This page is a companion for the
paper "Optimal sequential contests"
by Toomas Hinnosaar.
For the notation and the computation algorithm, please refer to the paper.
Download the Matlab codes here.
There are two relevant inputs:
Note: Condition 1 is satisfied => the characterization result holds.
| value | period | description | ||
|---|---|---|---|---|
| X* | 0.8849 | Total effort |  |
|
| x1* | 0.3628 | 1 | Effort by player 1 | |
| x2* | 0.2264 | 2 | Effort by player 2 | |
| x3* | 0.1436 | 3 | Effort by player 3 | |
| x4* | 0.0923 | 4 | Effort by player 4 | |
| x5* | 0.0599 | 5 | Effort by player 5 | |
g(X) = (2^(-X)-0.5)/(log(2))
—
g, —
0, yscale=[-0.001,0.7223]
h(X) = exp[-∫0X1/g(t) dt]
—
h, —
0, yscale=[-0.001,0.9872]
—
f5, —
0, yscale=[-0.001,1.001]
—
f4, —
0, yscale=[-0.7223,1.001]
—
f3, —
0, yscale=[-2.165,1.001]
—
f2, —
0, yscale=[-5.4111,1.001]
—
f1, —
0, yscale=[-13.8869,1.001]
—
f0, —
0, yscale=[-40.126,1.001]
g1(X)=-2^(-X)
—
g1, —
0, yscale=[-0.001,0.7223]
g2(X)=0.5 2^(-2 X) (2^X - 4.)
—
g2, —
0, yscale=[-0.001,0.7223]
g3(X)=-0.25 2^(-3 X) (2^X - 9.4641) (2^X - 2.5359)
—
g3, —
0, yscale=[-0.001,1.083]
g4(X)=0.125 2^(-4 X) (2^X - 21.798) (2^X - 4.) (2^X - 2.20204)
—
g4, —
0, yscale=[-0.001,2.3454]
g5(X)=-0.0625 2^(-5 X) (2^X - 48.4078) (2^X - 6.64495) (2^X - 2.86115) (2^X - 2.08619)
—
g5, —
0, yscale=[-0.001,6.7636]
—
X h(X), —
0, yscale=[-0.001,0.1828]