Approachability in population games
This paper reframes approachability theory within the context of population games. Thus, whilst a player still aims at driving her average payoff to a predefined set, her opponent is no longer malevolent but instead is extracted randomly at each instant of time from a population of individuals choos...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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American Institute of Mathematical Sciences
2020
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| _version_ | 1797079501360857088 |
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| author | Bauso, D Norman, T |
| author_facet | Bauso, D Norman, T |
| author_sort | Bauso, D |
| collection | OXFORD |
| description | This paper reframes approachability theory within the context of population games. Thus, whilst a player still aims at driving her average payoff to a predefined set, her opponent is no longer malevolent but instead is extracted randomly at each instant of time from a population of individuals choosing actions in a similar manner. First, we define the notion of 1st-moment approachability, a weakening of Blackwell's approachability. Second, since the endogenous evolution of the population's play is then important, we develop a model of two coupled partial differential equations (PDEs) in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution, the other capturing the macroscopic evolution of average payoffs if every player plays her best response. Third, we provide a detailed analysis of existence, nonuniqueness, and stability of equilibria (fixed points of the two PDEs). Fourth, we apply the model to regret-based dynamics, and use it to establish convergence to Bayesian equilibrium under incomplete information. |
| first_indexed | 2024-03-07T00:46:48Z |
| format | Journal article |
| id | oxford-uuid:84f5598d-83b7-4df0-9006-4c3550bf2810 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:46:48Z |
| publishDate | 2020 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:84f5598d-83b7-4df0-9006-4c3550bf28102022-03-26T21:54:23ZApproachability in population gamesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:84f5598d-83b7-4df0-9006-4c3550bf2810EnglishSymplectic ElementsAmerican Institute of Mathematical Sciences2020Bauso, DNorman, TThis paper reframes approachability theory within the context of population games. Thus, whilst a player still aims at driving her average payoff to a predefined set, her opponent is no longer malevolent but instead is extracted randomly at each instant of time from a population of individuals choosing actions in a similar manner. First, we define the notion of 1st-moment approachability, a weakening of Blackwell's approachability. Second, since the endogenous evolution of the population's play is then important, we develop a model of two coupled partial differential equations (PDEs) in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution, the other capturing the macroscopic evolution of average payoffs if every player plays her best response. Third, we provide a detailed analysis of existence, nonuniqueness, and stability of equilibria (fixed points of the two PDEs). Fourth, we apply the model to regret-based dynamics, and use it to establish convergence to Bayesian equilibrium under incomplete information. |
| spellingShingle | Bauso, D Norman, T Approachability in population games |
| title | Approachability in population games |
| title_full | Approachability in population games |
| title_fullStr | Approachability in population games |
| title_full_unstemmed | Approachability in population games |
| title_short | Approachability in population games |
| title_sort | approachability in population games |
| work_keys_str_mv | AT bausod approachabilityinpopulationgames AT normant approachabilityinpopulationgames |