Dynamic Shapley Value in the Game with Perishable Goods

Authors

  • Yin Li St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia; School of Economics and Management, Yanan University, Yan'an, 716000, China https://orcid.org/0000-0002-1731-4554
  • Ovanes Petrosian St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia https://orcid.org/0000-0001-7908-2261
  • Jinying Zou St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia https://orcid.org/0000-0003-4641-4017

DOI:

https://doi.org/10.21638/11701/spbu31.2021.20

Abstract

The paper investigates two-stage stochastic minimum spanning tree games with perishable goods. The cooperative behaviour of the players is defined. At each stage, all players jointly take action to construct a network with a cost matrix. At the second stage, a particular player may leave the game, and the probability of this leaving depends on the cooperative behaviour of all players at the first stage. At each stage game, the total cost of the spanning tree is calculated to include the sum of the costs of the contained edges and the cost of the loss of perishable goods expended on that edge of the spanning tree. The characteristic functions in the game are considered, and the dynamic Shapley values are modified. The time consistency of the dynamic Shapley values is studied.

Keywords:

dynamic games, minimum cost spanning tree game, stochastic games

Downloads

Download data is not yet available.
 

References

Bergantiños, G. and Vidal-Puga, J. J. (2007). A fair rule in minimum cost spanning tree problems. Journal of Economic Theory, 137(1), 326–352

Bird, C. G. (1976). On cost allocation for a spanning tree: A game theoretic approach. Networks, 6(4), 335–350

Claus, A. and Kleitman, D. J. (1973). Cost allocation for a spanning tree. Networks. Wiley Online Library, 3(4), 289–304

Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271

Dutta, B. and Kar, A. (2004). Cost monotonicity, consistency and minimum cost spanning tree games. Games and Economic Behavior, 48(2), 223–248

Janssen, L., Claus, T. and Sauer, J. (2016). Literature review of deteriorating inventory models by key topics from 2012 to 2015. International Journal of Production Economics. Elsevier, 182, 86–11

Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical society, 7(1), 48–50

Nahmias, S. (1982). Perishable Inventory Theory: a Review. Operations Research, 30(4), 680–708

Prim, R. C. (1957). Shortest Connection Networks And Some Generalizations. Bell System Technical Journal, 36(6), 1389–1401

Wan, G., Li, Q. and Cao, Y. (2019). Optimal price markdown strategy for perishable food products considering retailers service level. The theory and practice of finance and economics, 40(5), 142–147 (in Chinese)

Li, Y. (2016). The dynamic Shapley Value in the game with spanning tree. In Proceedings of 2016 International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference), STAB 2016

Li, Y. (2017). Dynamic Shapley Value for 2-stage cost sharing game with perishable products. In Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017, 3770–3774

Petrosyan, L. A., and Danilov, N. N. (1979). Stability of solutions in non-zero sum differential games with transferable payoffs. Viestnik of Leningrad Universtiy, 1, 52–59

Shapley, L. S. (1952). A value for n-person games. Rand corp santa monica ca

Downloads

Published

2021-10-30

How to Cite

Li, Y., Petrosian, O., & Zou, J. (2021). Dynamic Shapley Value in the Game with Perishable Goods. Contributions to Game Theory and Management, 14, 273–289. https://doi.org/10.21638/11701/spbu31.2021.20

Issue

Vol. 14 (2021)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.