Stochastické kooperativní hry
| Thesis title in Czech: | Stochastické kooperativní hry |
|---|---|
| Thesis title in English: | Stochastic cooperative games |
| Key words: | kooperativní hra|náhodná charakteristická funkce|problém prodejce novin |
| English key words: | cooperative game|random characteristic function|newsvendor problem |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | diploma thesis |
| Thesis language: | |
| Department: | Department of Applied Mathematics (32-KAM) |
| Supervisor: | RNDr. Martin Černý |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 11.03.2024 |
| Date of assignment: | 20.03.2024 |
| Confirmed by Study dept. on: | 20.03.2024 |
| Advisors: | doc. RNDr. Ing. Miloš Kopa, Ph.D. |
| Guidelines |
| Cooperative game theory, particularly the theory of TU coalitional games, has many applications, including economics, the behavior of autonomous systems, and machine learning, to name a few. Many researchers have introduced ways to incorporate randomness into the model, whether it was randomness in the number of players, introducing random scenarios under which different valuations occur, or randomness in the payoff distribution.
The aim of this thesis is to study randomness in the characteristic function while the number of players is fixed. The first step is to create a survey of the existing literature. The second step is to extend the existing results by utilizing methods like stochastic dominance in the computation of the payoff distribution. The achieved results will be applied to a case study of the newsvendor problem. A secondary goal of the thesis is to survey and investigate the problem of coalition formation under a randomness setting. |
| References |
| [1] Hans Peters. Game theory: A Multi-leveled approach. Springer, 2015.
[2] Bezalel Peleg and Peter Sudhőlter. Introduction to the theory of cooperative games, volume 34. Springer Science & Business Media, 2007 [3] Abraham Charnes and Daniel Granot. Prior solutions: Extensions of convex nucleus solutions to chance-constrained games. Center for Cybernetic Studies, University of Texas, 1973. [4] Jeroen Suijs, Peter Borm, Anja De Waegenaere, and Stef Tijs. Cooperative games with stochastic payoffs. European Journal of Operational Research, 113(1):193–205, 1999. [5] Panfei Sun, Dongshuang Hou, and Hao Sun. Optimization implementation of solution concepts for cooperative games with stochastic payoffs. Theory and Decision, 93(4):691–724, 2022. |