Papers

In metric social choice, voters rank candidates by their distances in an unknown metric space. A voting rule uses these rankings to select a candidate or a lottery over candidates, aiming to minimize the average distance to voters. Distortion measures the worst-case approximation ratio. While the best distortion of deterministic rules is $3$, prior work pins down the best distortion of randomized rules to $[2.1126,2.5]$. We improve the upper bound to $2.1441$, closing over $90\%$ of this gap. The proof introduces random-size stable lotteries, proves their existence, and derives the new bound through a potential argument. All the proofs were obtained using GPT-5.6-Sol with significant guidance from the author, who verified them and simplified the exposition.

Decision-time equilibrium search carried poker to superhuman play, but it has so far relied on tractable subgames: a handful of actions per decision, chance confined to card deals, one player moving at a time. Competitive Pokémon in its official doubles format (VGC) breaks all three assumptions at once. Both players act simultaneously from joint menus in the hundreds, each joint action resolves to hundreds of stochastic outcomes, and the opponent's reserves and stat allocations are hidden. No prior Pokémon agent performs equilibrium search, and whether it scales to this regime was open; we show that it does, and report what it took. PokaiEngine, our Rust battle engine, enumerates a joint action's full weighted outcome distribution in one pass, at ${\sim}99\%$ parity with Pokémon Showdown and a fraction of the cost of sampling it. PokaiTrainer adapts Student of Games to this scale and trains it by self-play over hundreds of human teams. Each decision is solved by counterfactual regret minimization as a Bayesian matrix game over public belief states, subgames grow under an explicit compute budget, and value targets are harvested from the interior of every solve and grounded by realized outcomes. The strength is in the search. The network's policy alone loses even to a shallow heuristic search. PokaiTrainer is, to our knowledge, the first VGC agent rated on the live Showdown ladder. Under open team sheets it wins 59% of 150 best-of-three sets against a human field averaging ${\sim}1320$ Elo, holds a 1350-1400 Elo band, and at its peak reached 1492 Elo, entering the format's top 500.

This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ “centers” from a metric space that fairly represent a set of agents who also lie in the metric space. Specifically, we focus on finding a clustering satisfying a fairness property known as the Droop core. In the practical special case in which the set of feasible center locations contains every agent location, the previous best-known result guaranteed a $(1 + \sqrt{2})$-approximation of the Droop core, while the best-known lower bound was $2$. In this paper, we show that this lower bound is tight and that a clustering in the $2$-Droop core always exists. Further, we show that such a clustering can be achieved by only selecting centers from locations in the metric space where an agent resides. We establish this using Scarf's theorem guaranteeing a nonempty core for balanced non-transferable utility games. This result has several interesting corollaries. Most notably, it resolves the $\beta$-plurality problem of Aronov et al. [2021] for general metric spaces. The main result of this paper was generated by $\mathtt{ChatGPT}$-$\mathtt{5.6}$-$\mathtt{Sol}$ through a series of interactions with the authors. The authors of this paper verified the generated proof and rewrote it for clarity.

We study active elicitation of agent preferences for collectively choosing among $m$ alternatives using prominent voting rules. We focus on the next-best query model, in which an agent responds to a query by revealing their next favorite alternative, and measure the competitive ratio, which is the worst-case ratio between the number of queries made by the active elicitation algorithm and the minimum number of queries needed to reveal the winning alternative(s) in hindsight. We show that sublinear competitive ratios are achievable for many positional scoring rules, whereas every Condorcet-consistent rule has competitive ratio linear in $m$. For Borda count, we develop two complementary techniques: level-wise pruning, whose analysis extends to general concave scoring rules, and multi-scale score thresholding, which gives an $O(\sqrt m)$ worst-case guarantee for Borda. We also demonstrate strong empirical performance of level-wise pruning on real data.

This paper introduces an innovative and bias-free variant of a three-player auction bridge, specifically designed to address structural limitations found in traditional formats. In a standard auction bridge, the partner of the winning bidder often plays a passive role, possessing minimal influence over the outcome once the bidding phase concludes. To rectify this, our proposed three-player model redistributes strategic agency, emphasising a framework where No Trump strategies statistically outperform specific trump card selections. The core of this research is a rule-based dual-algorithm framework. First, we implement an iterative bidding algorithm that allows players to calibrate their bids dynamically based on evolving hand strengths. Second, we introduce a predictive iterative algorithm designed to calculate the expected number of tricks a player will secure before the lead card is played. Unlike traditional approaches that rely on backtracking or high-complexity dynamic programming, our iterative method significantly reduces time complexity. This efficiency is crucial for real-time gameplay, enabling players to perform complex probability assessments instantly without computational lag. To validate the model, a simulation was conducted on a dataset of 1,00,000 game instances. This large-scale analysis allowed for a precise comparison between initial bidding, outcomes, and overall bidding accuracy. The empirical results demonstrate that our algorithm not only enhances the balance and fairness of the auction bridge but also exhibits high reliability in predictive accuracy. Beyond the realm of card games. By modelling uncertainty and strategic competition, the algorithm offers valuable insights into risk management and decision-making in volatile market environments.

