Axioms of invariance for TU-games

Abstract

We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TU-games. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used.

Values for environments with externalities – The average approach

“…It is worth noting that the extension of the consensus value through the average approach coincides with the one proposed by Ju (2007). 3 For each of the last two extensions, a family of values that satisfy the properties is found.…”

A decomposition of the space of TU-games using addition and transfer invariance

“…Besides, we mention that previous characterization results obtained by Béal et al [2] can be recovered by using this method.…”

“…The axiom of Transfer invariance requires that if the worth of two coalitions of the same size is affected by opposite amounts, then the payoff of a player belonging to both coalitions should not change. Béal et al [2] show that the class of allocation rules satisfying the combination of Addition invariance and Transfer invariance strictly contains the very popular class of Efficient, Linear and Anonymous allocation rules.…”

“…Such axioms specify either the same payoff vector or the same payoff for some specific players across TU-games that are somehow linked. In [2] two new axioms of invariance are introduced. The axiom of Addition invariance requires that if the worths of all coalitions of a given size, except the grand coalition, fluctuate by the same amount, then the allocation rule should prescribe the same payoff vector.…”

Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results

“…Capturing the idea that players may commit in distributing monotonically, but not equally, variations in their wealth, we introduce regular aggregate monotonicity. The center of imputations, which has been recently axiomatized in Béal et al (2014), Casajus and Huettner (2014), Chun and Park (2012) and van den Brink (2007) without making use of monotonicity properties, comes out to be the unique single-valued solution satisfying individual rationality and equal surplus division (or, alternatively, individual rationality, regular aggregatte monotonicity and symmetry).…”