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Éva Tardos

Publications and source records attributed to Éva Tardos.

At least 19 recordsLinked to original sources
arXiv2026

Learning vs. Optimizing Bidders in Budgeted Auctions

The study of repeated interactions between a learner and a utility-maximizing optimizer has yielded deep insights into the manipulability of learning algorithms. However, existing literature primarily focuses on independent, unlinked rounds, largely ignoring the ubiquitous practical reality of budget constraints. In this paper, we study this interaction in repeated second-price auctions in a Bayesian setting between a learning agent and a strategic agent, both subject to strict budget constraints, showing that such cross-round constraints fundamentally alter the strategic landscape. First, we generalize the classic Stackelberg equilibrium to the Budgeted Stackelberg Equilibrium. We prove that an optimizer's optimal strategy in a budgeted setting requires time-multiplexing; for a $k$-dimensional budget constraint, the optimal strategy strictly decomposes into up to $k+1$ distinct phases, with each phase employing a possibly unique mixed strategy (the case of $k=0$ recovers the classic Stackelberg equilibrium where the optimizer repeatedly uses a single mixed strategy). Second, we address the intriguing question of non-manipulability. We prove that when the learner employs a standard Proportional controller (the "P" of the PID-controller) to pace their bids, the optimizer's utility is upper bounded by their objective value in the Budgeted Stackelberg Equilibrium baseline. By bounding the dynamics of the PID controller via a novel analysis, our results establish that this widely used control-theoretic heuristic is actually strategically robust.

cs.GT↗
arXiv2026

Price of Anarchy of Algorithmic Monoculture

Several recent works investigate the effects of monoculture, the ever increasing phenomenon of (possibly) self-interested actors in a society relying on one common source of advice for decision making, with an archetypal driving example being the growing adoption and predictive power of machine learning models in matching markets, e.g. in hiring. Kleinberg and Raghavan (PNAS, 2021) introduced a model that captures the effects of monoculture in a one-sided matching market with advice, demonstrating that a higher accuracy common signal (such as an algorithmic vendor) might incentivize society as a whole to rationally adopt it, but as a collective it would be better off if each instead adopted less accurate, but private advice. We generalize their model and address the open question of their work in quantifying the social welfare loss. We find that monoculture and more generally decentralized optimization is close to optimal: we show a tight constant bound of 2 on the price of anarchy (and more general notions) for the induced game.

cs.GT↗
arXiv2026

Games with Payments between Learning Agents

In repeated games, such as auctions, players rely on autonomous learning agents to choose their actions. We study settings in which players have their agents make monetary transfers to other agents during play at their own expense, in order to influence learning dynamics in their favor. Our goal is to understand when players have incentives to use such payments, how payments between agents affect learning outcomes, and what the resulting implications are for welfare and its distribution. We propose a simple game-theoretic model to capture the incentive structure of such scenarios. We find that, quite generally, abstaining from payments is not robust to strategic deviations by users of learning agents: self-interested players benefit from having their agents make payments to other learners. In a broad class of games, such endogenous payments between learning agents lead to higher welfare for all players. In first- and second-price auctions, equilibria of the induced "payment-policy game" lead to highly collusive learning outcomes, with low or vanishing revenue for the auctioneer. These results highlight a fundamental challenge for mechanism design, as well as for regulatory policies, in environments where learning agents may interact in the digital ecosystem beyond a mechanism's boundaries.

