Jian Ni, Lecheng Zheng, John R Birge
Competing firms that serve shared customer populations face a fundamental information aggregation problem: each firm holds fragmented signals about risky customers, but individual incentives impede efficient collective detection. We develop a mechanism design framework for decentralized risk analytics, grounded in anti-money laundering in banking networks. Three strategic frictions distinguish our setting: compliance moral hazard, adversarial adaptation, and information destruction through intervention. A temporal value assignment (TVA) mechanism, which credits institutions using a strictly proper scoring rule on discounted verified outcomes, implements truthful reporting as a Bayes--Nash equilibrium (uniquely optimal at each edge) in large federations. Embedding TVA in a banking competition model, we show competitive pressure amplifies compliance moral hazard and poorly designed mandates can reduce welfare below autarky, a ``backfiring'' result with direct policy implications. In simulation using a synthetic AML benchmark, TVA achieves substantially higher welfare than autarky or mandated sharing without incentive design.
Sebastiano A. Piccolo, Andrea Tagarelli
Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent dependency relationships across the two groups only, remain largely unexplored. We formalize the CriticalSet problem: given an arbitrary bipartite graph modeling dependencies of items on contributors, identify the set of k contributors whose removal isolates the largest number of items. We prove that this problem is NP-hard and requires maximizing a supermodular set function, for which standard forward greedy algorithms provide no approximation guarantees. Consequently, we model CriticalSet as a coalitional game, deriving a closed-form centrality, ShapleyCov, based on the Shapley value. This measure can be interpreted as the expected number of items isolated by a contributor's departure. Leveraging these insights, we propose MinCov, a linear-time iterative peeling algorithm that explicitly accounts for connection redundancy, prioritizing contributors who uniquely support many items. Extensive experiments on synthetic and large-scale real datasets, including a Wikipedia graph with over 250 million edges, reveal that MinCov and ShapleyCov significantly outperform traditional baselines. Notably, MinCov achieves near-optimal performance, within 0.02 AUC of a Stochastic Hill Climbing metaheuristic, while remaining several orders of magnitude faster.
Song Gao, Hanyu Cheng, Chiwei Yan, Guocheng Jiang
We develop a Markovian traffic equilibrium model for ride-hailing in which vehicles, whether empty or hired, make sequential order-acceptance and link-choice decisions over a traffic network to maximize total discounted return in an infinite-horizon semi-Markov decision process. The model endogenizes both competition among empty vehicles for passenger demand and traffic congestion arising from road usage at the link level. We characterize equilibrium as the solution to a fixed-point system, establish its existence, and develop relaxed fixed-point iteration algorithms for equilibrium computation, with convergence results for specialized network structures. Computational experiments on realistic networks demonstrate the model's practical value for transportation planning. Ablation analyses reveal that ignoring either traffic congestion or drivers' forward-looking behavior can lead to potentially substantial biases in policy evaluation.
Bhavik Dodda, Garima Shakya
One-sided matching problems with ordinal preferences, such as hostel room allocation, are commonly solved using the Top Trading Cycles (TTC) mechanism, which guarantees Pareto-optimal (PO) outcomes. However, TTC does not yield a unique solution: multiple PO allocations may exist, and many distinct initial endowments can converge to the same outcome. Focusing on a single TTC result obscures the structure of the Pareto-efficient frontier and limits principled secondary optimization over fairness or welfare objectives. Therefore, the goal is to find the entire set of PO allocations for a given preference profile. We propose the Inverse Top Trading Cycles Enumeration Algorithm (ITEA), a novel method that efficiently computes the complete set of Pareto-optimal allocations in one-sided matching problems. We prove the soundness and completeness of the proposed algorithm and analyze its computational complexity. Although in the worst case, there can be $n!$ PO allocations; however, compared to the brute-force approach, our algorithm reduces time complexity when there are fewer PO allocations. Empirical results demonstrate substantial reductions in redundant TTC computations compared to brute-force enumeration, enabling efficient characterization of the Pareto frontier.
