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The notion of optimality naturally arises in many areas of appliedmathematics and computer science concerned with decision making. Here weconsider this notion in the context of three formalisms used for differentpurposes in reasoning about multi-agent systems: strategic games, CP-nets, andsoft constraints. To relate the notions of optimality in these formalisms weintroduce a natural qualitative modification of the notion of a strategic game.We show then that the optimal outcomes of a CP-net are exactly the Nashequilibria of such games. This allows us to use the techniques of game theoryto search for optimal outcomes of CP-nets and vice-versa, to use techniquesdeveloped for CP-nets to search for Nash equilibria of the considered games.Then, we relate the notion of optimality used in the area of soft constraintsto that used in a generalization of strategic games, called graphical games. Inparticular we prove that for a natural class of soft constraints that includesweighted constraints every optimal solution is both a Nash equilibrium andPareto efficient joint strategy. For a natural mapping in the other directionwe show that Pareto efficient joint strategies coincide with the optimalsolutions of soft constraints.

Comparing the notions of optimality in CP-nets, strategic games and soft constraints