Repository logo
  • English
  • Italiano
  • Log In
    Have you forgotten your password?
Repository logo
Repository logo
  • Archive
  • Series/Journals
  • EUT
  • Events
  • Statistics
  • English
  • Italiano
  • Log In
    Have you forgotten your password?
  1. Home
  2. EUT Edizioni Università di Trieste
  3. Periodici
  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.54 (2022)
  6. Geometry of dependency equilibria
 
  • Details
  • Metrics
Options

Geometry of dependency equilibria

Portakal, Irem
•
Sturmfels, Bernd
2022
Loading...
Thumbnail Image
ISSN
0049-4704
DOI
10.13137/2464-8728/33881
http://hdl.handle.net/10077/33881
  • Article

e-ISSN
2464-8728
Abstract
An n-person game is specified by n tensors of the same format. We view its equilibria as points in that tensor space. Dependency equilibria are defined by linear constraints on conditional probabilities, and thus by determinantal quadrics in the tensor entries. These equations cut out the Spohn variety, named after the philosopher who introduced dependency equilibria. The Nash equilibria among these are the tensors of rank one. We study the real algebraic geometry of the Spohn variety. This variety is rational, except for 2×2 games, when it is an elliptic curve. For 3×2 games, it is a del Pezzo surface of degree two. We characterize the payoff regions and their boundaries using oriented matroids, and we develop the connection to Bayesian networks in statistics.
Journal
Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics 
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
Subjects
  • Nash equilibria

  • dependency equilibria...

  • Spohn variety

  • conditional independe...

Publisher
EUT Edizioni Università di Trieste
Source
Irem Portakal, Bernd Sturmfels, "Geometry of dependency equilibria" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.54 (2022)", EUT Edizioni Università di Trieste, Trieste, 2022, pp. 221-246
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Licence
http://creativecommons.org/licenses/by-nc-nd/4.0/
File(s)
Loading...
Thumbnail Image
Download
Name

11-Portakal_Sturmfels.pdf

Format

Adobe PDF

Size

851.02 KB

Indexed by

 Info

Open Access Policy

Share/Save

 Contacts

EUT Edizioni Università di Trieste

OpenstarTs

 Link

Wiki OpenAcces

Archivio Ricerca ArTS

Built with DSpace-CRIS software - Extension maintained and optimized by 4Science

  • Cookie settings
  • Privacy policy
  • End User Agreement
  • Send Feedback