Elija Perrier
The First Fundamental Theorem of Welfare Economics assumes that welfare-bearing agents are autonomous and implicitly relies on a binary distinction between autonomy and instrumentality. Welfare subjects are those who have autonomy and therefore the capacity to choose and enter into utility comparisons, while everything else does not. In post-AGI economies this presupposition becomes nontrivial because artificial systems may exhibit varying degrees of autonomy, functioning as tools, delegates, strategic market actors, manipulators of choice environments, or possible welfare subjects. We argue that the theorem ought to be subject to an autonomy qualification where the impact of these changes in autonomy assumptions is incorporated. Using a minimal general-equilibrium model with autonomy-conditioned welfare, welfare-status assignment, delegation accounting, and verification institutions, we set out conditions for which autonomy-complete competitive equilibrium is autonomy-Pareto efficient. The classical theorem is recovered as the low-autonomy limit.
Jinliang Xu
The rapid collapse of decentralized game economies, often characterized by the \textit{death spiral,} remains the most formidable barrier to the mass adoption of Web3 gaming. This paper proposes that the sustainability of an open game economy is predicated on three necessary and sufficient conditions: Anti-Sybil Resilience, Anti-Capital Dominance, and Anti-Inflationary Saturation. The first section establishes a theoretical proof of these conditions, arguing that the absence of any single dimension leads to systemic failure. The second section explores the dialectical relationship between these dimensions, illustrating how unchecked automation and capital-driven monopolies accelerate asset hyperinflation. In the third section, we introduce the Identity-Bound Asset Integrity Model (IBAIM) as a comprehensive technical solution. IBAIM utilizes Zero-Knowledge (ZK) biometric hashing and Account Abstraction (AA) to anchor asset utility to unique human identities through a privacy-preserving and regulatory-compliant architecture. By exogenizing biometric verification to trusted local environments and utilizing Zero-Knowledge Proofs of Identity (zk-PoI), the model ensures absolute user privacy. Furthermore, by implementing an Asymmetric Utility Decay (AUD) engine-whereby assets suffer a vertical 50% utility cliff upon secondary transfer-and an entropy-driven thermodynamic degradation mechanism., the model successfully decouples financial speculation from in-game merit. Finally, we apply this framework to analyze prominent historical failures in the GameFi sector, demonstrating that their collapse was an inevitable consequence of violating these core economic constraints. Our findings suggest that trading a degree of asset liquidity for system integrity is the only viable path toward long-term economic viability in decentralized virtual worlds.
Spyros Galanis
Can Large Language Models (AI agents) aggregate dispersed private information through trading and reason about the knowledge of others by observing price movements? We conduct a controlled experiment where AI agents trade in a prediction market after receiving private signals, measuring information aggregation by the log error of the last price. We find that although the median market is effective at aggregating information in the easy information structures, increasing the complexity has a significant and negative impact, suggesting that AI agents may suffer from the same limitations as humans when reasoning about others. Consistent with our theoretical predictions, information aggregation remains unaffected by allowing cheap talk communication, changing the duration of the market or initial price, and strategic prompting-thus demonstrating that prediction markets are robust. We establish that "smarter" AI agents perform better at aggregation and they are more profitable. Surprisingly, giving them feedback about past performance makes them worse at aggregation and reduces their profits.
Sumit Mukherjee
We study how electoral rules shape polarization dynamics when voters and candidates both adapt to repeated election outcomes. We introduce two geometric primitives for comparing rules under this feedback: the \emph{winner radius} $R_t = \max_i \|x_i - w^{(t)}\|$, the distance from the winner to the farthest voter, and the \emph{supporter centroid radius} $S_t = \max_j \|c_j - s_j^{(t)}\|$, the largest gap between any candidate and their support base. We show that $R_t$ controls a one-step contraction bound on voter disagreement and $S_t$ plays the analogous role for candidate dispersion, and that these two objectives are in tension. Rules that reduce $R_t$ tend to increase $S_t$, and vice versa. A winner close to the voter median does not resolve the tension, since proximity to the median and proximity to the Chebyshev center are different objectives. We use this framing to organize a simulation study across seven standard electoral rules and one convex-combination benchmark, comprising 1000+ runs across diverse electorate profiles, voter mechanisms, and camp-balance settings. The empirical results confirm the theoretical tradeoff: winner-take-all rules achieve small $S_t$ at the cost of large $R_t$ and weaker voter depolarization, while convex-combination rules reverse this. An oracle comparison further shows that minimizing $R_t$ per step and minimizing voter disagreement per step are distinct objectives with different long-run consequences for both voter and candidate dynamics.
