  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 multi-agent systems: strategic games, CP-nets, 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 CP-net are exactly the Nash
equilibria of such games. This allows us to use the techniques of game theory
to search for optimal outcomes of CP-nets and vice-versa, to use techniques
developed 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 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.