We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Csóka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy.

This article introduces peer $k$-oversight, a property of sequential collective decision mechanisms requiring at least $k$ agents to be responsible for every harmful outcome. It is shown that whenever $k$-oversight can be achieved by redistributing control over the decisions in a mechanism, it can be achieved using just $k$ agents. A polynomial-time algorithm is also presented that determines whether such a redistribution exists and, when it does, constructs one. These results establish peer oversight as a tractable design principle for multiagent decision-making systems.

Ensuring the security of complex systems involves the strategic allocation of defensive resources to prevent various types of attacks from succeeding. A defender often has multiple types of defensive assets at its disposal, where it must decide how to optimally deploy their heterogeneous capabilities across different attack types. In this paper, we formulate a multi-resource allocation problem in the form of a General Lotto game where a defender possesses various types of resources. A feature that we introduce is that their individual effectiveness against different types of attacks is characterized by a network weight matrix. In our analysis, we derive upper and lower bounds on the performance of the defender, and provide numerical evidence suggesting that they are tight. For the case of two attack types, we analytically prove that the bounds coincide, establishing an exact equilibrium characterization. We then numerically compare our proposed networked multi-resource architecture to an independent-defense benchmark from the existing literature. These results highlight fundamental and tractable structures underlying multi-attack-type defense problems.

The VCG family and the AGV mechanism are two classical approaches to efficient implementation in the static social choice problem. In 2024, Csóka et al. showed that AGV has critical weaknesses. In contrast, the transferable-utility Guaranteed Utility Mechanism (TU-GUM) retains all the standard desirable properties of AGV while adding further ones, including collusion-proofness, because it implements efficiency in Guaranteed Utility Equilibrium. TU-GUM also applies to a more general dynamic setting with multiple extensions. Moreover, TU-GUM is a special case of an even more general and robust mechanism that combines contingent first-price tendering with the coordinated execution of dynamic stochastic multi-agent projects through a surprisingly simple rule. This paper summarizes and connects existing results from a different perspective, with some minor new observations.

We consider two-player GR(1) games on graphs, where the system player Eve must satisfy \[ \Box\Diamond A_1\land\cdots\land\Box\Diamond A_m \;\implies\; \Box\Diamond G_1\land\cdots\land\Box\Diamond G_n \] against the environment player Adam. Here $A_1,\ldots,A_m$ are assumptions on the environment, $G_1,\ldots,G_n$ are guarantees the system must provide, and $\Box\Diamond S$ denotes “always eventually $S$”. Traditional static strategies are overly conservative: they may actively violate assumptions to trivially satisfy the implication, or abandon all guarantees when any assumption is violated. Existing methods to prevent such behaviors incur doubly exponential blowup. We introduce an adaptive framework treating Adam as a non-adversarial agent with unknown objectives. Eve monitors which assumptions Adam actually meets and adapts her strategy at runtime to maximize satisfied guarantees. Central to our approach is a novel algorithm for monitoring liveness properties $\Box\Diamond S$, enabling Eve to maintain real-time likelihood estimates of which assumptions will be fulfilled. Eve pre-computes strategies optimal for different assumption subsets, deploying a probability distribution over them that dynamically adjusts based on monitor outputs. We prove that when assumptions are violated, Eve's randomized adaptive strategy converges asymptotically to the deterministic strategy maximizing guarantees. A prototype demonstrates effectiveness and superior computational performance compared to the state of the art.

In applications, it is often required to test objects or people to determine their qualities in terms of certain metrics. However, besides being naturally noisy, the test results can be corrupted by adversarial behaviors of objects or people being tested (test takers). For example, dishonest test takers can cheat in the exams to distort the test results. With the development of AI technologies, such distortions driven by cheating using AI technologies are becoming more commonplace and severe. In this paper, we propose optimal testing strategies which can still recover needed test results even if there are cheaters polluting the results. The proposed testing strategies will optimally re-test selected group of test takers using different testing security measures. We determine the optimal testing strategies using a dynamic programming method.

