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=-6$$k=6$$k=12$All $k$
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=-6$$k=6$$k=12$All $k$
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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