Optimal sequential contests

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:

g(X) =		= -h(X)/h'(X) characterizes the payoff function. Click here to specify h instead.
n = (n1,...,nT) =	(),	where n1 is the number of players before the first announcement, n2 the second, and so on.

Equilibrium

Note: Condition 1 is satisfied => the characterization result holds.

	value	period	description
X*	0.875		Total effort
x1*	0.1914	1	Effort by player 1
x2*	0.1914	1	Effort by player 2
x3*	0.1914	1	Effort by player 3
x4*	0.1914	1	Effort by player 4
x5*	0.1094	2	Effort by player 5

<->

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Figures

g(X)

g(X) = X*(1-X)

g, 0, yscale=[-0.001,0.251]

h(X)

h(X) = exp[-∫₀^X1/g(t) dt]

h, 0, yscale=[-0.001,0.3689]

f₂(X)

f₂, 0, yscale=[-0.001,1.001]

f₁(X)

f₁, 0, yscale=[-0.001,1.001]

f₀(X)

f₀, 0, yscale=[-0.7949,1.001]

g₁(X)

g₁(X)=1 - 2 X

g₁, 0, yscale=[-0.001,0.251]

g₂(X)

g₂(X)=-6 (X - 1) X - 1

g₂, 0, yscale=[-0.0972,0.0972]

X h(X)

X h(X), 0, yscale=[-0.001,0.0028]