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In section IVB, we reported that sorting was observed not only for k=6 but also for k=12. Although behavior in both treatments does not exactly follow the predictions from the timing equilibrium (notably, some subjects move early on in the game), the finding that subjects sort in k=12 is consistent with the idea that heterogeneous risk aversion enlarges the set of environments for which the timing equilibrium applies. A more direct implication of heterogeneous risk aversion is that the more risk-averse players should flee early more often. Table 2 presents panel data probit regressions of how the probability of choosing to flee before the endgame (T) depends on a subject's level of risk aversion, together with some controls. In agreement with the model of heterogeneous risk aversion, more risk-averse subjects are more likely to flee before the endgame when k=-6 and when k=12, and the effect survives when we combine all three treatments.12

Table 2.

Fleeing before Endgame

(1)(2)(3)(4)
k=-6k=6k=12All k
Risk aversion 0.037*** −0.001 0.041** 0.026*** 
 (0.007) (0.018) (0.018) (0.009) 
Female −0.025 −0.012 0.003 −0.008 
 (0.031) (0.052) (0.060) (0.030) 
Dominance 0.007 −0.028 −0.001 −0.006 
 (0.011) (0.023) (0.015) (0.010) 
Physical strength −0.015 −0.004 0.003 −0.002 
 (0.019) (0.020) (0.020) (0.011) 
Fighting ability −0.980*** −0.881*** −0.889*** −0.935*** 
 (0.003) (0.034) (0.016) (0.013) 
Round 0.000 −0.000 −0.000 −0.000 
 (0.001) (0.001) (0.001) (0.000) 
k=6    −0.127*** 
    (0.030) 
k=12    −0.112*** 
    (0.022) 
Observations 2,520 2,080 2,520 7,120 
(1)(2)(3)(4)
k=-6k=6k=12All k
Risk aversion 0.037*** −0.001 0.041** 0.026*** 
 (0.007) (0.018) (0.018) (0.009) 
Female −0.025 −0.012 0.003 −0.008 
 (0.031) (0.052) (0.060) (0.030) 
Dominance 0.007 −0.028 −0.001 −0.006 
 (0.011) (0.023) (0.015) (0.010) 
Physical strength −0.015 −0.004 0.003 −0.002 
 (0.019) (0.020) (0.020) (0.011) 
Fighting ability −0.980*** −0.881*** −0.889*** −0.935*** 
 (0.003) (0.034) (0.016) (0.013) 
Round 0.000 −0.000 −0.000 −0.000 
 (0.001) (0.001) (0.001) (0.000) 
k=6    −0.127*** 
    (0.030) 
k=12    −0.112*** 
    (0.022) 
Observations 2,520 2,080 2,520 7,120 

Panel data probit regressions, with random effects at the subject level. Coefficients are average marginal effects. Dependent variable is a dummy indicating whether the player decided to flee before the endgame or not. Risk aversion is measured as the number of rejected lotteries. Dominance and physical strength are normalized (mean 0 and SD 1). Fighting ability takes on values between 0 and 1. Standard errors (clustered at the matching group level) in parentheses. Additional specifications with fewer or more controls are reported in table A4 in appendix C. *p<0.10, **p<0.05, and ***p<0.01.

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