Table 2. Derivation and interpretation of DI and DP indices for gains and losses.

Gains (y ≻ x ≻ x0)
Patient (x, s) ≺ (x, t)	(y, s) ~ (x, t)	(y, s + σ) ~ (x, t + τ)	s	t	σ	τ	DP-index	Interpretation
Increasing	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 16)	0	5	4	8	0.2	Prefers waiting for gains, and willingness to wait increases by delays
Constant	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 12)	0	5	4	4	0	Prefers waiting for gains, and willingness to wait is constant
Decreasing	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 10)	0	5	4	2	-0.1	Prefers waiting for gains, and willingness to wait decreases by delays
Impatient (x, s) ≻ (x, t)	(x, s) ~ (y, t)	(x, s + σ) ~ (y, t + τ)	s	t	σ	τ	DI-index	Interpretation
Decreasing	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 16)	0	5	4	8	0.2	Dislikes waiting for gains, and willingness to wait increases by delay
Constant	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 12)	0	5	4	4	0	Dislikes waiting for gains, and willingness to wait is constant
Increasing	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 10)	0	5	4	2	-0.1	Dislikes waiting for gains, and willingness to wait decreases by delays
Losses (x0 ≻ x ≻ y)
Patient (x, s) ≻ (x, t)	(y, s) ~ (x, t)	(y, s + σ) ~ (x, t + τ)	s	t	σ	τ	DP-index	Interpretation
Increasing	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 16)	0	5	4	8	0.2	Dislikes waiting for losses, and willingness to wait increases by delays
Constant	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 12)	0	5	4	4	0	Dislikes waiting for losses, and willingness to wait is constant
Decreasing	(y, 0) ~ (x, 5)	(y, 4) ~ (x, 10)	0	5	4	2	-0.1	Dislikes waiting for losses, and willingness to wait decreases by delays
Impatient (x, s) ≺ (x, t)	(x, s) ~ (y, t)	(x, s + σ) ~ (y, t + τ)	s	t	σ	τ	DI-index	Interpretation
Decreasing	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 16)	0	5	4	8	0.2	Prefers waiting for losses, and willingness to wait increases by delays
Constant	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 12)	0	5	4	4	0	Prefers waiting for gains, and willingness to wait is constant
Increasing	(x, 0) ~ (y, 5)	(x, 4) ~ (y, 10)	0	5	4	2	-0.1	Prefers waiting for gains, and willingness to wait decreases by delays