EURO-Online login
- New to EURO? Create an account
- I forgot my username and/or my password.
- Help with cookies
(important for IE8 users)
1997. Games with incomplete preferences: a pointwise completion approach
Invited abstract in session MB-41: Vector and Set Optimization II, stream Vector and Set Optimization.
Monday, 10:30-12:00Room: 97 (building: 306)
Authors (first author is the speaker)
| 1. | Elena Molho
|
| Dipartimento di Scienze Economiche e Aziendali, Università di Pavia | |
| 2. | Elisa Caprari
|
| Dipartimento di Scienze Economiche e Aziendali, Università di Pavia | |
| 3. | Lorenzo Cerboni Baiardi
|
| Department of Mathematics, University of Bologna |
Abstract
We introduce a pointwise axiomatic approach to completion of incomplete preference relations through appropriate value functions. We consider an abstract scalarization framework, originally developed in the field of vector optimization, in order to tackle generic partial quasi orders. We apply this approach to study non cooperative games where players have incomplete preferences. In this context, our results allow us to obtain both necessary and sufficient Nash equilibrium conditions. We compare our representation results with other approaches to preference completion, in the special case where value functions are Aumann utilities. In detail, we identify minimal sets of Aumann utilities that allow us to find all Nash equilibria of a game with incomplete preferences, with no need of additional assumptions. As a special case, we reframe our pointwise approach in vector games, where players have vector-valued payoffs and partial orders on players' outcomes naturally arise. We characterize Nash equilibria in vector games by scalarization, extending to the non convex case the results originally developed by Shapley (1959).
Keywords
- Game Theory
- Decision Theory
- Multi-Objective Decision Making
Status: accepted
Back to the list of papers