Emergence and suppression of cooperation by action visibility in transparent games
Fig 5
Analytical pairwise comparison of iPD strategies.
For each pair of strategies the maps show if the first of the two strategies increases in frequency (up-arrow), or decreases (down-arrow) depending on visibility of the other player’s action and the already existing fraction of the respective strategy. The red lines mark the invasion thresholds, i.e. the minimal fraction of the first strategy necessary for taking over the population against the competitor second strategy. A solid-line invasion threshold shows the stable equilibrium fraction which allows coexistence of both strategies (see “Methods”). Dashed-line invasion thresholds indicate dividing lines above which only the first, below only the second strategy will survive. (A) WSLS has an advantage over GTFT
: the former takes over the whole population even if its initial fraction is as low as 0.25. (B) GTFT coexists with (prudent) version of cooperative strategy AllC (1111; 1111; 0000), which is more successful for psee ≥ 0.1. (C,D) L-F
performs almost as good as GTFT and WSLS, (E) but can resist the AllD strategy (0000; 0000; 0000) only for high transparency. (F) Note that WSLS may lapse into its treacherous version,
. This strategy dominates WSLS for psee > 0 but is generally weak and cannot invade when other strategies are present in the population. Notably, when treacherous WSLS takes a part of the population, it is quickly replaced by L-F, which partially explains L-F success for high psee.