cs.GT↗
arXiv2025

Robust Resource Allocation via Competitive Subsidies

A canonical setting for non-monetary online resource allocation is one where agents compete over multiple rounds for a single item per round, with i.i.d. valuations and additive utilities across rounds. With $n$ symmetric agents, a natural benchmark for each agent is the utility realized by her favorite $1/n$-fraction of rounds; a line of work has demonstrated one can robustly guarantee each agent a constant fraction of this ideal utility, irrespective of how other agents behave. In particular, several mechanisms have been shown to be $1/2$-robust, and recent work established that repeated first-price auctions based on artificial credits have a robustness factor of $0.59$, which cannot be improved beyond $0.6$ using first-price and simple strategies. In contrast, even without strategic considerations, the best achievable factor is $1-1/e\approx 0.63$. In this work, we break the $0.6$ first-price barrier to get a new $0.625$-robust mechanism, which almost closes the gap to the non-strategic robustness bound. Surprisingly, we do so via a simple auction, where in each round, bidders decide if they ask for the item, and we allocate uniformly at random among those who ask. The main new ingredient is the idea of competitive subsidies, wherein we charge the winning agent an amount in artificial credits that decreases when fewer agents are bidding (specifically, when $k$ agents bid, then the winner pays proportional to $k/(k+1)$, varying the payment by a factor of 2 depending on the competition). Moreover, we show how it can be modified to get an equilibrium strategy with a slightly weaker robust guarantee of $5/(3e) \approx 0.61$ (and the optimal $1-1/e$ factor at equilibrium). Finally, we show that our mechanism gives the best possible bound under a wide class of auction-based mechanisms.

cs.GT↗
arXiv2025

Robust Equilibria in Shared Resource Allocation via Strengthening Border's Theorem

We consider repeated allocation of a shared resource via a non-monetary mechanism, wherein a single item must be allocated to one of multiple agents in each round. We assume that each agent has i.i.d. values for the item across rounds, and additive utilities. Past work on this problem has proposed mechanisms where agents can get one of two kinds of guarantees: $(i)$ (approximate) Bayes-Nash equilibria via linkage-based mechanisms which need extensive knowledge of the value distributions, and $(ii)$ simple distribution-agnostic mechanisms with robust utility guarantees for each individual agent, which are worse than the Nash outcome, but hold irrespective of how others behave (including possibly collusive behavior). Recent work has hinted at barriers to achieving both simultaneously. Our work however establishes this is not the case, by proposing the first mechanism in which each agent has a natural strategy that is both a Bayes-Nash equilibrium and also comes with strong robust guarantees for individual agent utilities. Our mechanism comes out of a surprising connection between the online shared resource allocation problem and implementation theory, and uses a surprising strengthening of Border's theorem. In particular, we show that establishing robust equilibria in this setting reduces to showing that a particular subset of the Border polytope is non-empty. We establish this via a novel joint Schur-convexity argument. This strengthening of Border's criterion for obtaining a stronger conclusion is of independent technical interest, as it may prove useful in other settings.

cs.GT↗
arXiv2025

Dynamic Allocation of Public Goods with Approximate Core Equilibria

We consider the problem of repeatedly allocating multiple shareable public goods that have limited availability in an online setting without the use of money. In our setting, agents have additive values, and the value each agent receives from getting access to the goods in each period is drawn i.i.d. from some joint distribution $\mathcal{D}$ (that can be arbitrarily correlated between agents). The principal also has global constraints on the set of goods they can select over the horizon, which is represented via a submodular allocation-cost function. Our goal is to select the periods to allocate the good to ensure high value for each group of agents. We develop mechanisms for this problem using an artificial currency, where we give each agent a budget proportional to their (exogenous) fair share. The correlated value distribution makes this an especially challenging problem, as agents may attempt to free-ride by declaring low valuations for the good when they know other agents have high values-hoping those agents will bear a larger share of the cost of the resource. We offer a black-box reduction from monetary mechanisms for the allocation of a costly excludable public good. We focus on pacing strategies, the natural strategies when using AI agents, where agents report a scaled version of their value to the mechanism. Our main results show that when using a truthful monetary mechanism as our building block, the resulting online mechanism has a focal equilibrium in which each agent plays a pacing strategy whose outcome results in an allocation that is a $(\mathcal{H}_n-1)$-approximation of the core, where $\mathcal{H}_n$ is the Harmonic number, and $n$ is the number of agents. Remarkably, we are able to achieve an approximate core solution as a Nash outcome without explicit collaboration or coordination between the agents.