Approval voting is a simple and well-regarded voting rule: voters submit approval ballots (subsets of the candidates) and the candidate receiving the most approvals wins. One major limitation of approval voting is that it is not clear which candidates voters should approve if they have an underlying strict order over the candidates. In this paper, we initiate the study of approval voting under a simple kind of information: plurality polls. That is, we assume that for each candidate we know the share of voters who rank this candidate as their top choice. Using these plurality polls, we suggest a simple protocol parameterized by a fraction $k \in (0,1)$: every voter should approve the smallest prefix of their preference list containing the first choices of at least a fraction $k$ of the voters. We evaluate this protocol via the framework of metric distortion and show that for the optimal choice of $k$, this rule achieves a metric distortion of $2 + \sqrt{5} \simeq 4.236$. The proof techniques we use for this statement also show that the Bucklin voting rule has a metric distortion of at most $5$. Finally, we evaluate the robustness of our protocol to noise and show that the upper bounds obtained for our protocol are tight.

Automated bidding (autobidding) is a core component of modern online advertising systems. Within this component, advertisers delegate sequential bid decisions to algorithms that must maximize campaign value while adhering to constraints such as a limited budget and a target cost-per-click (CPC). One of the approaches to resolve the autobidding problem is to formulate it as a Markov decision process and use reinforcement learning (RL) to train a bid generation function. The standard RL framework is actor-critic, which consists of an actor network that generates actions and a critic network that estimates the value of those actions. In our setting, the action is typically a bid or related pacing multiplier, and the value is the expected return from the auction given the bid. However, the alternating training of actor-critic RL models leads to instability and reduced robustness to noise. To address these issues, we adapt the Group Relative Policy Optimization (GRPO) framework to the autobidding setting. This framework is a critic-free policy-gradient method originally developed for large language model post-training, where the ground-truth target is unknown. The autobidding setting shares this property, since the optimal bid is unknown in advance. Moreover, GRPO in the LLM domain is used to fine-tune the pre-trained model, and we use the same technique to enhance the performance of the strong heuristic baseline. We empirically compare Autobidding GRPO with actor-critic models, simple heuristics, and controller-based methods on the BAT, iPinYou, and AuctionNet benchmarks. Extensive experiments show that Autobidding GRPO consistently outperforms baselines in clicks and is the best or second-best method in conversion volume.

As large language models and increasingly capable AI agents are deployed in high-risk settings, aligning them with complex human values has become a central challenge. Existing alignment methods, while effective in improving helpfulness, harmlessness, and controllability, often struggle to capture real-world preferences that are context-dependent, non-transitive, and shaped by dynamic multi-party interactions. This survey reviews AI alignment through a game-theoretic lens. Specifically, it organizes recent progress around key game-theoretic elements and synthesizes the literature along three challenges: preference diversity, alignment priority, and temporal dynamics. This perspective clarifies where current alignment methods genuinely benefit from game-theoretic analysis, where the framework is looser, and what challenges remain in building robust, adaptive, and verifiable AI systems.

Coordination is a desirable feature in multi-agent systems, ranging from robotic swarms to socioeconomic networks. This paper is concerned with promoting coordination among heterogeneous agents, e.g., machines and humans, interacting in a stag-hunt game. In our model the agents exhibit bounded rationality at different levels, which leads to uncertainty and a propensity for errors during learning and decision-making processes. This paper addresses the problem of designing a network topology that maximizes a global metric of coordination under such constraints. While optimizing over the discrete space of finite graphs is generally computationally intractable, we employ a mean-field approach to lift the problem into the space of graphons. Within this framework, we analyze agents following a logit learning dynamics. Using calculus of variations, we show that for systems with a bimodal rationality profile, it suffices to search for optimal graphons in the ensemble of stochastic block models. We then propose a water-filling algorithm to find a locally optimal graphon. Finite graphs can then be sampled from the optimized graphon, bypassing the inherent combinatorial complexities of discrete graph optimization.

