big list - Problems known to be in both NP and coNP, but ...
One of my favorite problems in NP ∩ co-NP is deciding who wins a simple stochastic game. The game is played on a directed graph by two players, call them A and B. This graph contains several types of nodes. There is a source node and two sink nodes, one for each of the players. There are also random nodes (which include the source), "A" nodes, and "B" nodes.
DA: 41 PA: 35 MOZ Rank: 54