cs.GT↗
arXiv2025

Beyond Worst-Case Online Allocation via Dynamic Max-min Fairness

We study the allocation of shared resources over multiple rounds among competing agents, via the dynamic max-min fair (DMMF) mechanism: the good in each round is allocated to the requesting agent with the least number of allocations received to date. We show that in large markets when an agent has i.i.d. values across rounds, under mild distributional assumptions (e.g., bounded PDF function), the DMMF mechanism allows each agent to realize a $1 - o(1)$ fraction of her ideal utility -- her highest achievable utility given her nominal share of resources. This guarantee holds under arbitrary behavior by other agents and is achieved by characterizing the agent's utility under a rich space of strategies, wherein an agent can tune how aggressive to be in requesting the item. Our techniques also allow us to handle settings where an agent's values are correlated across rounds, thereby allowing an adversary to predict and block her future values. By tuning the aggressiveness, an agent can guarantee $Ω(γ)$ fraction of her ideal utility, where $γ\in [0, 1]$ is a parameter that quantifies dependence across rounds (with $γ= 1$ indicating full independence and lower values indicating more correlation). Finally, we extend our efficiency results to the case of reusable resources, where an agent might need to hold the item over multiple rounds to receive utility. Our results subsume previous guarantees obtained using a more complicated mechanism proving a half ideal utility guarantee under i.i.d. values sampled from worst-case distributions.

cs.GT↗
arXiv2025

Learning in Budgeted Auctions with Spacing Objectives

In many repeated auction settings, participants care not only about how frequently they win but also how their winnings are distributed over time. This problem arises in various practical domains where avoiding congested demand is crucial, such as online retail sales and compute services, as well as in advertising campaigns that require sustained visibility over time. We introduce a simple model of this phenomenon, modeling it as a budgeted auction where the value of a win is a concave function of the time since the last win. This implies that for a given number of wins, even spacing over time is optimal. We also extend our model and results to the case when not all wins result in "conversions" (realization of actual gains), and the probability of conversion depends on a context. The goal is to maximize and evenly space conversions rather than just wins. We study the optimal policies for this setting in second-price auctions and offer learning algorithms for the bidders that achieve low regret against the optimal bidding policy in a Bayesian online setting. Our main result is a computationally efficient online learning algorithm that achieves $\tilde O(\sqrt T)$ regret. We achieve this by showing that an infinite-horizon Markov decision process (MDP) with the budget constraint in expectation is essentially equivalent to our problem, even when limiting that MDP to a very small number of states. The algorithm achieves low regret by learning a bidding policy that chooses bids as a function of the context and the system's state, which will be the time elapsed since the last win (or conversion). We show that state-independent strategies incur linear regret even without uncertainty of conversions. We complement this by showing that there are state-independent strategies that, while still having linear regret, achieve a $(1-\frac 1 e)$ approximation to the optimal reward.

cs.GT↗
arXiv2025

Online Resource Sharing: Better Robust Guarantees via Randomized Strategies

We study the problem of fair online resource allocation via non-monetary mechanisms, where multiple agents repeatedly share a resource without monetary transfers. Previous work has shown that every agent can guarantee $1/2$ of their ideal utility (the highest achievable utility given their fair share of resources) robustly, i.e., under arbitrary behavior by the other agents. While this $1/2$-robustness guarantee has now been established under very different mechanisms, including pseudo-markets and dynamic max-min allocation, improving on it has appeared difficult. In this work, we obtain the first significant improvement on the robustness of online resource sharing. In more detail, we consider the widely-studied repeated first-price auction with artificial currencies. Our main contribution is to show that a simple randomized bidding strategy can guarantee each agent a $2 - \sqrt 2 \approx 0.59$ fraction of her ideal utility, irrespective of others' bids. Specifically, our strategy requires each agent with fair share $α$ to use a uniformly distributed bid whenever her value is in the top $α$-quantile of her value distribution. Our work almost closes the gap to the known $1 - 1/e \approx 0.63$ hardness for robust resource sharing; we also show that any static (i.e., budget independent) bidding policy cannot guarantee more than a $0.6$-fraction of the ideal utility, showing our technique is almost tight.

cs.GT↗
arXiv2025

Allocating Public Goods via Dynamic Max-Min Fairness: Long-Run Behavior and Competitive Equilibria

