Sylvain BEAL | Université de Franche-Comté (original) (raw)

Papers by Sylvain BEAL

We consider natural axioms for allocating the income of museum pass programs. Two allocation rule... more We consider natural axioms for allocating the income of museum pass programs. Two allocation rules are characterized and are shown to coincide with the Shapley value and the equal division solution of the associated TU-game introduced by Ginsburgh and Zang (2003).

We consider the problem of allocating the income of museum pass programs. Various properties of a... more We consider the problem of allocating the income of museum pass programs. Various properties of an allocation rule for such problems are introduced. Two allocation rules are characterized and are shown to coincide with the Shapley value and the equal division solution of the associated tu-game introduced by Ginsburgh and Zang [2003]. These two caracterizations are comparable in the sense

Economics Letters, 2012

We replace the axiom of fairness used in the characterization of the Myerson value by fairness fo... more We replace the axiom of fairness used in the characterization of the Myerson value by fairness for neighbors in order to characterize the component-wise egalitarian solution. When a link is broken, fairness states the two players incident to the link should be affected similarly while fairness for neighbors states that a player incident to the link and any of his other neighbors should be affected similarly. Fairness for neighbors is also used to characterize the component-wise egalitarian surplus solution and a two-step egalitarian solution. These results highlight that egalitarian and marginalistic allocation rules can be obtained by applying the same equal gain/loss property to different types of players.

We study values for transferable utility games enriched by a communication graph. The most well-k... more We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (2015) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (2012). We pursue this line of research by showing that the average tree solution (Herings et al., 2008) and the compensation solution (Béal et al., 2012a) admit similar unique efficient extensions, and that there exists no efficient extension of the position Value (Meessen, 1988; Borm et al., 1992). As byproducts, we o...

We introduce the sequential equal surplus division for sharing the total welfare resulting form t... more We introduce the sequential equal surplus division for sharing the total welfare resulting form the cooperation of agents along a river with a delta. This allocation rule can be seen as a generalization of the contribution vectors introduced by Ju, Borm and Ruys (2007) in the context of TU-games. We provide two axiomatic characterizations of the sequential equal surplus division.

Workshop on dynamic networks December 15, 2014 Béal, Rémila, Solal Characterization of the Averag... more Workshop on dynamic networks December 15, 2014 Béal, Rémila, Solal Characterization of the Average Tree solution and its kernel 1 / 26

Revue d'économie politique, 2010

This article addresses the question of data-sharing mechanisms under REACH. The members of an inf... more This article addresses the question of data-sharing mechanisms under REACH. The members of an information exchange forum have to share their data. This exchange requires the adoption of a compensation scheme : the owner of a data receives a monetary compensation in return for the access to his/her data. We are interested in the choice of a compensation scheme that

Social Choice and Welfare, 2015

We study values for transferable utility games enriched by a communication graph (COgames) where ... more We study values for transferable utility games enriched by a communication graph (COgames) where the graph does not necessarily a¤ect the productivity but can in ‡uence the way the players distribute the worth generated by the grand coalition. Thus, we can envisage values that are e¢ cient instead of values that are component e¢ cient. For CO-games with connected graphs, e¢ ciency and component e¢ ciency coincide. In particular, the Myerson value (Myerson, 1977) is e¢ cient for such games. Moreover, fairness is characteristic of the Myerson value. We identify the value that is e¢ cient for all CO-games, coincides with the Myerson value for CO-games with connected graphs, and satis…es fairness.

Operations Research Letters, 2015

We provide a new and concise characterization of the Banzhaf value on the (linear) space of all T... more We provide a new and concise characterization of the Banzhaf value on the (linear) space of all TU-games on a fixed player set by means of two transparent axioms. The first one is the wellknown Dummy player axiom. The second axiom, called Strong transfer invariance, indicates that a player's payoff is invariant to a transfer of worth between two coalitions he or she belongs to. To prove this result we derive direct-sum decompositions of the space of all TU-games. We show that, for each player, the space of all TU-games is the direct sum of the subspace of TU-games where this player is dummy and the subspace spanned by the TU-games used to construct the transfers of worth. This decomposition method has several advantages listed as concluding remarks.

Economics Letters, 2014

ABSTRACT We study the consequences of a solidarity property that specifies how a value for cooper... more ABSTRACT We study the consequences of a solidarity property that specifies how a value for cooperative games should respond if some player forfeits his productivity, i.e., becomes a null player. Nullified solidarity states that in this case either all players weakly gain together or all players weakly lose together. Combined with efficiency, the null game property, and a weak fairness property, we obtain a new characterization of the equal division value.

