Report
Lorenz Population Monotonic Allocation Schemes for TU-games
| Title: | Lorenz Population Monotonic Allocation Schemes for TU-games |
|---|---|
| Authors: | Izquierdo Aznar, Josep Maria, Montes, Jesús, Rafels, Carles |
| Source: | UB Economics – Working Papers [ERE] Dipòsit Digital de la UB Universidad de Barcelona |
| Publisher Information: | Universitat de Barcelona. Facultat d'Economia i Empresa, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | Teoria de jocs, Business mathematics, Functions of real variables, Matemàtica financera, Funcions de variables reals, Jocs d'atzar (Matemàtica), Game theory, Games of chance (Mathematics) |
| Description: | 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. |
| Document Type: | Research |
| File Description: | application/pdf; x p. |
| Language: | English |
| Access URL: | https://hdl.handle.net/2445/200322 http://hdl.handle.net/2445/200322 |
| Rights: | CC BY NC ND |
| Accession Number: | edsair.dedup.wf.002..8863ea68cc3dc28cb339601f63e68b88 |
| Database: | OpenAIRE |
| Description not available. |