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arXiv2026

Learning Fair Allocation of Indivisible Items from Limited Feedback

We study a setting in which an algorithm must output a fair allocation of indivisible items while "learning on the job". More specifically, the algorithm is to output an allocation satisfying EF1, PROP1, or similar fairness notions; however, the algorithm initially has no information about the agents' valuations, and can only learn about them by (repeatedly) proposing an allocation, and obtaining feedback about a fairness violation in the allocation. Importantly, the observed fairness violation may be adversarially chosen. The algorithm's goal is to converge to a fair allocation in rounds polynomial in the number of agents and items, ideally with only polynomial computation. We prove two main results: first, when the valuations are additive, then even for mixed items (goods and chores), an allocation satisfying EF1 or PROP1 can be found in polynomial time using the corresponding feedback. These results are instantiations of a more general framework which maintains a polytope of candidate valuations consistent with all past feedback. The algorithm repeatedly constructs putative valuations and uses them to propose allocations; the observed violations then define separating hyperplanes, allowing the algorithm to emulate the ellipsoid method. When the valuations are monotone, we present an algorithm which is guaranteed to find an EF1 allocation in polynomially many iterations; however, its internal calculations are not guaranteed to be polynomial. The algorithm again maintains putative valuations, and only considers allocations in which each agent obtains an interval plus one additional item with respect to an arbitrary ordering of the items. It is known that such an EF1 allocation always exists; however, because the existence proof is non-constructive, the internal step of constructing an allocation from the putative valuations is not known to take polynomial time.

cs.GT↗

arXiv2026

Refundable Deposits: How to Restore Cooperation in Finitely Repeated Games

While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have a much smaller and often inefficient one. We show how to enlarge this set using deposits: in each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed, the only commitment required being that of the intermediary to a refund rule fixed before play begins. The mechanism sustains payoff profiles more efficient than those of the standard equilibria, without altering the underlying game and without transfers between players. We demonstrate it on the prisoner's dilemma, a congestion game, and a public goods game, all settings where cooperation cannot emerge in the standard finitely repeated version. We also apply it to a dynamic common-pool resource, suggesting that the construction extends beyond repeated stage-games.

cs.GT↗

arXiv2026

Approval-Based Apportionment: Like Portioning, Approximately like Committee Voting

We study approval-based apportionment, a variant of committee elections in which candidates ("parties") can be selected several times. We show that the proportionality axioms EJR, EJR+, and FJR coincide, and so do PJR, PJR+, and FPJR; that Lindahl priceability, an axiom implying core stability, is equivalent to a notion of approximate optimality with respect to the proportional approval voting (PAV) score; and that locally PAV-optimal committees are priceable. Approval-based apportionment (where a candidate receives an integer number of seats) lies between committee elections (zero or one seat) and portioning (a fractional number of seats). We formally connect portioning and apportionment by giving a construction that lifts axioms from apportionment to portioning and preserves implications between them. Several of our new implications between apportionment axioms are natural from a portioning perspective, leading us to believe that apportionment sits closer to portioning than to committee elections. None of them holds in committee elections, but several extend approximately, which makes apportionment a fruitful setting for conjecturing approximate relationships in approval-based committee elections.

cs.GT↗

arXiv2026

Condorcet-Winning Sets and Peer Selection in Planar Metric Elections

In ranked-choice voting, a Condorcet-winning set is a group of candidates for which no outside candidate is preferred to every member of the group by a majority of voters. We study Condorcet-winning sets in planar metric elections, where voters rank candidates according to their distance under a given norm. We formulate general metric elections, peer selection, and the one-round Voronoi game as instances of a two-player Stackelberg game and place these problems in a common hierarchy. We also introduce a new variant, which we call strong peer selection. Our main result concerns peer selection under the $\ell_1$ and $\ell_\infty$ norms. We prove that every planar instance admits a Condorcet-winning set of size at most three, even under strong peer selection. This follows from a new result for strong rectangular $\varepsilon$-nets. We show that, for every set of points in the plane, one can choose at most three input points that intersect every axis-parallel rectangle containing more than half of the points, improving the previous threshold of $9 / 16$ due to Ashok et al. Under the $\ell_2$ norm, we prove that every planar metric election admits a Condorcet-winning set of size at most four, improving on the general bound of five due to Song et al. Finally, we give new norm-independent bounds for the one-round Voronoi game.

