Alternative Axiomatic Characterizations of the Grey Shapley Value
The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connectio...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Kharazmi University
2014-05-01
|
| Series: | International Journal of Supply and Operations Management |
| Subjects: | |
| Online Access: | http://ijsom.com/article_1904_366.html |
| _version_ | 1828873362260099072 |
|---|---|
| author | Sirma Zeynep Alparslan Gok Osman Palanci Mehmet Onur Olgun |
| author_facet | Sirma Zeynep Alparslan Gok Osman Palanci Mehmet Onur Olgun |
| author_sort | Sirma Zeynep Alparslan Gok |
| collection | DOAJ |
| description | The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends. |
| first_indexed | 2024-12-13T07:15:11Z |
| format | Article |
| id | doaj.art-144dade28d054865bea6b942d0e48e5a |
| institution | Directory Open Access Journal |
| issn | 2383-1359 2383-2525 |
| language | English |
| last_indexed | 2024-12-13T07:15:11Z |
| publishDate | 2014-05-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | International Journal of Supply and Operations Management |
| spelling | doaj.art-144dade28d054865bea6b942d0e48e5a2022-12-21T23:55:35ZengKharazmi UniversityInternational Journal of Supply and Operations Management2383-13592383-25252014-05-01116980Alternative Axiomatic Characterizations of the Grey Shapley ValueSirma Zeynep Alparslan Gok0Osman Palanci1 Mehmet Onur Olgun2Süleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, 32260 Isparta, TurkeySüleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, 32260 Isparta, TurkeySüleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, 32260 Isparta, TurkeyThe Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.http://ijsom.com/article_1904_366.htmlCooperative gamesUncertaintygrey numbersthe Shapley valuedividendsDecision makingOperations Research |
| spellingShingle | Sirma Zeynep Alparslan Gok Osman Palanci Mehmet Onur Olgun Alternative Axiomatic Characterizations of the Grey Shapley Value International Journal of Supply and Operations Management Cooperative games Uncertainty grey numbers the Shapley value dividends Decision making Operations Research |
| title | Alternative Axiomatic Characterizations of the Grey Shapley Value |
| title_full | Alternative Axiomatic Characterizations of the Grey Shapley Value |
| title_fullStr | Alternative Axiomatic Characterizations of the Grey Shapley Value |
| title_full_unstemmed | Alternative Axiomatic Characterizations of the Grey Shapley Value |
| title_short | Alternative Axiomatic Characterizations of the Grey Shapley Value |
| title_sort | alternative axiomatic characterizations of the grey shapley value |
| topic | Cooperative games Uncertainty grey numbers the Shapley value dividends Decision making Operations Research |
| url | http://ijsom.com/article_1904_366.html |
| work_keys_str_mv | AT sirmazeynepalparslangok alternativeaxiomaticcharacterizationsofthegreyshapleyvalue AT osmanpalanci alternativeaxiomaticcharacterizationsofthegreyshapleyvalue AT mehmetonurolgun alternativeaxiomaticcharacterizationsofthegreyshapleyvalue |