Emergence and suppression of cooperation by action visibility in transparent games

Real-world agents, such as humans, animals and robots, observe each other during interactions and choose their own actions taking the partners9 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 partner9s choice before one9s 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 Prisoner9s 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.