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In mechanism design, a process is incentive-compatible (IC) if all of the participants fare best when they truthfully reveal any private information asked for by the mechanism. As an illustration, voting systems which create incentives to vote dishonestly lack the property of IC. In the absence of dummy bidders, collusion, incomplete information, or other factors which interfere with process efficiency, a second price auction is an example of a mechanism that is IC.
There are different degrees of incentive-compatibility: in some games, truth-telling can be a dominant strategy. A weaker notion is that truth-telling is a Bayes-Nash equilibrium: it is best for each participant to tell the truth, provided that others are also doing so.
Incentive-compatible mechanisms in single-parameter domains
A single-parameter domain is a game in which each player i gets a certain positive value vi for "winning" and a value 0 for "losing". A simple example is a single-item auction, in which vi is the value that player i assigns to the item.
For this setting, it is easy to characterize IC mechanisms. Begin with some definitions.
A mechanism is called normalized if every losing bid pays 0.
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 IC iff the following two conditions hold:
- The assignment function is monotone in each of the bids, and:
- Every winning bid pays the critical value.
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