AAAI 2026 Papers

Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders---with the seller---to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders---these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques---and build upon existing quadratic programming techniques---to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model.Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVAkADD, a novel approximation method that fits a k-additive surrogate game. By taking advantage of k-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.

This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice---such as the Method of Equal Shares and the Nash Rule---and supports them through both theoretical analysis and extensive experimental evaluation.

We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled via a convex cost function. Additionally, items are partitioned into groups, and each platform also incurs group-specific convex cost over the number of items from each group that can be assigned to the platform. These costs promote group fairness by penalizing imbalances, yielding a soft variation of fairness notions introduced in prior work, such as Restricted Dominance and Minority protection. Restricted Dominance enforces upper bounds on group representation, while Minority protection enforces lower bounds. Our approach replaces such hard constraints with cost-based penalties, allowing more flexible trade-offs. Our model also captures Nash Social Welfare kind of objective. The cost of an assignment is the sum of the values of all the cost functions across all the groups and platforms. The objective is to find an assignment that minimizes the cost while achieving a total utility that is at least a user-specified threshold. The main challenge lies in balancing the overall platform cost with group-specific costs, both governed by convex functions, while meeting the utility constraint. We present an efficient polynomial-time approximation algorithm, supported by theoretical guarantees and experimental evaluation. Our algorithm is based on techniques involving linear programming and network flows. We also provide an exact algorithm for a special case with uniform utilities and establish the hardness of the general problem when the groups can intersect arbitrarily. This work has applications in cloud computing, logistics, resource-constrained machine learning deployment, federated learning, and network design, where resources must be allocated across platforms with diverse cost structures and diminishing returns.

We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions, nor sharing information. Prior works established polynomial-time convergence to an approximate Nash equilibrium under strong reachability and mixing time assumptions. We propose a convergent algorithm that significantly relaxes these assumptions, requiring only the existence of a single policy with bounded reachability and mixing time. Our key algorithmic novelty is introducing Tsallis entropy regularization to smooth the best-response policy updates. By suitably tuning this regularization, we ensure sufficient exploration, thus bypassing previous stringent assumptions on the MDP. We prove a polynomial-time convergence to an approximate Nash equilibrium by establishing novel properties of the value and policy updates induced by the Tsallis entropy regularizer.

Counterfactual Regret Minimization (CFR) algorithms are widely used to compute a Nash equilibrium (NE) in two-player zero-sum imperfect-information extensive-form games (IIGs). Among them, Predictive CFR+ (PCFR+) is particularly powerful, achieving an exceptionally fast empirical convergence rate via the prediction in many games. However, the empirical convergence rate of PCFR+ would significantly degrade if the prediction is inaccurate, leading to unstable performance on certain IIGs. To enhance the robustness of PCFR+, we propose Asymmetric PCFR+ (APCFR+), which employs an adaptive asymmetry of step sizes between the updates of implicit and explicit accumulated counterfactual regrets to mitigate the impact of the prediction inaccuracy on convergence. We present a theoretical analysis demonstrating why APCFR+ can enhance the robustness. To the best of our knowledge, we are the first to propose the asymmetry of step sizes, a simple yet novel technique that effectively improves the robustness of PCFR+. Then, to reduce the difficulty of implementing APCFR+ caused by the adaptive asymmetry, we propose a simplified version of APCFR+ called Simple APCFR+ (SAPCFR+), which uses a fixed asymmetry of step sizes to enable only a single-line modification compared to original PCFR+. Experimental results on five standard IIG benchmarks and two heads-up no-limit Texas Hold’em (HUNL) Subagems show that (i) both APCFR+ and SAPCFR+ outperform PCFR+ in most of the tested games, (ii) SAPCFR+ achieves a comparable empirical convergence rate with APCFR+, and (iii) our approach can be generalized to improve other CFR algorithms, e.g., Discount CFR (DCFR).

The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying participation costs and share a possibly heuristic belief about their pivotality (ability to influence the outcome). In a costly voting setup where voters abstain if their participation cost is greater than their pivotality estimate, we identify a single property of the heuristic belief---weakly vanishing pivotality---that gives rise to multiple stable equilibria in which elections are nearly tied. In contrast, strongly vanishing pivotality (as in the standard Calculus of Voting model) yields a unique, trivial equilibrium where only zero-cost voters participate as the population grows. We then characterize when nontrivial equilibria satisfy a version of the Jury Theorem: below a sharp threshold, the majority-preferred candidate wins with probability approaching one; above it, both candidates either win with equal probability.

