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Quasi-Owen Value for Games on Augmenting Systems with a Coalition Structure
Volume 34, Issue 3 (2023), pp. 635–663
Pub. online: 25 August 2023      Type: Research Article      Open accessOpen Access
Received
1 February 2023
Accepted
1 August 2023
Published
25 August 2023

Abstract

This paper focuses on games on augmenting systems with a coalition structure that can be seen as an extension of games with a coalition structure and games on augmenting systems. Considering the player payoffs, the quasi-Owen value is defined. To show the rationality of this payoff index, five representative axiomatic systems are established. The population monotonic allocation scheme (PMAS) and the core are introduced. Moreover, the relationships between the PMAS and quasi-Owen value as well as the core and quasi-Owen value are discussed. Finally, an illustrative example is given to show the concrete application of the new payoff indices.

References

 
Albizuri, M.J. (2008). Axiomatizations of the Owen value without efficiency. Mathematical Social Sciences, 55(1), 78–89.
 
Algaba, E., Bilbao, J.M., van den Brink, R., Jiménez-Losada, A.J. (2003). Axiomatizations of the Shapley value for cooperative games on antimatroids. Mathematical Methods of Operations Research, 57(1), 49–65.
 
Algaba, E., Bilbao, J.M., Slikker, M. (2010). A value for games restricted by augmenting systems. SIAM Journal on Discrete Mathematics, 24(3), 992–1010.
 
Alonso-Meijde, J.M., Fiestras-Janeiro, M.G. (2002). Modification of the Banzhaf value for games with a coalition structure. Annals of Operations Research, 109(1–4), 213–227.
 
Alonso-Meijide, J.M., Carreras, F.M., Fiestras-Janeiro, G., Owen, G. (2007). A comparative axiomatic characterization of the Banzhaf-Owen coalitional value. Decision Support Systems, 43(3), 701–712.
 
Amer, R., Carreras, F., Giménez, J.M. (2002). The modified Banzhaf value for games with coalition structure: an axiomatic characterization. Mathematical Social Sciences, 43(1), 45–54.
 
Aumann, R., Dreze, J. (1974). Cooperative games with coalition structures. International Journal of Game Theory, 3(3), 217–237.
 
Bilbao, J.M. (1998). Axioms for the Shapley value on convex geometries. European Journal of Operational Research, 110(2), 368–376.
 
Bilbao, J.M. (2003). Cooperative games under augmenting systems. SIAM Journal of Discrete Mathematics, 17(1), 122–133.
 
Bilbao, J.M., Ordón¯ez, M. (2009). Axiomatizations of the Shapley value for games on augmenting systems. European Journal of Operational Research, 196(3), 1008–1014.
 
Bilbao, J.M., Edelman, P.H. (2000). The Shapley value on convex geometries. Discrete Applied Mathematics, 103(1), 33–40.
 
Bilbao, J.M., Jimenez, A., Lopez, J.J. (1998). The Banzhaf power index on convex geometries. Mathematical Social Sciences, 36(2), 157–173.
 
Bilbao, J.M., Lebrón, E., Jiménez, N. (1999). The core of games on convex geometries. European Journal of Operational Research, 119(2), 365–372.
 
Bilbao, J.M., Driessen, T.S.H., Jiménez-Losada, A.J., Lebrón, E. (2001). The Shapley value for games on matroids: the static model. Mathematical Methods of Operations Research, 53(2), 333–348.
 
Bilbao, J.M., Driessen, T.S.H., Jiménez-Losada, A., Lebrón, E. (2002). The Shapley value for games on matroids: the dynamic model. Mathematical Methods of Operations Research, 56(2), 287–301.
 
Edelman, P.H., Jamison, R.E. (1985). The theory of convex geometries. Geometriae Dedicata, 19(3), 247–270.
 
Faigle, U., Kern, W. (1992). The Shapley value for cooperative games under precedence constraints. International Journal of Game Theory, 21(3), 249–266.
 
Grabisch, M. (1997). k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, 92(2), 167–189.
 
Hamiache, G. (1999). A new axiomatization of the Owen value for games with coalition structures. Mathematical Social Sciences, 37(3), 281–305.
 
Hart, S., Kurz, M. (1983). Endogeneous formation of coalitions. Econometrica, 51(4), 1047–1064.
 
Hart, S., Mas-Colell, A. (1989). Potential value and consistency. Econometrica, 57(3), 589–614.
 
Hu, X.F. (2021). New axiomatizations of the Owen value. Mathematical Methods of Operations Research, 93(3), 585–603.
 
