In this paper, we show how to take interval uncertainty into account when solving conflict situations. Algorithms for conflict situations under interval uncertainty are know under the assumption that each side of the conflict maximizes its worst-case expected gain. However, it is known that a more general Hurwicz approach provides a more adequate description of decision making under uncertainty. In this approach, each side maximizes the convex combination of the worst-case and the best-case expected gains. In this paper, we describe how to resolve conflict situations under the general Hurwicz approach to interval uncertainty.