Weighted boolean formula games (2007)
| Venue: | In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE |
| Citations: | 2 - 0 self |
BibTeX
@INPROCEEDINGS{Mavronicolas07weightedboolean,
author = {Marios Mavronicolas and Burkhard Monien and Klaus W. Wagner},
title = {Weighted boolean formula games},
booktitle = {In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE},
year = {2007}
}
OpenURL
Abstract
We introduce a new class of succinct games, called weighted boolean formula games. Here, each player has a set of boolean formulas he wants to get satisfied. The boolean formulas of all players involve a ground set of boolean variables, and every player controls some of these variables. The payoff of a player is the weighted sum of the values of his boolean formulas. For these games, we consider pure Nash equilibria [42] and their well-studied refinement of payoff-dominant equilibria [30], where every player is no worse-off than in any other pure Nash equilibrium. We study both structural and complexity properties for both decision and search problems with respect to the two concepts: • We consider a subclass of weighted boolean formula games, called mutual weighted boolean formula games, which make a natural mutuality assumption on the payoffs of distinct players. We present a very simple exact potential for mutual weighted boolean formula games. We also prove that each weighted, linear-affine (network) congestion game with player-specific constants is polynomial, sound Nash-Harsanyi-Selten homomorphic to a mutual weighted boolean formula game. In a general way, we prove that each weighted, linear-affine (network)