Dynamic max-min fair allocation (DMMF) is a simple and popular mechanism for the repeated allocation of a shared resource among competing agents: in each round, each agent can choose to request or not for the resource, which is then allocated to the requesting agent with the least number of allocations received till then. Recent work has shown that under DMMF, a simple threshold-based request policy enjoys surprisingly strong robustness properties, wherein each agent can realize a significant fraction of her optimal utility irrespective of how other agents' behave. While this goes some way in mitigating the possibility of a 'tragedy of the commons' outcome, the robust policies require that an agent defend against arbitrary (possibly adversarial) behavior by other agents. This however may be far from optimal compared to real world settings, where other agents are selfish optimizers rather than adversaries. Therefore, robust guarantees give no insight on how agents behave in an equilibrium, and whether outcomes are improved under one. Our work aims to bridge this gap by studying the existence and properties of equilibria under DMMF. To this end, we first show that despite the strong robustness guarantees of the threshold based strategies, no Nash equilibrium exists when agents participate in DMMF, each using some fixed threshold-based policy. On the positive side, however, we show that for the symmetric case, a simple data-driven request policy guarantees that no agent benefits from deviating to a different fixed threshold policy. In our proposed policy agents aim to match the historical allocation rate with a vanishing drift towards the rate optimizing overall welfare for all users. Furthermore, the resulting equilibrium outcome can be significantly better compared to what follows from the robustness guarantees.

cs.GT↗
arXiv2024

Calibrated Recommendations for Users with Decaying Attention

Recommendation systems capable of providing diverse sets of results are a focus of increasing importance, with motivations ranging from fairness to novelty and other aspects of optimizing user experience. One form of diversity of recent interest is calibration, the notion that personalized recommendations should reflect the full distribution of a user's interests, rather than a single predominant category -- for instance, a user who mainly reads entertainment news but also wants to keep up with news on the environment and the economy would prefer to see a mixture of these genres, not solely entertainment news. Existing work has formulated calibration as a subset selection problem; this line of work observes that the formulation requires the unrealistic assumption that all recommended items receive equal consideration from the user, but leaves as an open question the more realistic setting in which user attention decays as they move down the list of results. In this paper, we consider calibration with decaying user attention under two different models. In both models, there is a set of underlying genres that items can belong to. In the first setting, where items are represented by fine-grained mixtures of genre percentages, we provide a $(1-1/e)$-approximation algorithm by extending techniques for constrained submodular optimization. In the second setting, where items are coarsely binned into a single genre each, we surpass the $(1-1/e)$ barrier imposed by submodular maximization and give a $2/3$-approximate greedy algorithm. Our work thus addresses the problem of capturing ordering effects due to decaying attention, allowing for the extension of near-optimal calibration from recommendation sets to recommendation lists.

cs.DS↗
arXiv2024

Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions

We study the liquid welfare in sequential first-price auctions with budget-limited buyers. We focus on first-price auctions, which are increasingly commonly used in many settings, and consider liquid welfare, a natural and well-studied generalization of social welfare for buyers with budgets. We use a behavioral model for the buyers, assuming a learning style guarantee: the resulting utility of each buyer is within a $γ$ factor (where $γ\ge 1$) of the utility achievable by shading her value with the same factor at each round. Under this assumption, we show a $γ+1/2+O(1/γ)$ price of anarchy for liquid welfare assuming buyers have additive valuations. This positive result is in contrast to sequential second-price auctions, where even with $γ=1$, the resulting liquid welfare can be arbitrarily smaller than the maximum liquid welfare. We prove a lower bound of $γ$ on the liquid welfare loss under the above assumption in first-price auctions, making our bound asymptotically tight. For the case when $γ= 1$ our theorem implies a price of anarchy upper bound that is about $2.41$; we show a lower bound of $2$ for that case. We also give a learning algorithm that the players can use to achieve the guarantee needed for our liquid welfare result. Our algorithm achieves utility within a $γ=O(1)$ factor of the optimal utility even when a buyer's values and the bids of the other buyers are chosen adversarially, assuming the buyer's budget grows linearly with time. The competitiveness guarantee of the learning algorithm deteriorates somewhat as the budget grows slower than linearly with time. Finally, we extend our liquid welfare results for the case where buyers have submodular valuations over the set of items they win across iterations with a slightly worse price of anarchy bound of $γ+1+O(1/γ)$ compared to the guarantee for the additive case.

