The difficulty of achieving efficiency in strategic games, especially in the presence of private information, arises from the inherent tension between *cooperation* and *competition*. To address this, we propose the "coco" solution for two-person private-information strategic games with side payments. For zero-sum games, the coco solution coincides with the von-Neumann minmax value. For TU variable-threat bargaining, it coincides with the Nash (1953), Raiffa (1953), Kalai-Smorodinsky (1975), and egalitarian solutions. Following Selten (1960), we justify the coco value by axioms of monotonicity and efficiency, imposed directly on the class of Bayesian strategic games. Finally, we introduce a incentive-compatible efficient mechanism that implements the coco solution in a broad class of games. The mechanism is a simple two-part agreement between the players: (a) they form a team and share payoffs equally, thereby achieving complete efficiency, and (b) a separate side payment is made to compensate the player with the strategic advantage.