Tile-matching puzzle games serve hundreds of millions of players, yet the content-generation algorithms that decide which pieces to present at each turn remain proprietary, and no open platform exists for studying adaptive difficulty in this genre. We present an adaptive tile-matching platform whose central algorithmic contribution is a dual-track content-generation architecture: a deterministic rule-based generator that is always available, and an optional learned generator, both subject to a common verification gate that establishes, by exhaustive sequential-placement search, that every delivered piece set is fully placeable so the learned track can never degrade the constructive-feasibility guarantee of the rule track. A self-play reinforcement-learning placement agent, supervised by auxiliary tasks that expose per-shape placeability to shared representations, is used to diagnose the game's dominant failure mode: at high board fill, long-bar pieces lose the majority of their legal placements. Across 234,000+ self-play episodes the agent reaches a 35.6% win rate (median score 4,200), and controlled simulation shows that at board fill rates of 70–75%, 33–56% of long-bar pieces have no legal placement, while spawn difficulty distributions are statistically indistinguishable between won and lost games—evidence that board-state degeneration, not content difficulty, drives late-game failure. Head-to-head ablations show that per-shape placeability supervision—not aggregate difficulty features—drives the representation gain, and a 14-day online gray rollout (48,000 players; sample-ratio verified, CUPED-adjusted) lifts day-1 retention by 1.8 percentage points and session duration by 7% over the rule track alone, quantifying the neural track's asymmetric upside in live play.

Connectivity can turn separate contributions into a public good that benefits participants and nonparticipants alike. Yet only participants pay for it, and each can avoid her charge by withdrawing while enjoying whatever public output survives. How do network connections constrain who can or must pay, and how large a cost can the group bear? We study a participation game in which public output equals the size of the largest connected group of active players, whose members divide a fixed operating cost. The output a participant destroys by withdrawing is her withdrawal responsibility and bounds her payment. These bounds determine the group's cost-bearing capacity and, whenever the group can be kept active, which participants must pay. We prove that among connected networks with at least five players, the path uniquely maximizes the cost-bearing capacity of a group, yet minimizes the expected surviving output after a uniformly selected participant withdraws. As the group grows, the ratio of maximal capacity to gross social benefit under full participation converges to one quarter. Fragility can therefore strengthen voluntary finance, but even the most financeable network cannot close the gap between the value it creates and what its participants will pay to sustain it.

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.

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.

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.

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.

In this paper, we consider Robbins' problem, which is a full information variant of the well-known secretary selection problem. In this version of the problem, the goal is to minimize the expected rank of the selected candidate among $n$ that are interviewed sequentially, and a decision to select or not the $m^{th}$ candidate needs to be taken right after the interview (so without seeing the last $n-m$ candidates and without recall). We first show how to model instances of Robbins' problem as infinite Markov Decision Processes (MDPs). Then we propose several finite-state abstractions of these MDPs that allow us to approximate the value of the problem for fixed $n$. While it is known that the full memory of past candidates' values is necessary for optimal expected rank minimization, making the analysis of the problem challenging, we highlight simple memory structures that are sufficient for obtaining near-optimal selection strategies. Additionally, we provide approximate values for Robbins' problem for numbers of candidates $n$ up to 100 for which no good approximations were previously known (the exact value is only known for instances where $n \leq 4$ and numerical approximations were for small values of $n$ not exceeding one digit), for all $n : 5 \leq n \leq 100$, we give better approximation than what was previously known.

Generative AI is transforming how people access information, challenging traditional advertising mechanisms built around predefined slots. Towards generation-native advertising, we propose the Latent Advertiser Mixture Auction (LAMA), a token-level advertising mechanism that embeds advertiser influence directly into the generation process. Advertisers report local continuation values that induce advertiser-specific next-token policies, from which the platform decodes through a latent mixture while updating an allocation posterior. We show that LAMA satisfies Markov DSIC and IR, and achieves near-optimal KL-regularized welfare. We further develop a learning-based implementation that reconstructs the required reports online from learned local advantages and root values. Proof-of-concept experiments on real-world commercial-search query splits show that LAMA improves platform welfare and revenue while maintaining user-facing response quality, providing initial evidence for the feasibility of generation-native advertising.

We study pursuit-evasion games on graphs with a single pursuer and an invisible evader. The pursuer may assign integer travel times to the edges of the graph and specify a finite sequence of vertices to query, one per time step. The evader then chooses a walk over the same time horizon, aiming to elude all queries. With unit travel times, the setting in which the evader must move at every time step is known as the hunter and rabbit game, while the variant in which the evader can wait at a vertex can be phrased as a firefighting game: the vertices of a burning graph must be extinguished, and any vertex left burning reignites its neighbors. For both settings, we show that the power to choose travel times allows a single pursuer to succeed in polynomial time on any graph. This contrasts with unweighted graphs, where the number of hunters or firefighters needed can grow linearly in the number of vertices. If the evader, in addition to waiting, may start at an earlier time unknown to the pursuer, we show that the pursuer still wins on any graph given exponential time.

