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Risk sensitivity and theory of mind in human coordination

Fig 1

Utility and probability weighting functions used in cumulative prospect theory.

(a) Utility functions for gains (u(r − b|γ) = (r − b)^γ, for r > b) and losses (u(r − b|λ, γ) = −λ|r − b|^γ, for r < b) used in the calculation of value under cumulative prospect theory. These are convex for gains and concave for losses, to mimic a diminishing marginal returns effect on relative rewards. Steeper utility function for losses shows loss aversion, by amplifying the perception of a loss when compared to a gain of similar magnitude. (b) Prelec’s probability weighting function, w(p|α, δ) = exp{−α(−log(p))^δ}, is plotted for different values of the Prelec parameter α and for fixed δ = 0.75. The probability weighting function presented originally, , is represented by the black dashed line, for γ = 0.85. Notice that Prelec’s function is very similar to the originally proposed probability weighting function when α = 1, demonstrating both overweighting of low probabilities and underweighting of high probabilities, corresponding to the possibility and certainty effects. (c) Probability anomaly, w(p|α) − p. Blue indicates positive anomaly, whereas red indicates negative anomaly. Here it is easy to see the effects of the probability weighting function; for low values of α, low probabilities are overweighted, causing the so-called possibility effect—i.e. highly unlikely events are perceived as more probable than they actually are ---, and, for high values of α, high probabilities are underweighted, demonstrating the certainty effect—i.e. highly likely events are perceived as less probable than they actually are. Notice that both the certainty and possibility effects come into play when α ≈ 1.

doi: https://doi.org/10.1371/journal.pcbi.1009167.g001