Backward Induction for Repeated Games
We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of 'topologically compact' nondeter...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2018-07-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1804.07074v2 |
| id |
doaj-123c645575554e0b89942656f27a937a |
|---|---|
| record_format |
Article |
| spelling |
doaj-123c645575554e0b89942656f27a937a2020-11-25T01:18:00ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802018-07-01275Proc. MSFP 2018355210.4204/EPTCS.275.5:6Backward Induction for Repeated GamesJules Hedges0 University of Oxford We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of 'topologically compact' nondeterminism, and a simple model of computable real numbers. This is the first application of Escardó and Oliva's theory of higher-order sequential games to games of imperfect information, in which (as well as its mathematical elegance) lazy evaluation does nontrivial work for us compared with a traditional game-theoretic analysis. Since a full theoretical understanding of this method is lacking (and appears to be very hard), we consider this an 'experimental' paper heavily inspired by theoretical ideas. We use the famous Iterated Prisoner's Dilemma as a worked example.http://arxiv.org/pdf/1804.07074v2 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jules Hedges |
| spellingShingle |
Jules Hedges Backward Induction for Repeated Games Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Jules Hedges |
| author_sort |
Jules Hedges |
| title |
Backward Induction for Repeated Games |
| title_short |
Backward Induction for Repeated Games |
| title_full |
Backward Induction for Repeated Games |
| title_fullStr |
Backward Induction for Repeated Games |
| title_full_unstemmed |
Backward Induction for Repeated Games |
| title_sort |
backward induction for repeated games |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2018-07-01 |
| description |
We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of 'topologically compact' nondeterminism, and a simple model of computable real numbers. This is the first application of Escardó and Oliva's theory of higher-order sequential games to games of imperfect information, in which (as well as its mathematical elegance) lazy evaluation does nontrivial work for us compared with a traditional game-theoretic analysis. Since a full theoretical understanding of this method is lacking (and appears to be very hard), we consider this an 'experimental' paper heavily inspired by theoretical ideas. We use the famous Iterated Prisoner's Dilemma as a worked example. |
| url |
http://arxiv.org/pdf/1804.07074v2 |
| work_keys_str_mv |
AT juleshedges backwardinductionforrepeatedgames |
| _version_ |
1725144375322738688 |