This paper presents a novel strategy for a multi-agent pursuit-evasion game involving multiple faster pursuers with heterogenous speeds and a single slower evader. We define a geometric region, the evader's safe-reachable set, as the intersection of Apollonius circles derived from each pursuer-evader pair. The capture strategy is formulated as a zero-sum game where the pursuers cooperatively minimize the area of this set, while the evader seeks to maximize it, effectively playing a game of spatial containment. By deriving the analytical gradients of the safe-reachable set's area with respect to agent positions, we obtain closed-form, instantaneous optimal control laws for the heading of each agent. These strategies are computationally efficient, allowing for real-time implementation. Simulations demonstrate that the gradient-based controls effectively steer the pursuers to systematically shrink the evader’s safe region, leading to guaranteed capture. This area-minimization approach provides a clear geometric objective for cooperative capture.

Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for mechanisms: a mechanism is said to satisfy PEF1 if for any pair of agent orderings, no agent prefers their bundle determined under one ordering to that under another ordering by more than the utility of a single good. First, we propose a scale-invariant, polynomial-time mechanism that satisfies PEF1 and yields an envy-freeness up to one good (EF1) allocation. For the case of two agents, we establish that any mechanism producing a maximum Nash welfare allocation eliminates envy based on positions by removing one good, provided that utilities are positive. Additionally, we present a polynomial-time mechanism based on the adjusted winner procedure, which satisfies PEF1 and produces an EF1 and Pareto optimal allocation for two agents. In contrast, we demonstrate that well-known mechanisms such as round-robin and envy-cycle elimination do not generally satisfy PEF1.

Audit games are an important variant of the Stackelberg security game, a widely studied game-theoretic model over the past years. It has been acknowledged that a pre-audit phase can notably enhance the audit's efficiency by informing and directing the following audit procedures. In this paper, we model the above process with a two-stage audit game. The game encompasses two stages: an investigation stage where the auditor gathers information about potential policy breaches, and an audit stage where the auditor allocates the audit resources based on the investigation results. We formulate the problem as a set of mathematical programs. Due to the non-convexity of the programs, we consider a restricted strategy space and show that the optimal strategy in the restricted space can be determined by solving a polynomial number of convex optimization problems. Finally, we conduct extensive experiments to evaluate the effect of introducing the initial investigation stage and our algorithm. Our experiments show that even a small budget for the initial investigations can significantly enhance the defender's utility.

Real-world security applications (e.g., cybersecurity) often involve multiple attack paths, each with layers of defenses that an attacker needs to sequentially overcome before a successful attack on the entire system. Each defensive resource changes dynamically in efficacy as the attack unfolds. In this paper, we study the case where attackers are adaptive, potentially switching paths over time in response to these changes with the goal to minimize the expected time until a successful attack. We formalize this as a min-max game and give examples where adaptive attackers are more powerful than non-adaptive ones. We show that defenses that do not account for adaptivity can perform arbitrarily worse. A connection between the attacker's optimal strategy with the classical theory of multi-armed bandits and the Gittins index is made, yielding a simple gradient based algorithm to solve our proposed min-max game. Experiments on synthetic settings validate our approach.

We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.

We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations. As fair we consider the allocations that are envy-free-up-to-any-good (EFX). Finding if EFX allocations always exist, even for agents with additive valuations, is a major open problem in Fair Division. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph, respectively, and only the endpoints of an edge may have non-zero marginal value for it. We show that for hypergraphs with girth at least 4 and agents with general monotone valuations there always exists an EFX allocation and can be constructed in polynomial time. We generalize our approach to also show that multi-hypergraphs with girth (on the simple hypergraph) at least 4 always admit an EFX allocation, as long as there exists a single vertex whose adjacent edges have multiplicity at most the size of that edge minus 2; our construction in this case needs pseudo-polynomial time.

In Facility Location problems there are agents that should be connected to facilities and locations where facilities may be opened so that agents can connect to them. We depart from Uncapacitated Facility Location and by assuming that the connection costs of agents to facilities are congestion dependent, we define a novel problem, namely, Facility Location for Congesting (Selfish) Commuters. The connection costs of agents to facilities come as a result of how the agents commute to reach the facilities in an underlying network with cost functions on the edges. Inapproximability results follow from the related literature and thus approximate solutions is all we can hope for. For when the cost functions are nondecreasing we employ in a novel way an approximate version of Caratheodory’s Theorem to show how approximate solutions for different versions of the problem can be derived. For when the cost functions are nonincreasing we show how this problem generalizes the Cost-Distance problem and provide an algorithm that for this more general case achieves the same approximation guarantees.