In the study of Nash equilibria of finite-player games, one often seeks equilibria that are compatible with predetermined constraints, either determined by the players or by an external agent. We discuss the algebraic loci, called Nash loci, of games whose Nash equilibrium scheme intersects a fixed algebraic variety in a product of projective spaces. We determine their dimensions and multidegrees in multiprojective space, and their equations for two-player games and for small multiple-player games. The multilinear equations defining the Nash equilibrium scheme allow us to describe Nash loci in the language of Grassmannians and Plücker coordinates. Motivated by this fact, we relate Nash loci to multigraded associated varieties, which are subvarieties in products of Grassmannians that generalize the multigraded Cayley-Chow hypersurfaces of Osserman and Trager.

As electricity market participants increasingly adopt learning-based agents for their bidding strategies, electricity markets are becoming algorithmic. Evidence from algorithmic markets in other domains shows that tacit collusion can arise purely through independent learning. Moreover, electricity markets are typically oligopolistic and feature repeated interaction among a small number of participants, making them structurally susceptible to non-competitive behavior. In the face of these observations, this paper investigates the hypothesis that tacit collusion may emerge in electricity markets where participants' actions are controlled by autonomous learning-based algorithms. We model strategic bidding as a repeated game with imperfect public monitoring, and model the participants' emergent behavior using multi-agent reinforcement learning. We propose a multi-dimensional set of criteria (going beyond profit comparisons against Nash equilibria) to assess whether the resulting behavior constitutes tacit collusion. Our experimental results showcase that such a danger is realistic for electricity markets: there are cases where agents do learn to sustain supra-competitive outcomes that are supportive of tacit collusion indicators, even though the agents were never instructed to collude.

We study metric distortion in randomized social choice under bounded randomness: on every preference profile, the voting rule must deterministically identify a multiset of $K$ candidates and then select a uniformly random entry. Previous work showed that this restricted model can beat the optimal deterministic distortion of $3$. We show that it can in fact approach the current best unrestricted upper benchmark of $5/2$. For every integer $K\ge 802$, there exists a bounded-randomness rule with distortion at most $\frac{5}{2} +3\left(\frac{\pi}{8K}\right)^{1/3} +2\sqrt{\frac{\pi}{8K}}$. Consequently, $O(\varepsilon^{-3})$ entries suffice for distortion $5/2+\varepsilon$, independently of the numbers of voters and candidates. We also show that $164$ entries already achieve distortion strictly below $3$, giving $2\le N^\star\le 164$ for the minimum list size needed to break the deterministic barrier. Our main technical contribution is a dimension-free compression theorem: if a lottery has distortion at most $\rho$ and every candidate in its support has deterministic distortion at most $H$, then it admits a uniform $K$-entry approximation with distortion at most $\rho+(H+1)\sqrt{\pi/(8K)}$. Thus, lotteries whose possible outcomes are already well behaved incur only $O(K^{-1/2})$ compression loss. Mixed Integrated Veto does not satisfy this support condition, so we first remove early-eliminated outcomes, trading $O(\tau^2)$ distortion loss for an $O(1/\tau)$ bound on the deterministic distortion of every supported candidate. Balancing this repair cost against compression yields the $O(K^{-1/3})$ convergence rate.

In the subjective divisibility allocation model, all goods are divisible, every agent $i$ has a non-negative additive valuation function $v_i$, where for some goods $v_i$ is additive over fractions of the good, and for some goods, any fraction smaller than~1 has value~0. Previous work established the existence of $\frac{5}{9}$-MMS allocations in this setting. We show that $\frac{3}{5}$-MMS allocations exist. Our proof is based on an adaptation of the lone divider framework.

People's trust in AI advice diverges as they use it, deepening for some and eroding for others. We study this divergence in oligopoly pricing, where advice cannot prove itself: rivals' responses decide whether it pays off. In a laboratory experiment, 273 sellers compete across 91 three-seller markets over 30 rounds; we vary the presence of AI pricing recommendations and the gender composition of the market (female-only, male-only, or mixed). We find that the gender composition of the market shapes how sellers learn from the advice, and where prices settle as a result. In female-only markets, recommendations raise prices by 29% and profits by 39%; in male-only and mixed-gender markets, they have no significant effect. A Non-Homogeneous Hidden Markov Model reveals a composition-specific dynamic association: profitable rounds predict rising adherence to the AI in female-only markets and declining adherence otherwise, a pattern consistent with learned trust and self-serving attribution. The pattern reverses what recent evidence on gender and AI would predict. We discuss implications for platform governance and regulatory oversight, which should focus not only on the algorithm but on the human side that shapes its effects.

Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. For normalized binary goods, we give a polynomial-time algorithm for computing an EF1+EQ1 allocation with at most seven agents, but also construct a normalized instance with a larger number of agents for which no such allocation exists. In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante and ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.