cs.GT↗
arXiv2024

Modeling reputation-based behavioral biases in school choice

A fundamental component in the theoretical school choice literature is the problem a student faces in deciding which schools to apply to. Recent models have considered a set of schools of different selectiveness and a student who is unsure of their strength and can apply to at most $k$ schools. Such models assume that the student cares solely about maximizing the quality of the school that they attend, but experience suggests that students' decisions are also influenced by a set of behavioral biases based on reputational effects: a subjective reputational benefit when admitted to a selective school, whether or not they attend; and a subjective loss based on disappointment when rejected. Guided by these observations, and inspired by recent behavioral economics work on loss aversion relative to expectations, we propose a behavioral model by which a student chooses schools to balance these behavioral effects with the quality of the school they attend. Our main results show that a student's choices change in dramatic ways when these reputation-based behavioral biases are taken into account. In particular, where a rational applicant spreads their applications evenly, a biased student applies very sparsely to highly selective schools, such that above a certain threshold they apply to only an absolute constant number of schools even as their budget of applications grows to infinity. Consequently, a biased student underperforms a rational student even when the rational student is restricted to a sufficiently large upper bound on applications and the biased student can apply to arbitrarily many. Our analysis shows that the reputation-based model is rich enough to cover a range of different ways that biased students cope with fear of rejection, including not just targeting less selective schools, but also occasionally applying to schools that are too selective, compared to rational students.

cs.GT↗
arXiv2023

Robust Pseudo-Markets for Reusable Public Resources

We study non-monetary mechanisms for the fair and efficient allocation of reusable public resources, i.e., resources used for varying durations. We consider settings where a limited resource is repeatedly shared among a set of agents, each of whom may request to use the resource over multiple consecutive rounds, receiving utility only if they get to use the resource for the full duration of their request. Such settings are of particular significance in scientific research where large-scale instruments such as electron microscopes, particle colliders, or telescopes are shared between multiple research groups; this model also subsumes and extends existing models of repeated non-monetary allocation where resources are required for a single round only. We study a simple pseudo-market mechanism where upfront we endow each agent with a budget of artificial credits, proportional to the fair share of the resource we want the agent to receive. The endowments thus define for each agent her ideal utility as that which she derives from her favorite allocation with no competition, but subject to getting at most her fair share of the resource across rounds. Next, on each round, and for each available resource item, our mechanism runs a first-price auction with a selective reserve, wherein each agent submits a desired duration and a per-round-bid, which must be at least the reserve price if requesting for multiple rounds; the bidder with the highest per-round-bid wins, and gets to use the item for the desired duration. We consider this problem in a Bayesian setting and show that under a carefully chosen reserve price, irrespective of how others bid, each agent has a simple strategy that guarantees she receives a $1/2$ fraction of her ideal utility in expectation. We also show this result is tight, i.e., no mechanism can guarantee that all agents get more than half of their ideal utility.

