Truth Telling Mechanisms
In our discussion on game theory and dominant strategies, we have learned and frequently emphasized that the dominant strategy of a second price sealed-bid auction is to bid truthfully. I found it very interesting and practical to devise a game such that one’s dominant strategy is to tell the truth. I wanted to find other mechanisms in different scenarios where people’s dominant strategy is to tell the truth despite there being an incentive to exaggerate their true value so that the outcome would occur in their favor.
The mechanism that I looked into was the Clark/Pivotal Mechanism, which can apply to providing public goods depending on the marginal benefit it would give society. The marginal benefit of society is the sum of all the marginal benefits of each individual in the society. It is like the social welfare we defined in class. If a government were deciding whether or not to build a bridge, they would build the bridge if marginal benefit of society were greater than 0, and would not build the bridge if the marginal benefit of society were less than 0. If the bridge were built, each individual would receive their marginal benefit, and if it is not built, then everybody receives a marginal benefit of 0. Without loss of generality, we assume the cost of the bridge is covered and does not affect the game.
To implement this mechanism, each individual of society would have to give a report of what they claim their true value of having the bridge built is. If the sum of these claims is greater than or equal to 0, then the bridge is built. If it is less than 0, it is not built.
The key part of this mechanism is that if you are considered “pivotal”, you have the pay a tax. You are pivotal either if the bridge is being built, but would not have been built if your claim were not considered, or, if the bridge is not being built, but would have been built if your claim were not considered. If you are pivotal, the tax you pay is the sum of everybody else’s claims.
To give a more concrete example, suppose there are three people in a society, A, B, and C. A’s true value is 5, B’s is 10 and C’s is -9. The marginal benefit of society would be 6, and thus, the bridge would be built. In this scenario, we can see that person C would have an incentive to exaggerate his claim in hopes of not having the bridge built. Currently, C’s value is -9, and he is not pivotal so he doesn’t have to pay a tax, so his marginal benefit would be -9. The only way C could change the outcome and have the bridge not be built would be if he claimed his true value was over 15. At this point, he is pivotal, and would have to pay a tax of the sum of the marginal benefits of A and B, which is 15. Then his payoff would be 0 (marginal benefit of bridge not being built) – 15 (sum of A and B’s values) = -15, which makes him much worse off than -9. Had C’s true value actually been greater than 15, paying the tax would still leave him at a positive payoff. However if C exaggerates his value, his payoff will be worse than truth telling. As a result, the dominant strategy of this mechanism is to tell the truth.
http://www.cs.cmu.edu/~arielpro/15896/docs/notes14.pdf