Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting
We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coin...
| Autori principali: | , |
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| Natura: | Journal article |
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Cambridge University Press
2015
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| _version_ | 1826293747607928832 |
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| author | Abramsky, S Winschel, V |
| author_facet | Abramsky, S Winschel, V |
| author_sort | Abramsky, S |
| collection | OXFORD |
| description | We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics. |
| first_indexed | 2024-03-07T03:34:56Z |
| format | Journal article |
| id | oxford-uuid:bbf58673-5549-445c-a2e6-248401216c32 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:34:56Z |
| publishDate | 2015 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:bbf58673-5549-445c-a2e6-248401216c322022-03-27T05:20:54ZCoalgebraic analysis of subgame-perfect equilibria in infinite games without discountingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bbf58673-5549-445c-a2e6-248401216c32Symplectic Elements at OxfordCambridge University Press2015Abramsky, SWinschel, VWe present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics. |
| spellingShingle | Abramsky, S Winschel, V Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title | Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title_full | Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title_fullStr | Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title_full_unstemmed | Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title_short | Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting |
| title_sort | coalgebraic analysis of subgame perfect equilibria in infinite games without discounting |
| work_keys_str_mv | AT abramskys coalgebraicanalysisofsubgameperfectequilibriaininfinitegameswithoutdiscounting AT winschelv coalgebraicanalysisofsubgameperfectequilibriaininfinitegameswithoutdiscounting |