Lorenz Population Monotonic Allocation Schemes for TU-games

Sprumont (1990) introduces Population Monotonic Allocation Scheme (PMAS) and proves that every assignment game with at least two sellers and two buyers, where each buyer-seller pair derives a positive gain from trade, lacks a PMAS. In particular glove games lacks PMAS. We propose a new cooperative TU-game concept, Lorenz-PMAS, which relaxes some population monotonicity conditions by requiring that the payoff vector of any coalition is Lorenz dominated by the corresponding restricted payoff vector of larger coalitions. We show that every TU-game having a Lorenz-PMAS is totally balanced, but the converse is not true in general. We obtain a class of games having a Lorenz-PMAS, but not PMAS in general. Furthermore, we prove the existence of Lorenz-PMAS for every glove game and for every assignment game with at most five players. Additionally, we also introduce two new notions, Lorenz-PMAS-extendability and Lorenz-PMAS-exactness,and discuss their relationships with the convexity of the game

Monotonicity of the core-center of the airport game

Abstract One of the main goals of this paper is to improve the understanding of the way in which the core of a specific cooperative game, the airport gam

A NOTE ON THE MONOTONIC CORE

The monotonic core of a cooperative game with transferable utility is the set formed by all its Population Monotonic Allocation Schemes. In this paper we show that this set always coincides with the core of a certain game, with and without restricted cooperation, associated to the initial game.Population Monotonic Allocation Schemes, monotonic core, games with restricted cooperation, 91A12