Khmelnitskaya, A.B., Yanovskaya, E.B. (2007). Owen coalitional value without additivity axiom. Mathematical Methods of Operations Research, 66(2), 255–261.
 
Lorenzo-Freire, S. (2017). New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property. Top, 25, 579–600.
 
Lorenzo-Freire, S. (2019). On the Owen value and the property of balanced contributions within unions. Journal of Optimization Theory and Applications, 183(2), 757–762.
 
Meng, F.Y., Zhang, Q. (2012). Cooperative games on convex geometries with a coalition structure. Journal of Systems Science Complexity, 25(5), 909–925.
 
Meng, F.Y., Chen, X.H., Zhang, Q. (2015). A coalitional value for games on convex geometries with a coalition structure. Applied Mathematics and Computation, 266, 605–614.
 
Meng, F.Y., Zhang, Q., Chen, X.H. (2016). A value for games on augmenting systems with a coalition structure. Operations Research Letters, 44(3), 324–328.
 
Meng, F.Y., Li, Z.J., Dong, Q., Fu, L.X., Zhang, Y.Q. (2023). Profit allocation on a four-echelon supply chain in perspective of cooperative games on augmenting systems. Expert Systems with Applications, 219, 119639.
 
Myerson, R.B. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2(3), 225–229.
 
Myerson, R.B. (1980). Conference structures and fair allocation rules. International Journal of Game Theory, 9(3), 169–182.
 
Owen, G. (1977). Values of games with a priori unions. In: Henn, R., Moeschlin, O. (Eds.), Mathematical Economics and Game Theory., Lecture Notes in Economics and Mathematical Systems, Vol. 141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45494-3_7.
 
Owen, G. (1978). Characterization of the Banzhaf-Coleman index. SIAM Journal on Applied Mathematics, 35(2), 315–327.
 
Peleg, B. (1986). On the reduced game property and its converse. International Journal of Game Theory, 15(3), 187–200.
 
Peleg, B. (1989). Introduction to the Theory of Cooperative Games, chapter 8 the Shapley value. RM 88 Center for Research in Mathematical Economics and Game Theory, The Hebrew University, Jerusalem Israel.
 
Pulido, M.A., Sánchez-Soriano, J. (2009). On the core the weber set and convexity in games with a priori unions. European Journal of Operational Research, 193(2), 468–475.
 
Sprumont, Y. (1990). Population monotonic allocation schemes for cooperative games with transferable utility. Games and Economic Behavior, 2(4), 378–394.
 
Wang, G.M., Cui, Z.G., Shan, E.F. (2022). An axiomatization of the value α for games restricted by augmenting systems. Mathematics, 10(15), 2803.
 
Winter, E. (1992). The consistency and potential for values of games with coalition structure. Games and Economic Behavior, 4(1), 132–144.
 
Young, H. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14(1), 65–72.
 
Zou, R., Xu, G.J., Li, W.Z., Hu, X.F. (2020). A coalitional compromised solution for cooperative games. Social Choice and Welfare, 55(4), 735–758.

Biographies

Tang Jie
tang_112017@163.com

J. Tang received the MS degree from Qingdao Technological University in 2008 and the PhD degree from Central South University in 2020. Currently, she is an associated professor in Nanjing University of Information Science and Technology Nanjing. Her research interests include game theory, decision making and preference relation. At present, she has published more than 30 papers.

Li Zijun
lizijun1127@csu.edu.cn

Z. Li is carrying out her PhD degree in School of Business, Central South University. She received his master degree in Chongqing University in 2016. Her research interests include fuzzy game, stochastic game and decision making. At present, she has published 3 papers.

Meng Fanyong
mengfanyongtjie@163.com

F. Meng received the MS degree from Guangxi University in 2008 and the PhD degree from Beijing Institute of Technology, China in 2011. From 2014 to 2016, he was a Post-Doctoral Researcher with the School of Business, Central South University. Currently, he is a professor in Nanjing University of Information Science & Technology, and Central South University. His research interests include fuzzy mathematics, decision making and game theory. At present, he has published more than 150 papers.


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© 2023 Vilnius University
Open access article under the CC BY license.

Keywords
cooperative game with a coalition structure augmenting system axiomatic system quasi-Owen value

Funding
This work was supported by the National Natural Science Foundation of China (No. 72371134), the Ministry of Education Humanities and Social Science Foundation of China (No. 22YJ630061), the Research Institute for Risk Governance and Emergency Decision-Making, Nanjing University of Information Science & Technology, and the Startup Foundation for Introducing Talent of NUIST (No. 2020r001).

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