Cheat Perish? A Theory Scientific Customs

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016
as:
β t = 1 −
ku L (yt L )
(1 − π)u L (y H min ) + µu L (yt L )
(1 − π)u L (y H min )β t−1, (21)
which is the equation of a line with positive slope.
The interior stationary value of β is attained when β t = β t−1 = β, that is when:
β =
1 − uL (y L t )
(1−π)u L (y H min )k
1 − uL (y L t )
(1−π)u L (y H min )µ . (22)
By definition, an interior stationary point β is stable if the absolute value of the derivative
of β t with respect to β t−1 in equation (21) is strictly less than 1, and unstable if it is strictly
greater than 1. This derivative is the slope of the line. Hence, the equilibrium is stable if
µ < (1 − π)uL (y H min )
u L (y L t )
= k 0 (23)
In addition, note that, since β ∈ [0,1], two corner stationary equilibria may exist:
β = 0 if k > (1 − π)uL (y H min )
u L (y L t )
= k 0 and β = 1 if k > µ. (24)
Figure 4 shows the possible sets of equilibria for different values of the peer-pressure
function k and µ. Equation (21) is depicted by the black lines. On these equilibrium curves, β t
is only a function of β t−1 , and all other variables are held constant. The model parameters were
chosen for graphical convenience: y H min = 100, yL t = 37.5, u(y) = y 0.6 , π = 0.05, and p = 0.5.
The intersections with the 45-degree line indicate the interior stationary point (equation (22)).
If µ = 0, or equivalently v(β t−1 ) = k, the moral costs of cheating are independent of past
cheating. The slope is zero and the equilibrium level of fraud is reached immediately. This
is shown in Figure 4a. From equation (21), fraud is equal to 1 − ku L (y L t )/[(1 − π)u L (y H min )].
Fraud is then zero only if k exceeds the following value:
k 0 = (1 − π)uL (y H min )
u L (y L t )
(25)
For instance, in Figure 4a, β = 0 holds for k 0 = 1.7. When k is lower, the moral costs
exogenously fall for the whole scientific community and the level of fraud becomes non-zero.
When 0 < µ < k 0 the slope of the line is less than one. If µ < k < k 0 (Figure 4b), there
is a unique stable interior solution at the intersection of the 45-degree line and the equilibrium
curve. From equation (24), the conditions that µ < k and k < k 0 imply that the stationary point
is less than 1 and greater than 0, respectively, i.e. we obtain an interior solution. On the other
hand, if k > k 0 (Figure 4c), the unique stable equilibrium is zero.
Last, if 0 < k 0 < µ the slope of the line is over one. Two corner equilibria coexist (see
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