Characterizing Truthfulness In Discrete Domains AHUVA MU ALEM Social and Information Sciences Laboratory, California Institute of Technology and MICHAEL SCHAPIRA The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel1 Algorithmic mechanism design [9; 10] focuses on the design of algorithms that aim to achieve global objectives in settings in which the input is provided by self-interested strategic players2 . This necessitates the design of algorithms that are incentive-compatible (a.k.a. truthful 3 ) in the sense that players are incentivized via payments to behave as instructed. The most natural approach to designing incentive-compatible algorithms is coming up with an algorithm and an explicit payment scheme that guarantees its incentive-compatibility. However, nding appropriate payments is often a di cult, setting-speci c, task, which is mostly achievable for very simple types of algorithms. A more general approach is the following: Any algorithm that interacts with sel sh players and then outputs an outcome, can be regarded as computing a function, called a social-choice function, from the players input to some outcome space. Certain properties of social-choice functions are known to imply their implementability, that is, the existence of a payment scheme that guarantees incentivecompatibility.
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