The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations.