Four dimensions of the precautionary principle (PP), involving threat, uncertainty, action, and command, are formalized at the level of set theory and the level of individual players and natural and technological factors. Flow and decision diagrams with a feedback loop are developed to open up a new research agenda. The role of strategic interaction and games in the PP is underdeveloped or nonexistent in today's literature. To rectify this deficiency, six kinds of games are identified in the four PP dimensions. The games can be interlinked since player sets can overlap. Characteristics are illustrated. Accounting for strategic interaction, the article illustrates uncertainty in the PP regarding which game is played, which players participate in which game, strategy sets, payoffs, incomplete information, risk attitudes, and bounded rationality. The insurance and lottery games analyzed earlier for the safe minimum standard (SMS) for species extinction are revisited and placed into a broader context illustrating strategic interaction. Uncertainty about payoffs illustrates transformations back and forth between the chicken game, battle of the sexes, assurance game, and prisoner's dilemma.