In real-life strategic interactions, a player's belief about the possible payoffs of a strategy profile is often ambiguous due to limited information, and this ambiguity is not be appropriately captured by the traditional game-theoretic framework. In order to address this issue, we introduce a new game model, called an ambiguous game, which incorporates human cognitive factors of ambiguity aversion and minimax regret. Moreover, we also study how the degrees of ambiguity in beliefs about possible payoffs can influence the solutions of an ambiguous game. In particular, we identify the conditions under which a player should release more or less information to his or her opponents. This result provides some insight on how to manage our private information in an ambiguous game, which helps us obtain a better outcome.