Stochastické kooperativní hry
| Název práce v češtině: | Stochastické kooperativní hry |
|---|---|
| Název v anglickém jazyce: | Stochastic cooperative games |
| Klíčová slova: | kooperativní hra|náhodná charakteristická funkce|problém prodejce novin |
| Klíčová slova anglicky: | cooperative game|random characteristic function|newsvendor problem |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | diplomová práce |
| Jazyk práce: | čeština |
| Ústav: | Katedra aplikované matematiky (32-KAM) |
| Vedoucí / školitel: | RNDr. Martin Černý |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 11.03.2024 |
| Datum zadání: | 20.03.2024 |
| Datum potvrzení stud. oddělením: | 20.03.2024 |
| Datum odevzdání elektronické podoby: | 02.05.2024 |
| Datum odevzdání tištěné podoby: | 02.05.2024 |
| Oponenti: | doc. RNDr. Petr Lachout, CSc. |
| Konzultanti: | doc. RNDr. Ing. Miloš Kopa, Ph.D. |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| [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. |