Gabriele Farina, Juan Carlos Perdomo
We give a Gordon-Greenwald-Marks (GGM) style black-box reduction from online learning to online multicalibration. Concretely, we show that to achieve high-dimensional multicalibration with respect to a class of functions H, it suffices to combine any no-regret learner over H with an expected variational inequality (EVI) solver. We also prove a converse statement showing that efficient multicalibration implies efficient EVI solving, highlighting how EVIs in multicalibration mirror the role of fixed points in the GGM result for $Φ$-regret. This first set of results resolves the main open question in Garg, Jung, Reingold, and Roth (SODA '24), showing that oracle-efficient online multicalibration with $\sqrt{T}$-type guarantees is possible in full generality. Furthermore, our GGM-style reduction unifies the analyses of existing online multicalibration algorithms, enables new algorithms for challenging environments with delayed observations or censored outcomes, and yields the first efficient black-box reduction between online learning and multiclass omniprediction. Our second main result is a fine-grained reduction from high-dimensional online multicalibration to (contextual) $Φ$-regret minimization. Together with our first result, this establishes a new route from external regret to Phi-regret that bypasses sophisticated fixed-point or semi-separation machinery, dramatically simplifies a result of Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25) while improving rates, and yields new algorithms that are robust to richer deviation classes, such as those belonging to any reproducing kernel Hilbert space.
Itai Zilberstein, Ratip Emin Berker, George Li, Ruben Martins
In an election where $n$ voters rank $m$ candidates, a Condorcet winning set is a committee of $k$ candidates such that for any outside candidate, a majority of voters prefer some committee member. Condorcet's paradox shows that some elections admit no Condorcet winning sets with a single candidate (i.e., $k=1$), and the same can be shown for $k=2$. On the other hand, recent work proves that a set of size $k=5$ exists for every election. This leaves an important theoretical gap between the best known lower bound $(k\geq 3)$ and upper bound $(k \leq 5)$ for the number of candidates needed to guarantee existence. We aim to close the gap between the existence guarantees and impossibility results for Condorcet winning sets. We explore an automated reasoning approach to tighten these bounds. We design a mixed-integer linear program (MILP) to search for elections that would serve as counter-examples to conjectured bounds. We employ a number of optimizations, such as symmetry breaking, subsampling, and constraint generation, to enhance the search and model effectively infinite electorates. Furthermore, we analyze the dual of the linear programming relaxation as a path towards obtaining a new upper bound. Despite extensive search on moderate-sized elections, we fail to find any election requiring a committee larger than size 3. Motivated by our experimental results in this direction, we simplify the dual linear program and formulate a conjecture which, if true, implies that a winning set of size 4 always exists. Our automated reasoning results provide strong empirical evidence that the Condorcet dimension of any election may be smaller than currently known upper bounds, at least for small instances. We offer a general-purpose framework for searching elections in ranked voting and a new, concrete analytical path via duality toward proving that smaller committees suffice.
Shaun Hargreaves Heap, Mehmet Mars Seven
We study whether zero-sum decision rules, maximin and minimax, harm agents' interests in positive-sum strategic environments relative to Nash equilibrium behavior or, more generally, than best response behaviour. Contrary to an influential evolutionary view, we give illustrations where maximin serves an agent's interests better than Nash equilibrium behaviour. We also show that these illustration are not atypical or idiosyncratic because, in our main result, the class of such games where a maximin profile strictly Pareto dominates all Nash equilibria has the same cardinality as the class of games in which a Nash equilibrium strictly Pareto dominates all maximin profiles. Thus, neither behavior is generally superior. We further identify additional mechanisms favoring maximin over Nash equilibrium, including coordination failures under multiple equilibria, where maximin can outperform Nash play in realised-pay-off terms. A systematic analysis of strictly ordinal symmetric 3x3 games shows that these effects arise with non-trivial frequency. Our findings, therefore, suggest that the observed rise in zero-sum thinking in many rich countries, when associated with a maximin decision rule, will not be readily displaced through its generation of inferior pay-offs.
Siddharth Chandak, Ramanan Tamizholi, Nicholas Bambos
We establish finite-time last-iterate guarantees for vanilla stochastic gradient descent in co-coercive games under noisy feedback. This is a broad class of games that is more general than strongly monotone games, allows for multiple Nash equilibria, and includes examples such as quadratic games with negative semidefinite interaction matrices and potential games with smooth concave potentials. Prior work in this setting has relied on relative noise models, where the noise vanishes as iterates approach equilibrium, an assumption that is often unrealistic in practice. We work instead under a substantially more general noise model in which the second moment of the noise is allowed to scale affinely with the squared norm of the iterates, an assumption natural in learning with unbounded action spaces. Under this model, we prove a last-iterate bound of order $O(\log(t)/t^{1/3})$, the first such bound for co-coercive games under non-vanishing noise. We additionally establish almost sure convergence of the iterates to the set of Nash equilibria and derive time-average convergence guarantees.
