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In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multidimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality.

Over the years, private file-sharing communities built on the BitTorrent protocol have developed their own policies and mechanisms for motivating members to share content and contribute resources. By requiring members to maintain a minimum ratio between uploads and downloads, private communities effectively establish credit systems, and with them full-fledged economies. We report on a half-year-long measurement study of DIME -a community for sharing live concert recordings -that sheds light on the economic forces affecting users in such communities. A key observation is that while the download of files is priced only according to the size of the file, the rate of return for seeding new files is significantly greater than for seeding old files. We find via a natural experiment that users react to such differences in resale value by preferentially consuming older files during a 'free leech' period. We consider implications of these finding on a user's ability to earn credits and meet ratio enforcements, focusing in particular on the relationship between visitation frequency and wealth and on low bandwidth users. We then share details from an interview with DIME moderators, which highlights the goals of the community based on which we make suggestions for possible improvement.

For decades researchers have struggled with the problem of envy-free cake cutting: how to divide a divisible good between multiple agents so that each agent likes his own allocation best. Although an envy-free cake cutting protocol was ultimately devised, it is unbounded, in the sense that the number of operations can be arbitrarily large, depending on the preferences of the agents. We ask whether bounded protocols exist when the agents' preferences are restricted. Our main result is an envy-free cake cutting protocol for agents with piecewise linear valuations, which requires a number of operations that is polynomial in natural parameters of the given instance.

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