher costs. Nevertheless, we also show the conditions under which the upstream manufacturer can have strong power as in traditional supply chains.     

Various characterizations of convex fuzzy games

This note enlarges the literature on convex fuzzy games with new characterizing properties of such games besides the increasing average marginal return property, namely: the monotonicity of the first partial derivatives, the directional convexity and forC ²-functions the non-negativity of the second order partial derivatives.     

The equivalence of uniform and Shapley value-based cost allocations in a specific game

This paper concerns the possible equivalence of the Shapley value and other allocations in specific games. For a group buying game with a linear quantity discount schedule, the uniform allocation results in the same cost allocation as the Shapley value. In this paper, we explore whether the Shapley axioms can be used to make such connections. We also characterize the functions that result in the equivalence of these two allocations among the class of polynomial total cost functions.