Comparing the notions of optimality in CPnets, strategic games and soft constraints
Abstract
The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning about multiagent systems: strategic games, CPnets, and soft constraints. To relate the notions of optimality in these formalisms we introduce a natural qualitative modification of the notion of a strategic game. We show then that the optimal outcomes of a CPnet are exactly the Nash equilibria of such games. This allows us to use the techniques of game theory to search for optimal outcomes of CPnets and viceversa, to use techniques developed for CPnets to search for Nash equilibria of the considered games. Then, we relate the notion of optimality used in the area of soft constraints to that used in a generalization of strategic games, called graphical games. In particular we prove that for a natural class of soft constraints that includes weighted constraints every optimal solution is both a Nash equilibrium and Pareto efficient joint strategy. For a natural mapping in the other direction we show that Pareto efficient joint strategies coincide with the optimal solutions of soft constraints.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2909
 Bibcode:
 2007arXiv0711.2909A
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Computer Science and Game Theory;
 I.2.11;
 D.3.3
 EPrint:
 39 pages. To appear in Annals of Mathematics and Artificial Intelligence