Real-world agents, such as humans, animals and robots, observe each other during interactions and choose their own actions taking the partners' ongoing behaviour into account. Yet, classical game theory assumes that players act either strictly sequentially or strictly simultaneously (without knowing the choices of each other). To account for action visibility and provide a more realistic model of interactions under time constraints, we introduce a new game-theoretic setting called transparent game, where each player has a certain probability to observe the choice of the partner before deciding on its own action. Using evolutionary simulations, we demonstrate that even a small probability of seeing the partner's choice before one's own decision substantially changes evolutionary successful strategies. Action visibility enhances cooperation in a Bach-or-Stravinsky game, but disrupts cooperation in a more competitive iterated Prisoner's Dilemma. In both games, strategies based on the "Win-stay, lose-shift" and "Tit-for-tat" principles are predominant for moderate transparency, while for high transparency strategies of "Leader-Follower" type emerge. Our results have implications for studies of human and animal social behaviour, especially for the analysis of dyadic and group interactions.One of the most interesting questions in economics, biological, and social sciences is the emergence and maintenance of cooperation. A popular framework for studying cooperation (or the lack thereof) is Game Theory, which is frequently used to model interactions between "rational" decision-makers. In particular, a model for repeated interactions is provided by iterated games; two settings were previously used [1]:• Simultaneous games: players act at the same time without having any information about the current choice of the partners. Consequently, all players must make a decision under uncertainty concerning the choices of others.• Sequential games: players act in a certain order and the player acting later in the sequence is guaranteed to see the choices of the preceding players. Here the burden of uncertainty only applies to the first player or -if there are more than two players -becomes lighter with every turn in the sequence.Both settings place a simplifying restriction on the decisional context: either all players have no information about the choices of the partners (simultaneous game), or some players always have more information than others (sequential game). This simplification might be disadvantageous for modelling certain behaviours, since humans and animals usually act neither strictly simultaneously nor