A weighted position value

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in their communication links. The player who invests the most in a communication link obtains a compensation from the second one. We characterize this new allocation rule on the class of communication situations with cycle-free graphs by means of six axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. Link decomposability captures the fact that the insurance system only allows compensations between players who share a link. Weak positivity states that if the communicative strength of a link is non null, its adjacent players cannot obtain a null payoff. Finally, weak power inversion reflects the compensation mechanism.Weighted position value; MonotonicityWeighted position value; Monotonicity

A weighted position value

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in communication links. The player who invests the most in a communication link obtains transfers of worth from the second one. We characterize this new allocation rule on the class of cycle free graphs by means of four axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Meessen (1988), Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. The weighting axiom captures the fact that the allocation of players should be increasing with their level of investment.Weighted position value; Monotonicity

Marginalism and the Shapley value

We survey axiomatic results concerning the Shapley value (Shapley (1953)). This marginalist allocation rule results from an axiomatic study of the class of coalitional games. Shapley (1953) specifies a list of desirable properties of solutions for this class of games, and he shows that the combination of these properties determines a unique allocation rule, now called the Shapley value. Several authors have enriched Shapley’s axiomatic study and have provided new characterizations of this allocation rule. The aim of this article is to put into perspective these characterizations. We highlight the logical relations between the axioms. Moreover, we show how the marginalist criterion, which was not explicitely present in Shapley’s characterisation, is progressively introduced into the axiomatic.Shapley value - axiomatic study - marginalismShapley value - axiomatic study - marginalism

A weighted position value

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in communication links. The player who invests the most in a communication link obtains transfers of worth from the second one. We characterize this new allocation rule on the class of cycle free graphs by means of four axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Meessen (1988), Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. The weighting axiom captures the fact that the allocation of players should be increasing with their level of investment

A probabilistic position value

In this article, we generalize the position value, defined by Meessen (1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (G´omez et al. (2008)). We provide two characterizations of this new allocation rule. Following in Slikker’s (2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component eciency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Finally, we show that these two characterizations are logically equivalent.Game Theory, TU Games, Graph-restricted Games, Position Value.Game Theory, TU Games, Graph-restricted Games, Position Value.

A probabilistic position value

In this article, we generalize the position value, defined by Meessen (1988) for the class of deterministic communication situations, to the class of generalized probabilistic com- munication situations (G ́ Gomez et al. (2008)). We provide two characterizations of this new allocation rule. Following in Slikker's (2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link con- tributions. Then we generalize the notion of link potential, defined by Slikker (2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Finally, we show that these two characterizations are logically equivalent

Assignment of Heterogeneous Agents in Trees under the Permission Value

We investigate assignment of heterogeneous agents in trees where the allocation rule is given by the permission value. We focus on efficient hierarchies,namely those, for which the payoff of the top agent is maximized. For additive games, such hierarchies are always cogent, namely, more productive agents occupy higher positions. The result can be extended to non-additive games with appropriate restrictions on the value function. Finally, we consider auctions where agents bid for positions in a two agent vertical hierarchy. Under simultaneous bidding, an equilibrium does not exist while sequential bidding always results in a non-cogent hierarchy

Assignment of Heterogeneous Agents in Trees under the Permission Value

We investigate assignment of heterogeneous agents in trees where the allocation rule is given by the permission value. We focus on efficient hierarchies,namely those, for which the payoff of the top agent is maximized. For additive games, such hierarchies are always cogent, namely, more productive agents occupy higher positions. The result can be extended to non-additive games with appropriate restrictions on the value function. Finally, we consider auctions where agents bid for positions in a two agent vertical hierarchy. Under simultaneous bidding, an equilibrium does not exist while sequential bidding always results in a non-cogent hierarchy

Az erős,a gyenge, meg a ravasz: Hatalom és stratégiai viselkedés szavazási játékokban = The Strong, the Weak and the Cunning: Power and Strategy in Voting Games

Kutatási eredményeink három téma köré csoportosíthatók. Ezek közül az első a stratégiai megfontolások vizsgálata. Megmutatjuk, hogy a szavazók növelhetik befolyásukat, ha veszekednek más szavazókkal és a stratégiai hatalmi indexek jól definiáltak a játékok bizonyos osztályaira. Egy másik vonal a kooperatív játékok olyan kulcsfontosságú tulajdonságait vizsgálja, mint a konvexitás, vagy az egzaktság. Bizonyos esetekben a nyerő koalíciók halmaza külső okok miatt korlátozott: erre a leggyakoribb példa, mikor egy hálózaton elhelyezkedő csúcsok helyzeti befolyását vizsgáljuk. A csúcsok csak az őket összekötő élek mentén kommunikálhatnak és csak szomszédaikkal. Több érték és index is kiterjesztésre, illetve bevezetésre kerül ilyen hálózati játékokra, illetve az értékekhez axiomatikus karakterizációt adunk. Végül a hatalmi indexeket olyan játékokra is kiterjesztjük, ahol egyes szavazók hiányozhatnak. A nem stratégiai hiányzást vizsgáljuk és a Shapley értéket teljesen karakterizáljuk az általánosított súlyozott szavazási játékok osztályán. Modellünket különböző parlamentekre alkalmazzuk, illetve az elméleti módszerek több egyéb alkalmazását is vizsgáltuk, úgymint a Lisszaboni Szerződés hatását a Miniszterek Tanácsában folyó súlyozott szavazás hatalmi viszonyaira. | The results of the project centre around three themes. The first is strategic considerations. We have shown that voters are able to increase their power by strategic quarrelling and the strategic power indices are well defined for certain classes of games. Additional papers provide tests on key properties, such as convexity and exactness of cooperative games. In some situations the set of feasible (winning) coalitions is restricted exogenously. The most common example is to study positional power over a network where the voters are located at the nodes and can only communicate with their neighbours. Several values and indices are introduced and characterised for games over networks. At last we generalised power indices to weighted voting games where representatives may be absent. We study non-strategic absenteeism and characterise the Shapley value for the class of generalised weighted voting games. We have also studied applications studying the effect of absent voters in various national parliaments or the effect of the Lisbon Treaty of the European Union to the power balance in the Council of Ministers

A weighted position value

International audienceThe goal of this article is to generalize the position value (Meessen, 1988) in order to take into account the negotiation powers of players on the allocation of the worth. These negotiation powers are formalized via a weight scheme similar to the one defined by Haeringer (2006). We define and characterize a class of allocation rules such that the payoffs of the players are increasing with respect to weights