We introduce a bidding language for expressing negative value externalities in position auctions for online advertising. The unit-bidder constraints (UBC) language allows a bidder to condition a bid on its allocated slot and on the slots allocated to other bidders. We introduce a natural extension of the Generalized Second Price (GSP) auction, the expressive GSP (eGSP) auction, that induces truthful revelation of constraints for a rich subclass of unit-bidder types, namely downward-monotonic UBC. We establish the existence of envy-free Nash equilibrium in eGSP under a further restriction to a subclass of exclusion constraints, for which the standard GSP has no pure strategy Nash equilibrium. The equilibrium results are obtained by reduction to equilibrium analysis for reserve price GSP (Even-Dar et al. 2008). In considering the winner determination problem, which is NP-hard, we bound the approximation ratio for social welfare in eGSP and provide parameterized complexity results.

We study a problem of dynamic allocation without money. Agents have arrivals and departures and strict preferences over items. Strategyproofness requires the use of an arrival-priority serial-dictatorship (APSD) mechanism, which is ex post Pareto efficient but has poor ex ante efficiency as measured through average rank efficiency. We introduce the scoring-rule (SR) mechanism, which biases in favor of allocating items that an agent values above the population consensus. The SR mechanism is not strategyproof but has tolerable manipulability in the sense that: (i) if every agent optimally manipulates, it reduces to APSD, and (ii) it significantly outperforms APSD for rank efficiency when only a fraction of agents are strategic. The performance of SR is also robust to mistakes by agents that manipulate on the basis of inaccurate information about the popularity of items.

Cake cutting is a common metaphor for the division of a heterogeneous divisible good. There are numerous papers that study the problem of fairly dividing a cake; a small number of them also take into account self-interested agents and consequent strategic issues, but these papers focus on fairness and consider a strikingly weak notion of truthfulness. In this paper we investigate the problem of cutting a cake in a way that is truthful and fair, where for the first time our notion of dominant strategy truthfulness is the ubiquitous one in social choice and computer science. We design both deterministic and randomized cake cutting algorithms that are truthful and fair under different assumptions with respect to the valuation functions of the agents.