Population solidarity, population fair-ranking, and the egalitarian value

Abstract

We investigate the implications of two axioms specifying how a value should respond to changes in the set of players for TU games. Population solidarity requires that the arrival of new players should affect all the original players in the same direction: all gain together or all lose together. On the other hand, population fair-ranking requires that the arrival of new players should not affect the relative positions of the original players. As a result, we obtain characterizations of the egalitarian value, which assigns to each player an equal share over an individual utility level. It is the only value satisfying either one of the two axioms together with efficiency, symmetry, and strategic equivalence.

Consistency, population solidarity, and egalitarian solutions for TU-games

“…In a similar way we can show the following theorem. The proof is essentially the same as that in Chun and Park (2012) and can be found in the appendix. It is an immediate consequence of Theorems 3.6 and 5.2 that adding anonymity characterizes all solutions on G, that is a solution ψ on G belongs to if and only if it satisfies efficiency, homogeneity, local monotonicity, nonnegativity, weak covariance, weak fairness, anonymity, and population solidarity.…”

“…Population solidarity requires that upon the arrival of a new player all the original players should be affected in the same direction, all weakly gain or all weakly lose. Its implications have been studied in various contexts (Thomson 1983;Chun 1986), and for TU-games by Chun and Park (2012).…”

“…Since linearity is only used for two-player games, and in many (economic) applications it is a technical axiom, we prefer to have a characterization of α-standardness without linearity. On the other hand, in their characterization of the CIS-value, Chun and Park (2012) use covariance. However, the CIS-value is the only covariant solution in the class considered here.…”

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

“…Moreover, ϕ satisfies aggregate monotonicity but not regular aggregate monotonicity (see Table 1). 5 Next, we introduce consistency properties, that is, properties that relate the payoff vectors chosen for the games with variable population. Before doing this, we need to define the concept of a reduced game.…”

“…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).…”