When is the risk of cooperation worth taking? The prisoner’s dilemma as a game of multiple motives

Figures & data

Table 1. Generalized representation of a two-person two-action prisoner’s dilemma.

	C	D
C	R,R	S,T
D	T,S	P,P

C, cooperation; D, defection.

Figure 1. Choices in the prisoner’s dilemma. (a) Effect of safety pay-off P on defection; beliefs are elicited for the shaded pay-off ($P=2.45$). (b) Switching points in the prisoner’s dilemma.

Table 2. Explaining switching points by motives.

Tobit, robust standard errors
Dependent variable: lowest punishment pay-off at which participant defects
	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
Gains from Cooperation	1.676*** (.290)					1.475*** (.124)	1.794*** (.124)	1.831*** (.118)
Optimism		8.816*** (1.612)				2.814*** (.511)	2.440*** (.317)	2.694*** (.329)
λ			.849 (1.197)			.349 (.456)	−.579* (.249)	−.654* (.261)
Relative riskaversion				.617 (.968)		.249 (.327)	−3.401*** (.425)	−4.115*** (.546)
λ × Relative riskaversion							2.841*** (.292)	3.426*** (.394)
β					−1.916 (3.628)	−4.112** (1.146)	−3.070** (.876)	−2.405** (.877)
Female								−.590* (.285)
Age								−.055^+ (.031)
Econ, math or technical								−.321 (.273)
Law								.095 (.303)
Humanity								.496 (.442)
Social science								.533 (.382)
Cons	−5.707** (1.696)	−3.039*** (1.042)	.922 (1.817)	1.816* (.689)	2.645* (1.287)	−5.886*** (1.618)	−6.906*** (.943)	−5.769*** (1.103)
N	83	83	83	81	83	81	81	81
Left censored	26	26	26	26	26	26	26	26
Right censored	18	18	18	17	18	17	17	17
p Model	<.001	<.001	.4803	.5253	.5988	<.001	<.001	<.001
Pseudo R^2	.4150	.1086	.0018	.0019	.0011	0.5071	.6077	.6335

Gains from cooperation: when switching to defection at a certain point; optimism: estimated percentage of cooperation; λ: degree of loss aversion; relative risk aversion: degree of relative risk aversion; β: degree of aversion against advantageous inequity; standard errors in parentheses.

***p < .001; **p < .01; * p < .05; ⁺p < .1.