Emergence and suppression of cooperation by action visibility in transparent games
Fig 8
Analytical pairwise comparison of i(A)CG 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. Solid-line invasion thresholds show 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. In all strategies, 1 stands for 0.999 and 0—for 0.001, the entries s9 = … = s12 = 1 are the same for all strategies and are omitted. (A) Turn-taker (q01q; 0000) with q = 5/8 for psee > 0 outperforms Aggressive Challenger , (B) but not Challenger
. (C) Challenger can coexist with Aggressive Challenger for low transparency, but is dominated for psee > 1/3. (D) Leader-Follower (1111; 0000) clearly outperforms Turn-taker for psee > 0.4 and (E,F) other strategies for psee > 1/3.