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1. Optimal consumption of multiple goods in incomplete markets

   https://doi.org/10.1017/jpr.2018.51  

   Mostovyi, Oleksii (September 2018, Journal of Applied Probability)

   We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models. 

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2. On the Optimality of Greedy Policies in Dynamic Matching

   https://doi.org/10.1287/opre.2021.0596  

   Kerimov, Süleyman; Ashlagi, Itai; Gurvich, Itai (September 2023, Operations Research)

   Hindsight Optimality in Two-Way Matching Networks In “On the Optimality of Greedy Policies in Dynamic Matching”, Kerimov, Ashlagi, and Gurvich study centralized dynamic matching markets with finitely many agent types and heterogeneous match values. A matching policy is hindsight optimal if the policy can (nearly) maximize the total value simultaneously at all times. The article establishes that suitably designed greedy policies are hindsight optimal in two-way matching networks. This implies that there is essentially no positive externality from having agents waiting to form future matches. Proposed policies include the greedy longest-queue policy, with a minor variation, as well as a greedy static priority policy. The matching networks considered in this work satisfy a general position condition. General position is a weak (but necessary) condition that holds when the static-planning problem (a linear program that optimizes the first-order matching rates) has a unique and nondegenerate optimal solution. 

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3. Cyber vulnerability maintenance policies that address the incomplete nature of inspection

   https://doi.org/10.1002/asmb.2487  

   Liu, Enhao; Allen, Theodore T.; Roychowdhury, Sayak (October 2019, Applied Stochastic Models in Business and Industry)

   Abstract In cybersecurity, incomplete inspection, resulting mainly from computers being turned off during the scan, leads to a challenge for scheduling maintenance actions. This article proposes the application of partially observable decision processes to derive cost‐effective cyber maintenance actions that minimize total costs. We consider several types of hosts having vulnerabilities at various levels of severity. The maintenance cost structure in our proposed model consists of the direct costs of maintenance actions in addition to potential incident costs associated with different security states. To assess the benefits of optimal policies obtained from partially observable Markov decision processes, we use real‐world data from a major university. Compared with alternative policies using simulations, the optimal control policies can significantly reduce expected maintenance expenditures per host and relatively quickly mitigate the most important vulnerabilities. 

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4. Pricing Multi-Unit Markets

   Ezra, Tomer; Feldman, Michal; Roughgarden, Tim; Suksompong, Warut (December 2018, 14th Conference on Web and Internet Economics (WINE))

   This paper studies the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. The paper shows upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer’s information and agents’ valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices. 

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5. Online Team Formation Under Different Synergies

   Eichhorn, Matthew; Banerjee, Siddhartha; Kempe, David (December 2022, ACM)

   Team formation is ubiquitous in many sectors: education, labor markets, sports, etc. A team’s success depends on its members’ latent types, which are not directly observable but can be (partially) inferred from past performances. From the viewpoint of a principal trying to select teams, this leads to a natural exploration-exploitation trade-off: retain successful teams that are discovered early, or reassign agents to learn more about their types? We study a natural model for online team formation, where a principal repeatedly partitions a group of agents into teams. Agents have binary latent types, each team comprises two members, and a team’s performance is a symmetric function of its members’ types. Over multiple rounds, the principal selects matchings over agents and incurs regret equal to the deficit in the number of successful teams versus the optimal matching for the given function. Our work provides a complete characterization of the regret landscape for all symmetric functions of two binary inputs. In particular, we develop team-selection policies that, despite being agnostic of model parameters, achieve optimal or near-optimal regret against an adaptive adversary. 

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