cs.GT↗

arXiv2026

Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games

We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted case, we show that, under a sufficiently large discount rate, finite-horizon MFGs admit a horizon-independent contraction condition, which also coincides with the corresponding infinite-horizon non-stationary contraction condition. As a byproduct, we obtain an explicit convergence rate between finite- and infinite-horizon mean-field equilibria. For each finite horizon, we further derive a refined contraction criterion from the spectral radius of a positive operator that majorizes the propagation of policy errors, and show that its large-horizon limit agrees with the horizon-independent contraction factor. Finally, we provide an explicit error bound between discounted and undiscounted finite-horizon regularized equilibria.

cs.GT↗

arXiv2026

Truth Revelation, Information Hiding, or Misinformation: Characterization of Equilibrium Outcomes in Signaling Games

In signaling games where a sender and a receiver have misaligned criteria, equilibrium behavior may lead to fully revealing, quantized, or randomized policies. Notably, the first arises in statistical decision theory and classical communication theoretic problems involving a fully aligned sensor and receiver, the second arises in Nash theoretic simultaneous signaling games, and the last may appear in Stackelberg type (leader-follower) Bayesian signaling games. In this paper, we investigate the Bayesian persuasion problem involving a receiver that tries to estimate the source. We show that for certain payoff structures, the equilibrium solution is such that a source observation is mapped to distinct messages with nonzero probabilities. More specifically, we completely characterize conditions under which the sender requires randomization for the Bayesian persuasion problem involving general sources with finite cardinality. In particular, regardless of whether the equilibrium solution under a deterministic policy restriction is fully revealing, quantized or noninformative, there exists a randomized sender policy that improves the sender's payoff under certain conditions characterized in the paper. Moreover, we provide an algorithmic procedure to obtain the Bayesian persuasion solution, where the algorithm compares the payoffs with finitely many posterior probability combinations. We also consider fully aligned and completely misaligned payoff structures, where the solutions respectively involve a fully revealing sender and a noninformative sender. Then, we unify these results by proving that if the sender's expected payoff with respect to posterior distributions is continuous, then the equilibrium solution involves either a fully revealing sender or a noninformative sender.

cs.GT↗

arXiv2026

Absence of critical scaling in the Schelling segregation model

We find no evidence of critical scaling in the Schelling segregation model, in either the Moore neighborhood or its dense-spectrum extension to Chebyshev radii up to $r_0 = 6$ ($k = 168$ neighbors). On periodic grids up to $L = 320$ with 50 trials per point (> 12,500 runs), every finite-size scaling diagnostic in the Moore baseline fails: the per-$L$ $T_c$ does not drift, Var$(S) \sim L^{-2.02 \pm 0.09}$ matches trivial averaging, $γ/ν\approx 0$, and the scaling collapse never reaches a finite optimum. The 8-site Moore neighborhood restricts satisfaction to ratios $j/k$ with $k \leq 8$, giving $S(T)$ a staircase structure with 23 rational thresholds; discreteness alone does not forbid criticality (cf. the Ising model), but the scaling evidence rules it out empirically. A branching-ratio calculation predicts subcritical cascades of mean size $1/(1-R)$ and is validated by perturbation experiments to within 15%; the multiscalar dissimilarity length stays finite across the transition. The dense-spectrum extension strengthens the negative verdict: across $r_0 \in {3,4,5,6}$ on $L \in {40,80,160}$ the Binder cumulant has no $L$-curve crossing and the per-$L$ $T_c$ drift is monotonic and unsaturated; at $r_0 = 4$, extending to $L = 320$ gives $α= -2.70$, below the critical boundary $α= -2$, dissolving an apparent $α= +0.81$ signal visible only on $L \in {40,80}$. The mechanism is the absence of long-range correlation in equilibrium plus deterministic high-$k$ dynamics, not the staircase structure. With a Beta-distributed heterogeneous tolerance, the intolerant tail drives segregation even at moderate population-average tolerance. The staircase theorem and cascade mechanism together account for the Schelling transition without invoking critical phenomena.

