Table 1.
Strategy set in the repeated prisoner's dilemma with one round memory.
Figure 1.
Repeated prisoner's dilemma: Average abundance in stationarity.
Panel A shows uniform mutations, and Panel B shows the results for the bitwise kernel. Continuous lines represent the theoretical approximation. Dots represent simulation results averaged over 500 repetitions of generations each, and a mutation probability
. Plus signs represent a larger mutation probability,
. In this case of larger
, which is harder to address analytically, the mutation kernel also affects the average abundance. Values for the game are
,
,
,
. The continuation probability is
, and population size is
.
Figure 2.
Repeated prisoner's dilemma: structure of selection and mutation for bitwise mutation.
Arrows indicate the direction of selection, and dashed lines indicate neutral paths. Blue strategies are completely cooperative and red strategies are completely uncooperative when paired with themselves. The kernel structure shuts down paths that would normally be available with the standard assumption that all mutation paths are possible.
Figure 3.
Repeated prisoner's dilemma: Fraction of time spent on fully cooperative states in the stationary distribution.
,
,
,
. The continuation probability is
, population size is
, and mutation probability is
. Continuous lines are theoretical approximations for small mutation rates and dots represent simulation results.
Figure 4.
Optional public goods game with uniform mutations.
Panel A shows abundance in stationarity as a function of the intensity of selection. Continuous lines represent the theoretical approximation. Dots represent simulation results averaged over 500 repetitions of generations each, and a mutation probability
. Plus signs represent a larger mutation probability,
.
,
,
,
,
. Panel B shows transitions (
) between monomorphic states and abundance as a function of population size in the limit of strong selection (
).
Figure 5.
Optional public goods game with non-uniform mutations.
Panel A shows abundance in stationarity as a function of the intensity of selection (,
,
,
,
) using kernel
with
. Continuous lines represent the theoretical approximation. Dots and plus signs represent simulation results. Panel B shows transitions (
) between monomorphic states and abundance as a function of population size, using kernel
, in the limit of strong selection (
).
Figure 6.
Optional public goods game with bitwise-like mutations.
Abundance in stationarity as a function of the intensity of selection (,
,
,
,
). Panel A shows results for uniform mutation structure. Panel B shows results for bitwise-like mutations. The reference intensity of selection (
) is marked with a vertical black line.