-transition intervals for different types of neighborhoods.

<p>von Neumann (r = 1,2), Moore (r = 1,2,3) well-mixed (everybody is neighbor with everybody) and scale-free (power law connections mapped on the lattice). Averaged values for 100 runs are observed after 500 game rounds.</p

Variation of -player rate with the punishment severity .

<p>Averaged values for 100 runs are observed after 500 game rounds. Punishment probability is: , and . The game starts with 50%, randomly distributed, -players.</p

Experimental -transition intervals.

<p>Experimental -transition intervals for , and . The game starts with 50% -players randomly distributed. Average -player rate values for 100 runs are observed after 500 game rounds.</p

-player rate dynamics in the population, first 300 rounds.

<p>Different game runs are depicted, corresponding to different punishment probabilities: (3 runs, blue), (3 runs, red), (3 runs, green), and (3 runs, black). . The initial population contains 50% -players, randomly distributed.</p

-player rate dynamic in a population in the first 300 rounds ().

<p>The initial population contains 50%, randomly distributed, -players. The rate drops dramatically in the first three rounds, to about 2%. -player rate constantly increases in the next rounds. After 20 rounds the -player rate is about 8%. After 50 rounds there are 24% -players. After 300 rounds the -player rate is about 60% and remains almost constant indicating that an equilibrium is reached.</p

-player averaged rate (100 runs) after 500 rounds, function of punishment probability , for = 2.

<p>Two initial states are considered: one with 95% and the second with 12% -players, both containing already formed clusters of players. The -transition intervals are very similar, despite the initial player rate. A granularity measure (0 gran. 1) is used for characterizing the clusters (a high value indicates few large clusters).</p

SH game normal-form.

<p>The payoff matrix of the Social Honesty game. Two-player normal-form game.</p

-cluster formation in a population after , and rounds ().

<p>The initial population contains 50%, randomly distributed, -players. Few small clusters of -players appear in the very first rounds, containing only 2% -players after round 3. After 50 rounds the -clusters become larger (25% -players). After 150 rounds -clusters may be found all over the population (57% -players). The color code is: blue - is honest/was honest; red - is dishonest/was dishonest; green - is honest/was dishonest; yellow - is dishonest/was honest.</p

-transition intervals for different types of strategy update rules.

<p>‘Best’ rule - players imitate the best player (i.e. the neighbor with the highest payoff). ‘Best Myopic’ rule - players imitate the best player with probability and a randomly chosen neighbor with probability . ‘Best Fermi’ rule - the best player is imitated with a probability given by a particular form of Fermi function. Averaged values for 100 runs are observed after 500 game rounds.</p

-cluster formation in a population after 1000 rounds, for different punishment probabilities , , and . .

<p>The initial population contains 50%, randomly distributed, -players. The color code is: blue - is honest/was honest; red - is dishonest/was dishonest; green - is honest/was dishonest; yellow - is dishonest/was honest.</p