Discrete Applied Mathematics, 2015

In Béal et al. (2013) two new axioms of invariance, called Addition invariance and Transfer invar... more In Béal et al. (2013) two new axioms of invariance, called Addition invariance and Transfer invariance respectively, are introduced to design allocation rules for TU-games. Here, we derive direct sum decompositions of the linear space of TU-games by using the TU-games selected to construct the operations of Addition and Transfer. These decompositions allow us to recover previous characterization results obtained by Béal et al. (2013), to provide new characterizations of well-known (class of) of allocation rules and also to design new allocation rules.

Games, 2010

We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial coopera... more We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.

This article shows that, for any transferable utility game in coalitional form with nonempty coal... more This article shows that, for any transferable utility game in coalitional form with nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to (n*n+4n)/4, where n is the cardinality of the player set. This number considerably improves the upper bound found so far by Koczy and Lauwers (2004).

Revue de l'OFCE, 2011

La réglementation REACH (Registration, Evaluation, Autorisation and Restriction of Chemicals) ent... more La réglementation REACH (Registration, Evaluation, Autorisation and Restriction of Chemicals) entrée en vigueur le 1 er juin 2007 contraint les entreprises à faire la preuve de l'innocuité sanitaire et environnementale des substances utilisées. L'implémentation de cette réglementation nécessite la production et l'échange d'un volume substantiel d'information technique et concurrentielle. Cet article vise à identifier les risques anticoncurrentiels liés à la mise en place de la réglementation. Les acteurs pourraient mettre en place une pénurie stratégique d'information, destinée à forclore les concurrents du processus de partage des coûts, ou au contraire organiser une abondance stratégique d'information, dans une visée d'ententes ou de stratégie d'augmentation des coûts des rivaux.

Mathematical Social Sciences, 2008

We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes tha... more We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given.

Mathematical Social Sciences, 2012

We present the axiom of weighted component fairness for the class of forest games, a generalizati... more We present the axiom of weighted component fairness for the class of forest games, a generalization of component fairness introduced by Herings, Talman and van der Laan (2008) in order to characterize the average tree solution. Given a system of weights, component efficiency and weighted component fairness yield a unique allocation rule. We provide an analysis of the set of allocation rules generated by component efficiency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions.

Mathematical Social Sciences, 2007

We define a finite-horizon repeated network formation game with consent, and study the difference... more We define a finite-horizon repeated network formation game with consent, and study the differences induced by different levels of individual rationality. We prove that perfectly rational players will remain unconnected at the equilibrium, while nonempty equilibrium networks may form when, following Neyman (1985), players are assumed to behave as finite automata. We define two types of equilibria, namely the Repeated Nash Network (RNN), in which the same network forms at each period, and the Repeated Nash Equilibrium (RNE), in which different networks may form. We state a sufficient condition under which a given network may be implemented as a RNN. Then, we provide structural properties of RNE. For instance, players may form totally different networks at each period, or the networks within a given RNE may exhibit a total order relationship. Finally we investigate the question of efficiency for both Bentham and Pareto criteria.

Mathematical Methods of Operations Research, 2013

This article shows that, for any transferable utility game in coalitional form with a nonempty co... more This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to (n 2 + 4n)/4, where n is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation. We would like to thank two anonymous referees for very valuable suggestions which have led to an improvement of the article. We have also benefited from comments of participants at the SING VII conference in Paris where an earlier draft of the article circulated under the title "On the number of blocks required to access the coalition structure core". Financial support the National Agency for Research (ANR)-research programs "Models of Influence and Network Theory" ANR.09.BLANC-0321.03 and "Mathématiques de la décision pour l'ingénierie physique et sociale" (MODMAD)-is gratefully acknowledged.

International Journal of Game Theory, 2011

We consider communication situations games being the combination of a TU-game and a communication... more We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al.

International Journal of Game Theory, 2012

We consider an alternative expression of the Shapley value that reveals a system of compensations... more We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give an interpretation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph. Firstly, we consider cooperative games with a forest (cycle-free graph). We extend the compensation vector by considering all rooted spanning trees of the forest (see Demange ) instead of orderings of the players. The associated allocation rule, called the compensation solution, is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component. Secondly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively.