1.5 More about the Scope of Game Theory 31 set is denoted by -C): i K, C K, s C , u i (s ) u i (s C , s ). -C (1.16) A less strong requirement is to consider k-strong equilibria. In this case, the solution is stable to k 1 deviations. Obviously, strong and k-strong equilibria are very desir- able solutions. The question is whether such solutions exist. Here is one of the rare existence theorems for such a solution concept. ·························································································· · · · · · · · Any strong equilibrium is a Pareto-optimal Nash equilibrium point and vice versa. · Theorem 33: Characterization of Strong Equilibria This means that if a Nash equilibrium can be found, and confirmed to be socially optimal, it is also a strong equilibrium. Below we provide an example of a non- cooperative game that has strong equilibria. Example 34: Collision Channel Game Consider the following collision game with two users. If the two users decide to transmit simultaneously, there is a collision. If one of the users transmits (T) and the other stays