Emergence and suppression of cooperation by action visibility in transparent games
Fig 9
Evolutionary dynamics of iPD-population consisting of two types of players: With WSLS and AllD strategies.
(A) Initially, both types have the same frequency, but after 40 generations the fraction of WSLS-players x1(t) converges to 0 for probabilities to see partner’s choice psee = 0.0, 0.2 and to 1 for psee = 0.4, 0.5. (B) This is due to the decrease of the invasion threshold h1 for WSLS: while h1 = 1 for psee = 0 (AllD dominates WSLS and the fraction of WSLS-players unconditionally decreases), AllD and WSLS are bistable for psee > 0 and WSLS wins whenever x1(t)>h1. Arrows indicate whether frequency x1(t) of WSLS increases or decreases. Interestingly, h1 = 0.5 holds for psee ≈ 1/3, which corresponds to the maximal uncertainty since the three cases (“Player 1 knows the choice of Player 2 before making its own choice”; “Player 2 knows the choice of Player 1 before making its own choice”; “Neither of players knows the choice of the partner”) have equal probabilities.