Vickery-Clarke-Groves Mechanism: Concept & Explanation

In 1972, Edward H Clarke introduced a taxation scheme for consumers to reveal their true preferences for public goods. In this mechanism, everyone truthfully reveals their preferences even if they are not required to do so.

Clarke’s demand scheme, also called as the pivotal mechanism, which gives each user of the public good the choice of either to leave the outcome as it is or change its cost equal to the net loss of others.

He explained this concept with the help of the quasi-linear utility function. The Vickery-Clarke-Groves mechanism is a direct quasilinear mechanism (x,p) where,

X(ѵ) = argx ∑i v(x)

P(v) = ∑j ≠ 1vj (x (v-i)- ) = ∑ j ≠ 1vj (x(v)

This equation can be explained with the help of the following example.

The government has decided to install a number of public benches in the town. There are three beneficiaries, X, Y, and Z, with four alternatives available, n=0,1,2,3, where n is the number of public benches. The government’s objective is to provide good-quality benches to the people living in the town.

Total benefits and costs:

Number of Public Benches
Resident	0	1	2	3
X	0	60	90	155
Y	0	80	120	140
Z	0	120	200	360
Social Net Benefit	0	140	170	155

As the social net benefit is maximum at 2, that is the socially efficient number.

Net benefits with an equal cost share:

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	155

If n= 1, the total cost is 120. Hence, the cost share for each is 40. The private net benefit for X is then 60-40=20. Similarly, for Y and Z and n = 2, 3.

Now, this example is being explained when the Groves and Clarke tax is being applied.

Groves-Clarke Taxes

Person X

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	155

Number of Public Benches
Resident	0	1	2	3
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	120	60	120

Person X is not playing an important role. Without him, the net benefit is maximum at n=2. With him, the net benefit is maximum at n=2. So, his tax is zero.

Person Y

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	155

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Z	0	80	120	100
Social Net Benefit	0	100	130	135

Person Y, however, is playing an important role. With him, the net benefit is maximum at n=2. Without him, the net benefit is maximum at n=3. Y tax is, therefore, the difference between the sum of net benefits of others at n=3 and the sum of net benefits of others at n=2, i.e. 135-130=5.

Y is paying the tax because his report changes the decision from n=3 to n=2.

Person Z

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	155

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	35
Y	0	40	40	20
Social Net Benefit	0	60	50	55

Person Z is also playing an important role. With him, the net benefit is maximum at n=2. Without him, the net benefit is maximum at n=1. Z tax is, however, the sum of others benefits at n=1, and the sum of others benefits at n=2, i.e., 60-50= 10.

Net benefits with taxes:

Number of Public Benches
Resident	0	1	2	3	Tax
X	0	20	10	35	0
Y	0	40	40	20	5
Z	0	80	120	100	10
Social Net Benefit	0	140	170	155

Post-tax net benefit from this scheme is 10, for X 40-5= 35, for Y, 120-10= 110 for Z.

Incentives for truthful revelation:

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	70
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	190

It is to be noted that X net benefit is maximum at n=3.

Number of Public Benches
Resident	0	1	2	3
X	0	20	10	70
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	140	170	190

Number of Public Benches
Resident	0	1	2	3
Y	0	40	40	20
Z	0	80	120	100
Social Net Benefit	0	120	160	120

X’s role is very important. Without him, the sum of net benefits is maximum at n=2. His report will change the decision from n=2 to n=3. So he has to pay the tax, which will be equal to 160-120=40. If X lies and does not report truly, then the net benefit from n=3- tax. Therefore 35-40=-5. If X truly reports, then the net benefit will be 10. Thus, no point arises that X should tell a lie.

Thus, this was the VCG mechanism (Vickery-Clarke-Groves) mechanism for public goods.

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25. Samuelson’s Model of Public Expenditure
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68. Need for Public Debt or Public Borrowing
69. Sources of Public Debt
70. Classification of Public Debt
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