Strategyproof

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In game theory, an asymmetric game where players have private information is said to be strategyproof (or truthful) if there is no incentive for any of the players to lie about or hide their private information from the other players.

Although the strategyproof concept has applications in several areas of game theory and economics, it is most natural to the theory of payment schemes for network routing. As an example, consider a network as a graph where each edge (i.e. link) has an associated cost of transmission, privately known to the owner of the link. The owner of a link wishes to be compensated for relaying messages.

As the sender of a message on the network, one wants to find the least cost path. There are efficient methods for doing so, even in large networks. However, there is one problem: the costs for each link are unknown. A naive approach would be to ask the owner of each link the cost, use these declared costs to find the least cost path, and pay all links on the path their declared costs. However, it can be shown that this payment scheme is not strategyproof, that is, the owners of some links can benefit by lying about the cost. We may end up paying far more that the actual cost.

It can be shown that given certain assumptions about the network and the players (owners of links), there do exist strategyproof payment schemes. An important one is the Vickrey-Clarke-Groves (VCG) scheme. Thus, strategyproofness is a useful concept in game theory.

Strategyproofness can be thought of as two separate conditions:

• Incentive Compatibility: a player will reveal its true cost to maximize its profit regardless of the other players' actions.
• Individual Rationality: a player can choose whether or not to participate; in other words, the link will not relay a message if the payment is less than the cost.

[edit] References

• Parkes, David C. (2004), On Learnable Mechanism Design, in: Tumer, Kagan and David Wolpert (Eds.): Collectives and the Design of Complex Systems, New York u.a.O., pp.107-133.
• On Asymptotic Strategy-Proofness of Classical Social Choice Rules An article by Arkadii Slinko about strategy-proofness in voting systems.

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