Convexity of Bertrand oligopoly TU-games with differentiated products

In this article we consider Bertrand oligopoly TU-games with differentiated products. We assume that the demand system is Shubik's (1980) and that firms operate at a constant and identical marginal and average cost. First, we show that the alpha and beta- characteristic functions (Aumann 1959) lead to the same class of Bertrand oligopoly TU-games and we prove that the convexity property holds for this class of games. Then, following Chander and Tulkens (1997) we consider the gamma-characteristic function where firms react to a deviating coalition by choosing individual best reply strategies. For this class of games, we show that the Equal Division Solution belongs to the core and we provide a sufficient condition under which such games are convex.Bertrand oligopoly TU-games; Core; Convexity; Equal Division Solution

Cournot oligopoly interval games

In this paper we consider cooperative Cournot oligopoly games. Following Chander and Tulkens (1997) we assume that firms react to a deviating coalition by choosing individual best reply strategies. Lardon (2009) shows that if the inverse demand function is not differentiable, it is not always possible to define a Cournot oligopoly TU(Transferable Utility)-game. In this paper, we prove that we can always specify a Cournot oligopoly interval game. Furthermore, we deal with the problem of the non-emptiness of two induced cores: the interval gamma-core and the standard gamma-core. To this end, we use a decision theory criterion, the Hurwicz criterion (Hurwicz 1951), that consists in combining, for any coalition, the worst and the better worths that it can obtain in its worth interval. The first result states that the interval gamma-core is non-empty if and only if the oligopoly TU-game associated with the better worth of every coalition in its worth interval admits a non-empty gamma-core. However, we show that even for a very simple oligopoly situation, this condition fails to be satisfied. The second result states that the standard gamma-core is non-empty if and only if the oligopoly TU- game associated with the worst worth of every coalition in its worth interval admits a nonempty gamma-core. Moreover, we give some properties on every individual profit function and every cost function under which this condition always holds, what substantially extends the gamma-core existence results in Lardon (2009).Cournot oligopoly interval game; Interval gamma-core; Standard gamma-core; Hurwicz criterion;

The gamma-core in Cournot oligopoly TU-games with capacity constraints

In cooperative Cournot oligopoly games, it is known that the alpha-core is equal to the beta-core, and both are non-empty if every individual profit function is continuous and concave (Zhao 1999b). Following Chander and Tulkens (1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the gamma-core, by two different approaches. The first establishes that the associated Cournot oligopoly TU(Transferable Utility)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao's core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the gamma-core called NP(Nash Pro rata)-value. This result generalizes Funaki and Yamato's core existence result (1999) from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity and non-cooperative fairness.Cournot oligopoly TU-games; gamma-core; Balanced game; NP-value; Noncooperative fairness

The core of voting games with externalities

The purpose of this article is to analyze a class of voting games in which externalities are present. We consider a society in which coalitions can be formed and where a finite number of voters have to choose among a set of alternatives. A coalition is winning if it can veto any proposed alternative. In our model, the veto power of a coalition is dependent on the coalition formation of the outsiders. We show that whether or not the core is non-empty depends crucially on the expectations of each coalition regarding outsiders' behavior when it wishes to veto an alternative. On the one hand, if each coalition has pessimistic expectations, then the core is non-empty if and only if the dimension of the set of alternatives is equal to one. On the other hand, if each coalition has optimistic expectations, the non-emptiness of the core is not ensured.voting games; externalities; core

Stackelberg oligopoly TU-games: characterization of the core and 1-concavity of the dual game

In this article we consider Stackelberg oligopoly TU-games in gamma-characteristic function form (Chander and Tulkens 1997) in which any deviating coalition produces an output at a first period as a leader and outsiders simultaneously and independently play a quantity at a second period as followers. We assume that the inverse demand function is linear and that firms operate at constant but possibly distinct marginal costs. Generally speaking, for any TU-game we show that the 1-concavity property of its dual game is a necessary and sufficient condition under which the core of the initial game is non-empty and coincides with the set of imputations. The dual game of a Stackelberg oligopoly TU-game is of great interest since it describes the marginal contribution of followers to join the grand coalition by turning leaders. The aim is to provide a necessary and sufficient condition which ensures that the dual game of a Stackelberg oligopoly TU-game satisfies the 1-concavity property. Moreover, we prove that this condition depends on the heterogeneity of firms' marginal costs, i.e., the dual game is 1-concave if and only if firms' marginal costs are not too heterogeneous. This last result extends Marini and Currarini's core non-emptiness result (2003) for oligopoly situations.Stackelberg oligopoly TU-game; Dual game; 1-concavity

Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions

The Bertrand Oligopoly situation with Shubik's demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with respect to the distinct marginal costs. This Bertrand Oligopoly Game is shown to be totally balanced, but fails to be convex unless all the firms have the same marginal costs. Under the complementary circumstances, the Bertrand Oligopoly Game is shown to be convex and in addition, its Shapley value is fully determined on the basis of linearity applied to an appealing decomposition of the Bertrand Oligopoly Game into the difference between two convex games, besides two nonessential games. One of these two essential games concerns the square of one non- essential game.Bertrand Oligopoly situation, Bertrand Oligopoly Game, Convexity, Shapley Value, Total Balancedness.

The Average Tree Solution for Multi-choice Forest Games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.

Enseigner la compréhension en lecture à des élèves avec déficience intellectuelle : à quelles conditions ? Avec quels outils ? Et pour quels résultats !

Notre mémoire vise à répondre à la question suivante : des pratiques d’enseignement de la compréhension en lecture, adaptées aux besoins particuliers des élèves avec une déficience intellectuelle, peuvent-elles modifier durablement leurs capacités à comprendre et à raconter des textes narratifs ? Nous présentons les compétences simultanément requises pour comprendre selon Goigoux et Cèbe (2013) et les pratiques les plus efficaces pour les enseigner aux élèves : un enseignement explicite et intégratif, intensif et durable. Nous construisons des interventions didactiques et pédagogiques que nous proposons à 36 élèves de classes spécialisées (CLIS en France). Dans une étude quantitative, nous en mesurons les effets et analysons les résultats

Optimal Deterrence of Cooperation

We introduce axiomatically a new solution concept for cooperative games with transferable utility inspired by the core. While core solution concepts have investigated the sustainability of cooperation among players, our solution concept, called contraction core, focuses on the deterrence of cooperation. The main interest of the contraction core is to provide a monetary measure of the robustness of cooperation into the grand coalition. We motivate this concept by providing optimal fine imposed by competition authorities for the dismantling of cartels in oligopolistic markets. We characterize the contraction core on the set of balanced cooperative games with transferable utility by four axioms: the two classic axioms of non-emptiness and individual rationality, a superadditivity principle and a new axiom of consistency