Emergence and suppression of cooperation by action visibility in transparent games

Abstract

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

Human and macaque pairs employ different coordination strategies in a transparent decision game

“…The break of coordination was triggered by the faster agent slowing down and the slower one speeding up and selecting the own color; conversely, the transition to coordination was associated with the speeding up agent selecting the own color and the slowing down agent accommodating.In summary, both species exploited action visibility to achieve and/or maintain the turn-taking, emphasizing the importance of the "transparency" of interactive behavior as an important determinant of emerging strategies. Human agents initiated switches to and from their preferred colors to "fairly" balance the payoffs, similarly to the Conflict game37 , while macaques established competitive dynamics, as predicted by our evolutionary simulations8 . These results add to the body of literature indicating that humans in a social setting might base their decisions not only on pure reward maximization 59 .…”

“…To account for possible changes in strategies during action visibility compared to simultaneous ("opaque") discrete choices, we recently developed the concept of "transparent games" that extends classical evolutionary game-theoretic analysis to real-time interactions in which the visibility of partners' actions depends on their relative reaction times 8,9 . Here, we use the theoretical insights from that work and analyze short-and long-term dynamics of choices, mutual information and reaction times in humans and rhesus monkeys playing a transparent version of the iterated movement-based BoS game.…”

“…(H) The dynamic coordination reward (DCR). The error bars show 95% confidence intervals, 53% of pairs(3,1,13,2,12,7,9,17,8, and 6) showed significant DCR.…”

Evolutionary successful strategies in a transparent iterated Prisoner’s Dilemma

“…One may expect that action visibility would increase cooperation in nonzero-sum games, such as the iterated Prisoner's dilemma (iPD). However, evolutionary simulations in [3] show that this is not necessarily the case. Evolutionary agents successfully establish cooperation in the iPD for low and moderate transparency by using the classic "Win-stay, lose -shift" (WSLS) strategy [4].…”

“…Instead, social agents try to observe their partners and adversaries, and use the others' behavior to adjust their own actions accordingly [1,2]. Recently a new game-theoretic setting of "transparent games" has been introduced, taking into account action visibility and providing a more realistic model of interactions under time constraints [3]. In transparent games, each player has a certain probability to observe the partner's choice before deciding on its own action.…”