Strategyproofness

In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information,[1]: 244  i.e. given no information about what the others do, you fare best or at least not worse by being truthful.

SP is also called truthful or dominant-strategy-incentive-compatible (DSIC),[1]: 415  to distinguish it from other kinds of incentive compatibility.

An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off.[2]

Typical examples of SP mechanisms are majority voting between two alternatives, second-price auction, and any VCG mechanism.

Typical examples of mechanisms that are not SP are plurality voting between three or more alternatives, and first-price auction.

SP is also applicable in network routing. 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 SP, that is, the owners of some links can benefit by lying about the cost. We may end up paying far more than the actual cost. It can be shown that given certain assumptions about the network and the players (owners of links), a variant of the VCG mechanism is SP.

which expresses the value it has for each alternative, in monetary terms.

It is helpful to have simple conditions for checking whether a given mechanism is SP or not. This subsection shows two simple conditions that are both necessary and sufficient.

Conditions 1 and 2 are not only necessary but also sufficient: any mechanism that satisfies conditions 1 and 2 is SP.

For this setting, it is easy to characterize truthful mechanisms. Begin with some definitions.

A mechanism is called monotone if, when a player raises his bid, his chances of winning (weakly) increase.

For a monotone mechanism, for every player i and every combination of bids of the other players, there is a critical value in which the player switches from losing to winning.

A normalized mechanism on a single-parameter domain is truthful iff the following two conditions hold:[1]: 229–230 

A new type of fraud that has become common with the abundance of internet-based auctions is false-name bids – bids submitted by a single bidder using multiple identifiers such as multiple e-mail addresses.

False-name-proofness means that there is no incentive for any of the players to issue false-name-bids. This is a stronger notion than strategyproofness. In particular, the Vickrey–Clarke–Groves (VCG) auction is not false-name-proof.[3]

False-name-proofness is importantly different from group strategyproofness because it assumes that an individual alone can simulate certain behaviours that would normally require the collusive coordination of multiple individuals.