cond-mat.stat-mech↗

arXiv2026

Large Language Models as Strategic Bidding Agents in P2P Energy Trading Markets

Peer-to-peer (P2P) energy trading markets rely on double auction mechanisms to match prosumers and consumers in smart grid distribution networks. However, the strategic behavior of bidding agents in such markets remains not fully explored, particularly in repeated settings with bounded rationality. This paper proposes a novel framework that integrates large language models (LLMs) as reasoning-driven bidding agents in repeated P2P energy double auctions. We compare the performance of three bidding strategies: random bidding, an $\varepsilon$-greedy multi-armed bandit (MAB) approach, and an LLM-based strategy. Simulation results show that the LLM-based strategy achieves superior cleared trading volume over the first episodes compared to $\varepsilon$-greedy MAB and random bidding baselines, eliminating the exploration burn-in period that statistical learning algorithms inherently require before converging to productive price arms. Importantly, when tested in an environment different from the one used during learning, the performance of the $\varepsilon$-greedy strategy drops significantly, while that of the LLM-based bidding strategy continue to achieve higher surplus and successful trades. Nevertheless, the LLM's advanced contextual reasoning also gives rise to an important market dynamic. In a homogeneous population of LLM agents, sellers increasingly exploit buyers' rational outside options to drive clearing prices above the Nash equilibrium, resulting in a progressively more asymmetric allocation of surplus in favor of sellers that does not converge within the observed time horizon.

cs.GT↗

arXiv2026

Three-sided mobility-energy market design as a multiperiod stochastic assignment game

As mobility service providers (MSPs) and energy providers (EPs) expand electric vehicle ecosystems, models are needed to understand their interactions within a three-sided market. Existing frameworks often overlook the temporal interdependencies between mobility and charging demands. We address this gap by proposing a bilevel problem as an assignment game overseen by a market regulator. The upper level optimizes service pricing to maximize platform profitability. The lower level models a multi-stakeholder equilibrium using a scalable, link-based Perturbed Utility Route Choice (PURC) framework. The evaluation time frame is divided into discrete intervals, capturing the temporal lag between mobility and charging demand via an empirical affine function. We solve the model by chronologically decomposing the lower level into interacting mobility service and recharge subnetworks. Numerical experiments on the expanded Nguyen-Dupuis network reveal several key insights. First, a critical charging capacity threshold exists; operating below it forces a severe reduction in the deployable fleet and creates localized transit deserts. Second, modeling endogenous operating costs reveals a concave profit trajectory, demonstrating that total profit maximizes at a specific fleet size just before market saturation. Third, optimal dynamic pricing operates within a narrow range, where peak pricing acts as a steady revenue driver and off-peak pricing serves as a highly sensitive operational buffer. These findings provide actionable strategies for coordinating fleet sizing and charging infrastructure deployment.

cs.GT↗

arXiv2026

COAST: Congestion-Aware Start-Time Recommendations for Carbon-Aware HPC Jobs

High-performance computing (HPC) workloads consume substantial amounts of electricity, and their carbon emissions vary over time with the carbon intensity of grid electricity. However, uncoordinated shifting of carbon-aware HPC jobs toward low-carbon periods can concentrate recommended start times in the same time slots, creating congestion and eroding the resulting carbon benefits. This paper proposes COAST, a congestion-aware start-time recommendation mechanism that coordinates HPC jobs by balancing carbon savings against additional job delay and congestion in recommended start-time slots. COAST formulates each decision batch as an exact potential game, enabling best-response updates to converge to stable start-time recommendations. Under an idealized realization model that assumes each job can start at its recommended time, we conduct trace-driven simulations using public HPC energy data and historical grid carbon-intensity traces. The results show that COAST reduces estimated carbon emissions by 15.4\% with 1.5 hours of additional average start delay. Compared with carbon-greedy start-time recommendations, COAST reduces peak time-slot load by 23.8\% while preserving 93\% of the achievable carbon savings. These results quantify the potential benefits of congestion-aware start-time coordination for flexible, carbon-aware HPC jobs.

cs.DC↗