Arka Majhi, Satish B. Agnihotri
POSHAN Abhiyan envisages capacity building of AWWs or frontline health workers through 21 training modules of ILA (Incremental Learning Approach), modularising the net learning content into smaller learning topics to help them perform their daily activities. It envisions building skilled AWWs, strengthening supervisory hierarchies, and improving coordination between AWWs (ICDS) services and health programs to achieve common goals such as increasing awareness, improving access to health and nutrition services, and reducing deaths and malnutrition. To better understand the contents of ILA literature, we conducted a content analysis by further breaking down the modules into content types such as facts, concepts, procedures, and principles. Then we framed learning objectives for teaching AWWs. We applied CDT (Component Display Theory by David Merrill) to map the contents with the desired learning objective, following the Specification of Objective chart. In this way, one can easily develop pedagogies from a new training literature. The challenges in framing learning objectives and pedagogies are: The AWWs do not have a (formal/scientific) nutrition and epidemiology background. Therefore, it is important to teach them through examples, familiar to them. AWWs are not evenly and structurally trained across districts. Training materials should be customized based on language, location, and prior knowledge. Delayed refresher courses render them underprepared for their jobs. To overcome these problems, we are developing an Android app based on gamified learning to provide refresher training to AWWs. Conducting content analysis, framing learning objectives, and developing pedagogical approaches will help conceptualize the gamified application.
Yu-Wen Chen, Can Kizilkale, Murat Arcak
It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point correction mechanism in the dual update. By appropriate design choices, TMD recovers the proximal point algorithm, extragradient methods, splitting methods, Brown-von Neumann-Nash dynamics, forward-backward-forward dynamics, and discounted mirror descent as special cases. Thus, we establish a unified perspective on these landmark algorithms and their convergence. Beyond unification, we leverage the TMD framework to correct an equilibrium misalignment in discounted mirror descent and to generalize its higher-order extension beyond interior solutions. Moreover, a key structural feature of TMD is the explicit decoupling of the mirror map from the target determination, which enables \emph{geometric ensembles}: multiple algorithms solve the same problem in parallel using distinct mirror maps, while sharing a common dual update. We show that such an ensemble rigorously reduces to a single TMD with a synthesized mirror map, and thus inherits these convergence guarantees.
Jackie Baek, Atanas Dinev, Thodoris Lykouris
We study online learning for new products on a platform that makes capacity-constrained assortment decisions on which products to offer. For a newly listed product, its quality is initially unknown, and quality information propagates through social learning: when a customer purchases a new product and leaves a review, its quality is revealed to both the platform and future customers. Since reviews require purchases, the platform must feature new products in the assortment ("explore") to generate reviews to learn about new products. Such exploration is costly because customer demand for new products is lower than for incumbent products. We characterize the optimal assortments for exploration to minimize regret, addressing two questions. (1) Should the platform offer a new product alone or alongside incumbent products? The former maximizes the purchase probability of the new product but yields lower short-term revenue. Despite the lower purchase probability, we show it is always optimal to pair the new product with the top incumbent products. (2) With multiple new products, should the platform explore them simultaneously or one at a time? We show that the optimal number of new products to explore simultaneously has a simple threshold structure: it increases with the "potential" of the new products and, surprisingly, does not depend on their individual purchase probabilities. We also show that two canonical bandit algorithms, UCB and Thompson Sampling, both fail in this setting for opposite reasons: UCB over-explores while Thompson Sampling under-explores. Our results provide structural insights on how platforms should learn about new products through assortment decisions.
