Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that captures people’s propensity to overestimate extreme events and their different attitudes toward gains and losses. In this study, we design a lottery that maximizes the seller’s profit when the buyers’ decision-making adheres to the CPT framework. The main difficulty is the nonconvexity of the CPT framework, which we overcome by reformulating the problem as a three-level optimization problem and characterizing its optimal solution. Based on the analysis, we propose a linear-time algorithm that computes the optimal lottery. Furthermore, we present an efficient algorithm applicable to a broader setting with a ticket price constraint. This is the first study to employ the CPT framework in designing an optimal lottery with more than two outcomes.

In the course allocation problem, there are a set of students and a set of courses at a given university. University courses may have different numbers of credits, typically related to different numbers of learning hours, and there may be other constraints such as courses running concurrently. Students may have upper bounds on the number of credits they may be assigned, and courses may have upper quotas on the number of students that can be enrolled. Our goal is to allocate the students to the courses, taking these constraints into account, such that the resulting matching is stable, which means that no student and course(s) have an incentive to break away from the matching and become assigned to one another. We study several definitions of stability and for each we give a mixture of polynomial-time algorithms and hardness results for problems involving verifying the stability of a matching, finding a stable matching or determining that none exists, and finding a maximum size stable matching. We also study variants of the problem with master lists of students, and lower quotas on the number of students allocated to a course, establishing additional complexity results in these settings.

Allocating indivisible goods is a ubiquitous task in fair division. We study additive welfarist rules , an important class of rules which choose an allocation that maximizes the sum of some function of the agents' utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents' utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances.

We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and making payments to cover edge prices. Our focus is on the existence and computation of market equilibrium, where challenges arise from the interdependence between coalition formation among strategic agents with heterogeneous preferences and route selection that induces a network flow under integral capacity constraints. To address this interplay between coalition formation and network capacity utilization, we introduce a novel approach based on combinatorial auction theory and network flow theory. We establish sufficient conditions on the network topology and agents’ preferences that guarantee both the existence and polynomial-time computation of a market equilibrium. Additionally, we identify a particular market equilibrium that maximizes utilities for all agents and the outcome is equivalent to the classical Vickrey-Clarke-Groves mechanism. Furthermore, we extend our results to multi-period settings and general networks, showing that when the sufficient conditions are not met, an equilibrium may still exist but requires more complex, path-based pricing mechanisms that set differentiated prices based on agents’ preference parameters.

Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability. First, we prove that we can determine the existence of a non-uniformly stable matching in polynomial time. Next, we give a polyhedral characterization of the set of non-uniformly stable matchings. Finally, we prove that the set of non-uniformly stable matchings forms a distributive lattice.

How can individual agents coordinate their actions in a distributed manner to achieve a shared objective? This question arises across various systems—economic, technical, and sociological—all of which face common challenges such as scalability, heterogeneity, and conflicting individual and collective goals. In economic markets, these challenges are mitigated by the use of a common currency, which enables participants to coordinate their actions toward efficient outcomes. This raises the question of whether similar mechanisms, such as a common currency, can be applied to other systems, including technical and sociological contexts. In this paper, we explore this idea within the context of social media, where communities form around shared interests. We propose that social support (in the form of likes, shares, and comments) functions as a currency that coordinates the actions of users in content markets. We investigate two core questions: (1) Can social support serve as a currency that shapes the production and sharing of content, and (2) What role do influencers play in coordinating content creation and dissemination? Through formal modeling and analysis, we demonstrate that social support can act as an efficient coordination mechanism, similar to money in economic markets. Influencers play a dual role in aggregating content and acting as proxies for information, helping content producers navigate large markets. Our findings suggest that while social support as a currency leads to efficient outcomes in ideal markets, imperfections in information introduce a “price of influence,” resulting in suboptimal outcomes. However, as content markets grow, this price diminishes, and social welfare approaches optimal levels. These insights offer a framework for understanding coordination in distributed environments, with potential applications to both sociological and technical systems, including multi-agent AI systems.

We study the classic single-item auction setting of Myerson, but under the assumption that the buyers’ values for the item are distributed over finite supports. Using strong LP duality and polyhedral theory, we rederive various key results regarding the revenue-maximizing auction, including the characterization through virtual welfare maximization and the optimality of deterministic mechanisms, as well as a novel, generic equivalence between dominant-strategy and Bayesian incentive compatibility. Inspired by this, we abstract our approach to handle more general auction settings, where the feasibility space can be given by arbitrary convex constraints, and the objective is a linear combination of revenue and social welfare. We characterize the optimal auctions of such systems as generalized virtual welfare maximizers, by making use of their KKT conditions, and we present an analogue of Myerson’s payment formula for general discrete single-parameter auction settings. Additionally, we prove that integrality of the feasibility space is a sufficient condition to guarantee the optimality of auctions with integral allocation rules. Finally, we demonstrate this KKT approach by applying it to a setting where bidders are interested in buying feasible flows on trees with capacity constraints, and provide a combinatorial description of the (randomized, in general) optimal auction.

Congestion games allow to model competitive resource sharing in various distributed systems. Pure Nash equilibria, that are stable outcomes of a game, could be far from being socially optimal. Our goal is to identify combinatorial structures that limit the inefficiency of equilibria. This question has been mainly investigated for congestion games defined over networks. Instead, we focus on symmetric matroid congestion games, where the strategies of every player are the bases of a given matroid. We derive new upper bounds on the Price of Anarchy (PoA) of congestion games defined over k -uniform matroids and paving matroids with delay functions in class \({\mathcal {D}} \) . For both affine and polynomial delay functions, our bounds indicate that the inefficiency of pure Nash equilibria is limited by these combinatorial structures.

In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable partition always does and provides a succinct certificate for the unsolvability of an instance. Furthermore, apart from being a useful structural tool to study the problem, every stable partition corresponds to a stable half-matching , which has applications, for example, in sports scheduling and time-sharing. We establish new structural results for stable partitions and show how to enumerate all stable partitions and the cycles included in such structures efficiently. We also adapt optimality criteria from stable matchings to stable partitions and give complexity and approximability results for the problems of computing such “fair” and “optimal” stable partitions. Through this research, we contribute to a deeper understanding of stable partitions from a combinatorial point of view, as well as the computational complexity of computing “fair” or “optimal” stable half-matchings in practice, closing the gap between integral and fractional stable matchings and paving the way for further applications of stable partitions to unsolvable instances and computationally hard stable matching problems.

In this article, we introduce an over-time variant of the well-known prophet inequality with i.i.d. random variables. Instead of stopping with one realized value at some point in the process, we decide for each step how long we select the value. Then we cannot select another value until this period is over. The goal is to maximize the expectation of the sum of selected values. We describe the structure of the optimal stopping rule and give upper and lower bounds on the prophet inequality. In online algorithms terminology, this corresponds to bounds on the competitive ratio of an online algorithm. We give a surprisingly simple algorithm with a single threshold that results in a prophet inequality of ≈ 0.396 for all input lengths n . Additionally, as our main result, we present a more advanced algorithm resulting in a prophet inequality of ≈ 0.598 when the number of steps tends to infinity. We complement our results by an upper bound that shows that the best possible prophet inequality is at most 1/φ ≈ 0.618, where φ denotes the golden ratio.