Axiomatic characterizations under players nullification

Abstract

The views expressed are those of the authors and do not necessarily reflect those of CRESE.

Nullified equal loss property and equal division values

“…An ultimate argument in favor of NEL is that NEL implies the following axiom: Balanced cycle contributions under nullification, BCyCN. (Béal et al, 2016)…”

“…These terms are equal if NEL is invoked. BCyCN is an interesting and very weak axiom as, following (Béal et al, 2016), any linear symmetric value satisfies it.…”

“…This article deals with egalitarian solutions by introducing a new axiom for TU-games called the nullified equal loss property. This axiom rests on the nullification operation studied in Béal et al (2014) and Béal et al (2016). A player is nullified if the worth of any coalition to which she belongs becomes equal to the worth of the same coalition without the player, i.e.…”

Sharing the Surplus and Proportional Values

“…Separatorization 1 refers to a player's obstruction of cooperation in the sense that the worth of any coalition containing him equals the sum of the stand-alone worths of the players in this coalition, while the worth of any coalition without this player remains unchanged. This is not to be confused with dummification as introduced in Béal et al (2018) (strengthening nullification studied in, e.g., Gómez-Rúa and Vidal-Puga (2010); Béal et al (2016b); Ferrières (2017)), where a player becomes a dummy player. The first axiom, called proportional loss under separatorization, requires that if a player becomes a separator, then all other player's payoff change in proportion to their stand-alone worths.…”

Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games

“…Another version of balanced collective contributions is examined in Béal et al . (), where the subgame induced by the departure of an agent is replaced by the game obtained after the nullification of this agent.…”