In some games, a player can have a strategy that doesn't have a best response, even though it's computable. This is true for certain types of repeated games with discounted payoffs, like a more complex version of the Prisoner's Dilemma. Researchers have now figured out the specific conditions needed for this to happen in a two-player game. They found that the game must have a Nash equilibrium with certain properties related to the payoffs. It's possible to determine if a game meets these conditions in a reasonable amount of time.