TABLE 1.

Variations of the reckless or responsible game, predictions, and the observed responsible-rate.

	Predicted responsible-rate
	Cognitive hierarchy τ = 1.54	Naïve sampler ki = 5	SAW K = 9 ω = 0.5 ε = 0.4	Experimental results
Basic setting: Reckless: 1, 0.98; −60 otherwise (EV = −0.22) Responsible: 0 if all agents choose responsible; 0, 0.98; −60 otherwise (if at least one agent chooses Reckless)	0.11	0.09	0.18	0.09
(2) Protecting alert app: Reckless: 1, 0.98; −60 otherwise (EV = −0.22) Responsible: 0 with certainty	0.89	0.09	0.22	0.09
(3.1) Always enforce app: Reckless: [1, 0.98; −60 otherwise] – 1.2 with certainty (EV = −1.42) Responsible: 0 if all agents choose responsible; 0, 0.98; −60 otherwise (if at least one agent chooses Reckless)	0.89	1	0.87	0.85
(3.2) Mostly enforce app: Reckless: [1, 0.98; −60 otherwise] – [1.2, 0.95; 24 otherwise] (EV = −0.16) Responsible: 0 if all agents choose Responsible; 0, 0.98; −60 otherwise (if at least one agent chooses Reckless)	0.89	0.78	0.55	0.60

SAW, Sampling and Weighting model (see Supplementary Appendix 1).