Clarke groves mechanism

Clarke groves mechanism
public policy

1. Clarke Groves mechanism

2. Clarke Groves mechanism Truthful mechanism for achieving a socially-optimal solution. Consist of choice rule and payment rule Determine preferences for Public Goods. It has truth as dominant strategy as impact on others preferences is always a dominant strategy Makes efficient choices Incentive in terms of society

3. Example Consider two roommates who would like to buy a TV for their apartment. TV costs $100 They should decide: Do they want to buy a TV together? If so, how should they share the costs? Individual preferences have to be taken into consideration in deciding the efficient outcome.

4. Example Bidders are willing to pay v1 and v2 this is private information. Efficient outcome: buy if v1 + v2 > 100 VCG ensures: Efficient outcome. Truthful revelation. What are the VCG payments? Consider values v1 = 70, v2 = 80. With player 1: value for the others is 80. Without player 1: welfare for the others is 100. p1 = 100 − 80. Similarly for player 2, p2 = 100 − 70 But, total payment is 20 + 30 < 100! Cost is not covered

5. Strengths and weaknesses All players have an incentive to be honest about how they value the good. Individuals may be subject to a Tax that must then be 'thrown away' (at least not spent on any of the individuals benefitting from the public good). We might have to charge agents money in order to get this to work so it could be sum of payment greater than zero So either we have to follow them off to somebody who is not involved in decision process

6. Properties: Optimal to tell the truth Voter only pays when decisive. Payments < benefits received As population grows less of a problem with excess revenue.

7. Clark-Groves Mechanism Step 1 : Individuals report their value for the bridge v i Step 2 : Add up the reported values. Step 3 : If Sum of Reports – Cost of Bridge >0 Build Bridge If Sum of Reports – Cost of Bridge <0 Don’t Build Step 4 : If the individual’s value was decisive, i.e. Sum of Others’ Reports < Cost of Bridge < Sum of all Reports Charge the individual = Cost of Bridge – Sum of others’ reports