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Title: | Lorenz Population Monotonic Allocation Schemes for TU-games |
Author: | Izquierdo Aznar, Josep Maria Montes, Jesús Rafels, Carles |
Keywords: | Teoria de jocs Matemàtica financera Funcions de variables reals Jocs d'atzar (Matemàtica) Game theory Business mathematics Functions of real variables Games of chance (Mathematics) |
Issue Date: | 2023 |
Publisher: | Universitat de Barcelona. Facultat d'Economia i Empresa |
Series/Report no: | [WP E-Eco23/447] |
Abstract: | 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. |
It is part of: | UB Economics – Working Papers, 2023, E23/447 |
URI: | http://hdl.handle.net/2445/200322 |
Appears in Collections: | UB Economics – Working Papers [ERE] |
Files in This Item:
File | Description | Size | Format | |
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E23-447_Izquierdo et al.pdf | 379.93 kB | Adobe PDF | View/Open |
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