Weighted Boolean Formula Games

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 weigh...

• Type: Journal
• Year: 2015
• Where: BIRTHDAY
• Authors: Marios Mavronicolas, Burkhard Monien, Klaus W. Wagner
• Keywords: Applied Computing, BIRTHDAY 2015