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We study the design of core-selecting payment rules for combinatorial auctions, a challenging setting where no strategyproof rules exist. We show that the rule most commonly used in practice, the Quadratic rule, can be improved on in terms of efficiency, incentives, and revenue. We present a new computational search framework for finding good mechanisms, and we apply it toward a search for good core-selecting rules. Within our framework, we use an algorithmic Bayes–Nash equilibrium solver to evaluate 366 rules across 31 settings to identify rules that outperform the Quadratic rule. Our main finding is that our best-performing rules are large-style rules—that is, they provide bidders with large values with better incentives than does the Quadratic rule. Finally, we identify two particularly well-performing rules and suggest that they may be considered for practical implementation in place of the Quadratic rule.
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Optimal Scoring Rules for Multi-dimensional Effort
This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest, Krysta, and Vocking, 2005; Singer, 2010) and it is foundational to applying algorithmic mechanism design to the classroom. The paper identifies two simple families of scoring rules that guarantee constant approximations to the optimal scoring rule. The truncated separate scoring rule is the sum of single dimensional scoring rules that is truncated to the bounded range of feasible scores. The threshold scoring rule gives the maximum score if reports exceed a threshold and zero otherwise. Approximate optimality of one or the other of these rules is similar to the bundling or selling separately result of Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the approximate optimality of the best of those two simple scoring rules is robust when the agent’s choice of effort is made sequentially.
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- Award ID(s):
- 2229162
- PAR ID:
- 10555944
- Editor(s):
- Neu, Gergely; Rosasco, Lorenzo
- Publisher / Repository:
- Proceedings of Thirty Sixth Conference on Learning Theory
- Date Published:
- Volume:
- 195
- ISSN:
- 1938-7228
- Page Range / eLocation ID:
- 2624-2650
- Subject(s) / Keyword(s):
- Scoring rules mechanism design loss functions
- Format(s):
- Medium: X
- Location:
- Bangalore, India
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Proceeding:
- The DOI is not currently available.
