TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES
The paper analyzes average integral payoff indices for trajectories of the dynamic equilibrium and replicator dynamics in bimatrix coordination games. In such games, players receive large payoffs when choosing the same type of behavior. A special feature of a \(2\times2\) coordination game is the pr...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2024-12-01
|
| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/857 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850056257537310720 |
|---|---|
| author | Nikolay A. Krasovskii Alexander M. Tarasyev |
| author_facet | Nikolay A. Krasovskii Alexander M. Tarasyev |
| author_sort | Nikolay A. Krasovskii |
| collection | DOAJ |
| description | The paper analyzes average integral payoff indices for trajectories of the dynamic equilibrium and replicator dynamics in bimatrix coordination games. In such games, players receive large payoffs when choosing the same type of behavior. A special feature of a \(2\times2\) coordination game is the presence of three static Nash equilibria. In the dynamic formulation, the trajectories of coordination games are estimated by the average integral payoffs for a wide range of models arising in economics and biology. In optimal control problems and dynamic games, average integral payoffs are used to synthesize guaranteed strategies, which are involved, among other things, in the constructions of the dynamic Nash equilibrium. In addition, average integral payoffs are a natural tool for assessing the quality of trajectories of replicator dynamics. In the paper, we compare values of average integral indices for trajectories of replicator dynamics and trajectories generated by guaranteed strategies in constructing the dynamic Nash equilibrium. An analysis is provided for trajectories of mixed dynamics when the first player plays a guaranteed strategy, and the behavior of replicator dynamics guides the second player. |
| format | Article |
| id | doaj-art-e6eaae6c9f2140bab0a1515e65971aed |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-e6eaae6c9f2140bab0a1515e65971aed2025-08-20T02:51:45ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522024-12-0110210.15826/umj.2024.2.009220TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMESNikolay A. Krasovskii0Alexander M. Tarasyev1Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences,16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation; Ural Federal University, 19 Mira Str., Ekaterinburg, 620002The paper analyzes average integral payoff indices for trajectories of the dynamic equilibrium and replicator dynamics in bimatrix coordination games. In such games, players receive large payoffs when choosing the same type of behavior. A special feature of a \(2\times2\) coordination game is the presence of three static Nash equilibria. In the dynamic formulation, the trajectories of coordination games are estimated by the average integral payoffs for a wide range of models arising in economics and biology. In optimal control problems and dynamic games, average integral payoffs are used to synthesize guaranteed strategies, which are involved, among other things, in the constructions of the dynamic Nash equilibrium. In addition, average integral payoffs are a natural tool for assessing the quality of trajectories of replicator dynamics. In the paper, we compare values of average integral indices for trajectories of replicator dynamics and trajectories generated by guaranteed strategies in constructing the dynamic Nash equilibrium. An analysis is provided for trajectories of mixed dynamics when the first player plays a guaranteed strategy, and the behavior of replicator dynamics guides the second player.https://umjuran.ru/index.php/umj/article/view/857dynamic bimatrix games, coordination games, average integral payoffs, guaranteed strategies, replicator dynamics, dynamic nash equilibrium |
| spellingShingle | Nikolay A. Krasovskii Alexander M. Tarasyev TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES Ural Mathematical Journal dynamic bimatrix games, coordination games, average integral payoffs, guaranteed strategies, replicator dynamics, dynamic nash equilibrium |
| title | TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES |
| title_full | TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES |
| title_fullStr | TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES |
| title_full_unstemmed | TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES |
| title_short | TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES |
| title_sort | trajectories of dynamic equilibrium and replicator dynamics in coordination games |
| topic | dynamic bimatrix games, coordination games, average integral payoffs, guaranteed strategies, replicator dynamics, dynamic nash equilibrium |
| url | https://umjuran.ru/index.php/umj/article/view/857 |
| work_keys_str_mv | AT nikolayakrasovskii trajectoriesofdynamicequilibriumandreplicatordynamicsincoordinationgames AT alexandermtarasyev trajectoriesofdynamicequilibriumandreplicatordynamicsincoordinationgames |