Emergence and suppression of cooperation by action visibility in transparent games
Fig 3
Frequency of establishing effective cooperation and the forfeit reward in the iterated Prisoner’s Dilemma (iPD) and in the iterated (Anti-)Coordination Game (i(A)CG).
We performed 80 runs of evolutionary simulations tracing 109 generations of iPD and i(A)CG players. Agents with successful strategies reproduced themselves (had higher fraction in the next generation), while agents with unsuccessful strategies died out, see “Methods” for details. We considered a run as “cooperative” if the average payoff across the population was more than 0.9 times the pay-off of 3 units for cooperative behaviour in iPD [24], and more than 0.95 times the pay-off of 3.5 units for cooperative behaviour in the i(A)CG (i.e., 90% and 95% of the maximally achievable pay-off on average over both players). For i(A)CG we set a higher threshold due to the less competitive nature of this game. (A) In iPD cooperation was quickly established for low probability to see the partner’s choice psee, but it took longer to develop for moderate psee and it drastically decreased for high psee. (B) In contrast, for i(A)CG frequent cooperation emerges only for high visibility. The small drop in cooperation at psee = 0.4 is caused by a transition between two coordination strategies (see main text). (C) The forfeit payoff (maximal possible average payoff of the population minus actual average payoff obtained by the population) further illustrates the same tendencies: higher transparency reduces effectiveness of cooperation in iPD but increases in i(A)CG.