We study the computational complexity of winner determination problems in approval-based committee elections under Thiele voting rules. These form a class of rules parameterized by a fixed weight vector that specifies how a voter's satisfaction depends on the number of approved candidates elected. We first analyze the structure of optimal solutions based on the sets of voters who approve each candidate---that is, how voters' approval ballots induce dependencies between candidates---revealing constraints on a winning committee under any fixed Thiele voting rule. Using this, we design FPT algorithms for Proportional Approval Voting (PAV) and other Thiele rules on a natural restricted domain known as the Voter Interval domain---that is, after a suitable ordering of voters, each candidate is approved by a consecutive interval of voters. In particular, we show that every Thiele rule on Voter Interval is FPT with respect to a parameter for which the problem is NP-hard on general instances, even when the parameter takes constant values. Our results advance the understanding of the computational complexity of PAV on Voter Interval instances, which remains one of the central open questions in this area. We further resolve two open questions from the literature on PAV (and other Thiele voting rules) by providing a polynomial-time algorithm for instances where each candidate is approved by at most two voters, and an FPT algorithm parameterized by the total score of a winning committee.

We study a sequential selling problem in which an agent receives daily offers to sell a good, incurs a holding cost each day, and is subject to sunk cost bias---allowing past, irrecoverable costs to influence present decisions. We introduce a formal model parameterizing the degree of sunk cost bias and distinguish between three behavioral types: optimistic (who ignore future bias), naive (who assume their current bias persists), and sophisticated (who anticipate the evolution of their own bias). For each type, we characterize the optimal selling strategy and precisely quantify the worst-case gap in expected objective profit compared to an unbiased agent. Our results show that optimistic agents can suffer a quadratic loss in profit due to excessive waiting, naive agents perform identically to unbiased agents, and sophisticated agents limit their losses to a linear function of the time horizon. These findings clarify how different anticipations of sunk cost bias affect sequential decision-making and suggest targeted interventions to mitigate inefficiency.

We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the balanced constraint). While this constraint is common in real-world scenarios such as team drafts or asset division, it significantly complicates the search for allocations that are both fair and efficient. Envy-freeness up to one good (EF1) is a well-established fairness notion for indivisible goods. Pareto optimality (PO) and its stronger variant, fractional Pareto optimality (fPO), are widely accepted efficiency criteria. Our main contribution establishes both the existence and polynomial-time computability of allocations that are simultaneously EF1 and fPO under balanced constraints in two fundamental cases: (1) when agents have at most two distinct types of valuation functions, and (2) when each agent has a personalized bivalued valuation. Our algorithms leverage novel applications of maximum-weight matching in bipartite graphs and duality theory, providing the first polynomial-time solutions for these cases and offering new insights for constrained fair division problems.

We consider the problem of fairly allocating the vertices of a graph among n agents, where the value of a bundle is determined by its cut value---the number of edges with exactly one endpoint in the bundle. This model naturally captures applications such as team formation and network partitioning, where valuations are inherently non-monotonic: the marginal values may be positive, negative, or zero depending on the composition of the bundle. We focus on the fairness notion of envy-freeness up to one item (EF1) and explore its compatibility with several efficiency concepts such as Transfer Stability (TS) that prohibits any transfer of item that benefit one agent at another's expense. For general graphs, our results uncover a non-monotonic relationship between the number of agents n and the existence of allocations satisfying EF1 and transfer stability (TS): such allocations always exist for n=2, may fail to exist for n=3, but exist again for all n>= 4. We further show that existence can be guaranteed for any n by slightly weakening the efficiency requirement or by restricting the graph to forests. All of our positive results are achieved via efficient algorithms.

House allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents. Every agent must receive exactly one resource. We study algorithmic approaches towards ensuring fairness in such settings. Minimizing the number of envious agents is known to be computationally hard. We present two tractable approaches to deal with the hardness. When the agents are presented with an initial allocation of houses, we aim to refine this allocation by reallocating a bounded number of houses to reduce the number of envious agents. We show an efficient algorithm when the agents express preference for a bounded number of houses and houses are accepted by a bounded number of agents. Next, we consider single peaked preference domain and present a polynomial time algorithm for finding an allocation that minimize the number of envious agents. We further extend it to satisfy Pareto efficiency. Our former algorithm works for other measures of envy such as total envy, or maximum envy, with suitable modifications. Finally, we present an empirical analysis recording the fairness-welfare trade-off of our algorithms.