Hannaneh Akrami, Alexander Mayorov, Kurt Mehlhorn, Shreyas Srinivas, Christoph Weidenbach
SAT solving has recently been proven effective in tackling open combinatorial problems. We contribute two additional results in the context of fair distribution of indivisible goods. Specifically, we demonstrate that EFX (envy-freeness up to any good) allocations always exist for three agents and seven goods, while we provide a counterexample for the case of $n \ge 3$ agents and $m \ge n + 5$ goods. An allocation is EFX if no agent would envy the allocation of any other agent if any single item were to be removed from the other agent's bundle of goods. Each agent's preferences are modeled by a monotone valuation function on all potential bundles. After analyzing theoretical aspects of the problem, we encode the negation of the EFX instances into SAT. Satisfiability of the respective SAT formula constitute a counter-example to EFX, unsatisfiability of the respective SAT formula implies that EFX holds. The theoretical foundations of the encoding are proven correct in LEAN. For the three agents and seven goods case, we obtained a proof of unsatisfiability using SPASS-SAT of size about 30 GB in about 30 hours. It was shown to be correct by DRAT-trim. In the case of three agents and eight goods, SPASS-SAT computed satisfiability indicating a counterexample in the form of three specific agent valuations in about 20 hours. It was verified by probing all possible bundle assignments; the verification takes seconds. The extension of the counterexample to $n \ge 4$ agents and $m \ge n + 5$ goods does not involve SAT-solving. This counterexample resolves, in the negative, one of the central questions in the theory of discrete fair division.
Junyi Yao, Zihao Zheng, Jiayu Long
Pairwise ranking systems based on Maximum Likelihood Estimation (MLE), such as the Bradley-Terry model, are widely used to aggregate preferences from pairwise comparisons. However, their robustness under strategic data manipulation remains insufficiently understood. In this paper, we study the vulnerability of MLE-based ranking systems to adversarial perturbations. We formulate the manipulation task as a constrained combinatorial optimization problem and propose an Adaptive Subset Selection Attack (ASSA) to efficiently identify high-impact perturbations. Experimental results on both synthetic data and real-world election datasets show that MLE-based rankings exhibit a sharp phase-transition behavior: beyond a small perturbation budget, a limited number of strategic voters can significantly alter the global ranking. In particular, our method consistently outperforms random and greedy baselines under constrained budgets. These findings reveal a fundamental sensitivity of MLE-based ranking mechanisms to structured perturbations and highlight the need for more robust aggregation methods in collective decision-making systems.
Davin Choo, Paul W. Goldberg, Nicholas Teh
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a lottery over options that clears all stakeholders' acceptability bars? We study a query model where the algorithm proposes lotteries and receives only binary accept/reject feedback. We give deterministic and randomized algorithms that either find a unanimously acceptable lottery or certify infeasibility; adaptivity can avoid eliciting many stakeholders' constraints, and randomization further reduces the expected elicitation cost relative to full elicitation. We complement these upper bounds with worst-case lower bounds (in particular, linear dependence on the number of stakeholders and logarithmic dependence on precision are unavoidable). Finally, we develop learning-augmented algorithms that exploit natural forms of advice (e.g., likely binding stakeholders or a promising lottery), improving query complexity when predictions are accurate while preserving worst-case guarantees.
Quentin Cohen-Solal
In this article, we generalize Unbounded Minimax, the state-of-the-art search algorithm for zero sums two-player games with perfect information to the framework of multiplayer games with perfect information. We experimentally show that this generalized algorithm also achieves better performance than the main multiplayer search algorithms.
Terry R. Payne, Luke Riley
A key challenge in distributed coalition formation within characteristic function games is determining how to allocate the calculation of coalition values across a set of agents. The number of possible coalitions grows exponentially with the number of agents, and existing distributed approaches may produce uneven or redundant allocations, or assign coalitions to agents that are not themselves members. In this article, we present the \emph{Necklace-based Distributed Coalition Algorithm} (N-DCA), a communication-free algorithm in which each agent independently determines its own coalition value calculation allocation using only its identifier and the total number of agents. The approach builds on the notion of Increment Arrays (IAs), for which we develop a complete mathematical framework: equivalence classes under circular shifts, periodic IAs, and a rotated designation scheme with formal load-balance guarantees (tight bounds). We establish a bijection between canonical representative IAs and two-colour combinatorial necklaces, enabling the use of efficient necklace generation algorithms to enumerate allocations in constant amortised time. N-DCA is, to the best of our knowledge, the only distributed coalition value calculation algorithm for unrestricted characteristic function games to provably satisfy five desirable properties: no inter-agent communication, equitable allocation, no redundancy, balanced load, and self-interest. An empirical evaluation against DCVC (Rahwan and Jennings 2007) demonstrates that, although DCVC is faster by a constant factor, this difference becomes negligible under realistic characteristic-function evaluation costs, while N-DCA offers advantages in working memory, scalability, and the self-interest guarantee.