Suppose that the players apply security strategies, and . This results in a cost of . How do the players feel after the outcome? may feel satisfied because given that selected , it received the lowest cost possible. On the other hand, may regret its decision in light of the action chosen by . If it had known that would be chosen, then it could have picked to receive cost , which is better than . If the game were to be repeated, then would want to change its strategy in hopes of tricking to obtain a higher reward.
Is there a way to keep both players satisfied? Any time there is a gap between and , there is regret for one or both players. If and denote the amount of regret experienced by and , respectively, then the total regret is
Steven M LaValle 2012-04-20