Fictitious Play in Extensive-Form Games of Imperfect Information
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912346416349184 |
|---|---|
| author | Castiglione, Jason Arslan, Gürdal |
| author_facet | Castiglione, Jason Arslan, Gürdal |
| contents | We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at which the player is about to make a move, are made according to fixed random strategies, independently across all information sets. Accordingly, each player makes his moves at any of his information sets to maximize his expected payoff assuming that, at any other information set, the moves are made according to the empirical frequencies of the past moves. We extend the well-known Monderer-Shapley result [1] on the convergence of the empirical frequencies to the set of Nash equilibria to a certain class of extensive-form games with identical interests. We then strengthen this result by the use of inertia and fading memory, and prove the convergence of the realized play-paths to an essentially pure Nash equilibrium in all extensive-form games of imperfect information with identical interests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fictitious Play in Extensive-Form Games of Imperfect Information Castiglione, Jason Arslan, Gürdal Computer Science and Game Theory Optimization and Control We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at which the player is about to make a move, are made according to fixed random strategies, independently across all information sets. Accordingly, each player makes his moves at any of his information sets to maximize his expected payoff assuming that, at any other information set, the moves are made according to the empirical frequencies of the past moves. We extend the well-known Monderer-Shapley result [1] on the convergence of the empirical frequencies to the set of Nash equilibria to a certain class of extensive-form games with identical interests. We then strengthen this result by the use of inertia and fading memory, and prove the convergence of the realized play-paths to an essentially pure Nash equilibrium in all extensive-form games of imperfect information with identical interests. |
| title | Fictitious Play in Extensive-Form Games of Imperfect Information |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2504.18075 |