Transfer Rate Rules and Core Selections in NTU Games.

Dans cette note, on propose quelques applications directes d’un résultat d’existence de Bonnisseau et Iehlé (2003). Ces auteurs ont montré l’existence d’allocations du cœur dans les jeux NTU qui satisfont un équilibre de taux de transfert sous une condition de balancement dépendant. Il s’avère que la notion de balancement dépendant procure en fait un outil manipulable pour sélectionner le cœur. Pour illustrer ce fait, nous montrons que cette notion permet d’obtenir des résultats d’existence dans des modèles de cœur avec partenariat, cœur socialement stable, prekernel moyen intersecté avec le cœur et de cœur interne faible.Different kinds of asymmetries between players can occur in core allocations, in that case the stability of the concept is questioned. One remedy consists in selecting robust core allocations. We review, in this note, results that all select core allocations in NTU games with different concepts of robustness. Within a unified approach, we deduce the existence of allocations in: the partnered core, the social stable core, the core intersected with average prekernel, the weak inner core. We use a recent contribution of Bonnisseau and Iehle (2003) that states the existence of core allocations with a transfer rate rule equilibrium under a dependent balancedness assumption. It shall turn out to be manipulable tools for selecting the core.Sélections du coeur dans les jeux NTU; Balancement dépendant; Jeux coopératifs; Core Selections in NTU Games; Dependent balancedness; Cooperative game;

Sustainability in a Multiproduct and Multiple Agent Contestable Market.

We prove that a natural monopoly can set subsidy free pricing and sustainable pricing schedules in general economic environment. The setting is a multiproduct and multiple agent contestable market where demands are elastic and where rivals can enter the sub-markets composed by a set of the products line and a set of agents. Our results suggest that the existence results of the extant literature admit analogues even in an environment where rivals have enlarged possibilities to enter the market and where demands react to prices. The approach makes use of cooperative games to deduce the main results under conditions of fair sharing cost, threshold in the consumption and regularity of the profit function.Subsidy Free Princing; Existence Result; Cooperative game; Sustainability; Natural monopoly;

Transfer Rate Rules and Core Selections in NTU Games

Different kinds of asymmetries between players can occur in core allocations, in that case the stability of the concept is questioned. One remedy consists in selecting robust core allocations. We review, in this note, results that all select core allocations in NTU games with different concepts of robustness. Within a unified approach, we deduce the existence of allocations in: the partnered core, the social stable core, the core intersected with average prekernel, the weak inner core. We use a recent contribution of Bonnisseau and Iehlé (2003) that states the existence of core allocations with a transfer rate rule equilibrium under a dependent balancedness assumption. It shall turn out to be manipulable tools for selecting the core.Cooperative games, dependent balancedness, core selections in NTU games.

Stable pricing in monopoly and equilibrium-core of cost games

We prove the existence of subsidy free and sustainable pricing schedule in multiproduct contestable markets. We allow firms to discriminate the local markets that are composed by a set of the products line and a set of agents. Results are obtained under an assumption of fair sharing cost and under boundary condition of demand functions. The pricing problem is modelled in terms of equilibrium-core allocations of parameterized cost games.Cooperative games, contestable markets, sustainability, subsidy free, parameterized cost games.

The core-partition of hedonic games

A pure hedonic game describes the situation where player's utility depends only on the identity of the members of the group he belongs to. The paper provides a necessary and sufficient condition for the existence of core-partition in hedonic games. The condition is based on a new concept of balancedness, called pivotal balancedness. pivotal balancedness involves especially the notion pivotal distribution that associates to each coalition a sub-group of players in the coalition. Then, we proceed to a review of several sufficient conditions for core-partition existence showing how the results can be unified through suitably chosen pivotal distributions.Hedonic game, group formation, core-partition, balancedness.

The Core-Partition of Hedonic Games.

La classe des jeux hédonistiques purs modélisent des situations d’interactions sociales où l’utilité de chaque joueur dépend seulement de l’identité du groupe auquel il appartient. L’article propose une condition nécessaire et suffisante pour l’existence de partition stable, au sens du cœur, dans les jeux hédonistiques. La condition, appelée balancement avec pivot, raffine la condition usuelle de balancement. Elle fait notamment appel à des distributions pivots qui, à chaque coalition, associe un sous-groupe de joueurs dans la coalition. Nous unifions les résultats de la littérature sur les partitions stables en identifiant des distributions pivots adéquates.In a hedonic game the preference relation of each player is defined on the set of coalitions that contain the player. The paper provides a necessary and sufficient condition for core-partition existence in a hedonic game. The condition is based on a new concept of balancedness, called pivotal balancedness, involving subsets of players in any given family of coalitions. Pivotal balancedness highlights the existence of key players in each coalition that are relevant for the existence of a core-partition.Hedonic Game; Group Formation; Core-Partition; Balancedness; Jeu hédonistique; Formation de groupes; Coeur-partition; Balancement;

Essential Data, Budget Sets and Rationalization

According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An ”essential experiment” consists of observed consumption bundles (x1,xn) and a feasibility matrix α. Starting with a standard experiment, in which the economist has specific budget sets in mind, we show that the necessary and sufficient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full specification of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment (x1,...,xn;α), we show that the cyclical consistency of α, together with a further consistency condition involving both (x1,...,xn) and α, guarantees that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with (x1,...,xn;α). The conditions are also trivially necessary.Afriat’s theorem, budget sets, cyclical consistency, rational choice, revealed preference

Stable pricing in monopoly and equilibrium-core of cost games

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la MSE 2005.23 - Série Bleue - ISSN : 1624-0340We prove the existence of subsidy free and sustainable pricing schedule in multiproduct contestable markets. We allow firms to discriminate the local markets that are composed by a set of the products line and a set of agents. Results are obtained under an assumption of fair sharing cost and under boundary condition of demand functions. The pricing problem is modelled in terms of equilibrium-core allocations of parameterized cost games.L'existence de tarifications sans subventions croisées et soutenable est prouvée dans un marché contestable multiproduit où les firmes ont la possibilité de discriminer les marchés locaux, composés d'une partie de la ligne commerciale et d'une partie d'agents. Les résultats sont obtenus sous une hypothèse de fonction de coût à partage équitable, et sous des conditions de bord des fonctions de demandes. Le problème de tarification est modélisé par des coeurs-équilibres de jeux de coût paramétrés

Payoff-dependant Balancedness and Cores.

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parameterized cooperative games is introduced. This new setting and its associated equilibrium–core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium–core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non-convexities. Applications to extant results taken from game theory and economic theory are given.Balancedness; Cooperative game; Core; Parametrized game;

Stable pricing in multiproduct natural monopoly (in French)

We provide some existence results of stable pricings for natural monopoly as defined in the theory of contestable markets. The main addings are based on the assumption of separated markets and the possibilities of entries. We borrow tools from cooperative game theory. Following the work of Bendali et al. (Revista de Matematicas Aplicadas, 2000), we make full use of parameterized cores of games with side payments to characterize subsidy free and sustainable pricings.natural monopoly, contestable markets, multiproduct firms, sustainability, subsidy free prices.