C-complete sets for compromise stable games

The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets. Furthermore, we discuss the number of different larginal vectors corresponding to a c-complete set of orderings.     

The pseudo-average rule: bankruptcy,cost allocation and bargaining

A division rule for claims problems, also known as bankruptcy or rationing problems, based on the pseudo-average solution is studied (for 2-person problems). This solution was introduced in Moulin (Jpn Econ Rev 46:303–332, 1995) for discrete cost allocation problems. Using the asymptotic approach, we obtain a division rule for claims problems. We characterize the division rule axiomatically and show that it coincides with the rule associated to the equal area bargaining solution (this is not true for n = 3). Moreover, following Moulin and Shenker (J Econ Theor 64:178–201, 1994), we show that its associated solution for continuous homogeneous goods is precisely the continuous pseudo-average solution.     

Type monotonic allocation schemes for a class of market games

We consider an extension of glove markets, called T-markets, characterize a family of weighted allocation rules, and define related cooperative games. For the class of T-market games we introduce a new solution concept called the type monotonic allocation scheme. It turns out that the nucleolus and the τ-value generate the same type monotonic allocation scheme with nice extra properties. Initial research for this paper was supported by the Hungarian Scientific Research Fund grant OTKA T030945. The authors thank Ruud Hendrickx for his valuable comments. Research of T. Solymosi was also supported in part by OTKA grant T046194.     

Convex multi-choice games: Characterizations and monotonic allocation schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Furthermore, level-increase monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is extendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.     

Correction to: Equilibrium computation in resource allocation games

Mathematical Programming - This note contains a correction of Theorems 1 and 2 and the subroutine $$textsc {Restore}$$ of the article Harks, T., Timmermans, V. Equilibrium computation in resource...     

Maximal stable sets of two-player games

If a connected component of perfect equilibria of a two-player game contains a stable set as defined by Mertens, then the component is itself stable. Thus the stable sets maximal under inclusion are connected components of perfect equilibria. Received: October 1999/Revised: February 2001     

Resource allocation among competing activities: a lexicographic minimax approach

We examine an allocation problem in which the objective is to allocate resources among competing activities so as to balance weighted deviations from given demands. A lexicographic minimax algorithm that solves successive problems by A minimax optimizer is developed. The algorithm is extremely fast and can readily solve large-scale problems that may be encountered in applications, e.g., in production planning.     

Resource allocation in a large decentralized enterprise

We present a model of an enterprise comprising several operating units pursuing their production goals with a fair degree of autonomy, but under resource constraints imposed by a headquarters function. Specifically, each operating unit is assumed to seek a maximization of a perceived market value of its product output, subject to constraints on resources such as capital for plants and equipment, headcount, etc. imposed by headquarters. The headquarters function pursues a global optimization problem which takes into account the market values of all the products of the operating units, but also the cost of the resources and their regulation. Under suitable assumptions of linearity, the operation of the enterprise is formulated as a novel hierarchical structure of linear programming problems. An algorithm is presented for the solution of a class of such problems.     

Resource pricing games on graphs: existence of Nash equilibria

In this letter, we consider a non-cooperative resource pricing game on a graph where sellers (i.e., players) set the prices for their own resources to maximize the payoffs and buyers migrate to seek the least expensive resources. We present a model for the resource pricing game and prove the existence of Nash equilibria on regular and hierarchical graphs. The results obtained are applicable to the study of market economies, social networks and computer networks where individuals trade resources in a spatially extended environment.     

Resource allocation in light of a stochastic stream of opportunities

The problem of resource allocation over time in a world of uncertainty has proven to be formidable indeed. Efforts to date have either removed the essential dynamics from the formulation or have produced complex backward optimization expressions of questionable usefulness. We deal with the development of an optimal strategy for the situation where potential projects arrive in accordance with a specified stochastic process. A project, once revealed, possesses a nonstochastic cash flow stream. The investor seeks to maximize his long-run rate of return (μ). The resulting (implicit) expression involving μ requires numerical solution in general. However, under certain conditions, a direct solution is possible. An illustrative example is presented.     

The stable fixtures problem—A many-to-many extension of stable roommates

We study a many-to-many generalisation of the well-known stable roommates problem in which each participant seeks to be matched with a number of others. We present a linear-time algorithm that determines whether a stable matching exists, and if so, returns one such matching.     

Characterizations of the optimal stable allocation mechanism

The stable allocation problem is the generalization of (0,1)-matching problems to the allocation of real numbers (hours or quantities) between two separate sets of agents. The same unique-optimal matching (for one set of agents) is characterized by each of three properties: “efficiency”, “monotonicity”, and “strategy-proofness”.     

Additive stable solutions on perfect cones of cooperative games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described. Received: December 2001/Revised: July 2002 RID="*" ID="*"  This note contains the new results, which were presented by the first author in an invited lecture at the XIV Italian Meeting on Game Theory and Applications in Ischia, July 2001. The lecture was dedicated to Irinel Dragan on the occasion of his seventieth birthday.     

Every finitely generated regular field extension has a stable transcendence base

A fieldK is called stable if every finitely generaed regular field extensionF/K has a transcendence basex ₁, …,x _n with the following properties: The field extensionF/K(x ₁,…,x _n ) is separable and the Galois hull ofF/K(x ₁,…,x _n ) remains regular overK, i.e.K is algebraically closed in . We prove in this paper thatevery field is stable. This generalizes results from [FJ1] and [GJ] which prove that fields of characteristic 0 and infinite perfect fields are stable, respectively. [G] showed that finite fields are stable in dimension 1, i.e. every finitely generated regular field extension of transcendence degree 1 over a finite field has a stable transcendence base. In the last section of this paper we apply the theorem to the construction of PAC fields with additional properties. A fieldK is called PAC if every absolutely irreducible variety overK has at least oneK-rational point.     

The reactive bargaining set: Structure, dynamics and extension to NTU games

The reactive bargaining set (Granot [1994]) is the set of outcomes for which no justified objection exists. Here, in a justified objection the objector first watches how the target tries to act (if he has such an option), and then reacts by making a profit and ruining the target's attempt to maintain his share. In this paper we explore properties of the reactive bargaining set, set up the system of inequalities that defines it, and construct a dynamic system in the sense of Stearns' transfer scheme that leads the players to this set. We also extend the definition of the reactive bargaining set toNTU games in a way that keeps it nonempty. To shed light on its nature and its relative ease of computation, we compute the reactive bargaining set for games that played important role in the game theory literature.