Computing market equilibria is an important practical problem for market design (e.g. fair division, item allocation). However, computing equilibria requires large amounts of information (e.g. all valuations for all buyers for all items) and compute power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: 1) filling in unknown valuations using techniques from matrix completion, 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions.

Emergency workers engaged in strenuous work in hot environments risk overheating and mission failure. We describe a real-time application that would reduce these risks in terms of a real-time thermal-work strain index (SI) estimator; and a Markov Decision Process (MDP) to compute optimal work rate policies. We examined the thermo-physiological responses of 14 experienced U.S. Army Ranger students (26±4 years 1.77±0.04 m; 78.3±7.3 kg) who participated in a strenuous 8 mile time-restricted pass/fail road march conducted under thermally stressful conditions. A thermoregulatory model was used to derive SI state transition probabilities and model the students’ observed and policy driven movement rates. We found that policy end-state SI was significantly lower than SI when modeled using the student’s own movement rates (3.94±0.88 vs. 5.62±1.20, P<0.001). We also found an inverse relationship between our policy impact and maximum SI (r=0.64 P<0.05). These results suggest that modeling real world missions as an MDP can provide optimal work rate policies that improve thermal safety and allow students to finish in a “fresher” state. Ultimately, SI state estimation and MDP models incorporated into wearable physiological monitoring systems could provide real-time work rate guidance, thus minimizing thermal work-strain while maximizing the likelihood of accomplishing mission tasks.

In many large economic markets, goods are sold through sequential auctions. Such domains include eBay, online ad auctions, wireless spectrum auctions, and the Dutch flower auctions. Bidders in these domains face highly complex decision-making problems, as their preferences for outcomes in one auction often depend on the outcomes of other auctions, and bidders have limited information about factors that drive outcomes, such as other bidders' preferences and past actions. In this work, we formulate the bidder's problem as one of price prediction (i.e., learning) and optimization. We define the concept of stable price predictions and show that (approximate) equilibrium in sequential auctions can be characterized as a profile of strategies that (approximately) optimize with respect to such (approximately) stable price predictions. We show how equilibria found with our formulation compare to known theoretical equilibria for simpler auction domains, and we find new approximate equilibria for a more complex auction domain where analytical solutions were heretofore unknown.