cs.GT↗
arXiv2023

Approximately Stationary Bandits with Knapsacks

Bandits with Knapsacks (BwK), the generalization of the Bandits problem under global budget constraints, has received a lot of attention in recent years. Previous work has focused on one of the two extremes: Stochastic BwK where the rewards and consumptions of the resources of each round are sampled from an i.i.d. distribution, and Adversarial BwK where these parameters are picked by an adversary. Achievable guarantees in the two cases exhibit a massive gap: No-regret learning is achievable in the stochastic case, but in the adversarial case only competitive ratio style guarantees are achievable, where the competitive ratio depends either on the budget or on both the time and the number of resources. What makes this gap so vast is that in Adversarial BwK the guarantees get worse in the typical case when the budget is more binding. While ``best-of-both-worlds'' type algorithms are known (single algorithms that provide the best achievable guarantee in each extreme case), their bounds degrade to the adversarial case as soon as the environment is not fully stochastic. Our work aims to bridge this gap, offering guarantees for a workload that is not exactly stochastic but is also not worst-case. We define a condition, Approximately Stationary BwK, that parameterizes how close to stochastic or adversarial an instance is. Based on these parameters, we explore what is the best competitive ratio attainable in BwK. We explore two algorithms that are oblivious to the values of the parameters but guarantee competitive ratios that smoothly transition between the best possible guarantees in the two extreme cases, depending on the values of the parameters. Our guarantees offer great improvement over the adversarial guarantee, especially when the available budget is small. We also prove bounds on the achievable guarantee, showing that our results are approximately tight when the budget is small.

cs.LG↗
arXiv2022

Ordered Submodularity and its Applications to Diversifying Recommendations

A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very effective in allowing approximation algorithms for such subset selection problems. However, in several applications, we are interested not only in the elements of a set, but also the order in which they appear, breaking the assumption that all selected items receive equal consideration. One such category of applications involves the presentation of search results, product recommendations, news articles, and other content, due to the well-documented phenomenon that humans pay greater attention to higher-ranked items. As a result, optimization in content presentation for diversity, user coverage, calibration, or other objectives more accurately represents a sequence selection problem, to which traditional submodularity approximation results no longer apply. Although extensions of submodularity to sequences have been proposed, none is designed to model settings where items contribute based on their position in a ranked list, and hence they are not able to express these types of optimization problems. In this paper, we aim to address this modeling gap. Here, we propose a new formalism of ordered submodularity that captures these ordering problems in content presentation, and more generally a category of optimization problems over ranked sequences in which different list positions contribute differently to the objective function. We analyze the natural ordered analogue of the greedy algorithm and show that it provides a $2$-approximation. We also show that this bound is tight, establishing that our new framework is conceptually and quantitatively distinct from previous formalisms of set and sequence submodularity.

cs.DS↗
arXiv2022

Incentives in Dominant Resource Fair Allocation under Dynamic Demands

Every computer system -- from schedulers in clouds (e.g. Amazon) to computer networks to operating systems -- performs resource allocation across system users. The defacto allocation policies are max-min fairness (MMF) for single resources and dominant resource fairness (DRF) for multiple resources which guarantee properties like incentive compatibility, envy-freeness, and Pareto efficiency, assuming user demands are static (time-independent). However, in real-world systems, user demands are dynamic, i.e. time-dependant. As a result, there is now a fundamental mismatch between the goals of computer systems and the properties enabled by classic resource allocation policies. We aim to bridge this mismatch. When demands are dynamic, instant-by-instant MMF can be extremely unfair over longer periods of time, i.e. lead to unbalanced user allocations as previous allocations have no effect in the present. We consider a natural generalization of MMF and DRF for multiple resources and users with dynamic demands: this algorithm ensures that user allocations are as max-min fair as possible up to any time instant, given past allocations. This dynamic mechanism remains Pareto optimal and envy-free, but not incentive compatible. However, our results show that the possible increase in utility by misreporting is bounded and, since this can lead to significant decrease in overall useful allocation, this suggests that it is not a useful strategy. Our main result is to show that our dynamic DRF algorithm is $(1+ρ)$-incentive compatible, where $ρ$ quantifies the relative importance of a resource for different users; we show that this factor is tight even with only two resources. We also present a $3/2$ upper bound and a $\sqrt 2$ lower bound for incentive compatibility when there is only one resource. We also offer extensions for the case when users are weighted to prioritize them differently.

cs.GT↗
arXiv2021

Polarization in Geometric Opinion Dynamics

In light of increasing recent attention to political polarization, understanding how polarization can arise poses an important theoretical question. While more classical models of opinion dynamics seem poorly equipped to study this phenomenon, a recent novel approach by Hązła, Jin, Mossel, and Ramnarayan (HJMR) proposes a simple geometric model of opinion evolution that provably exhibits strong polarization in specialized cases. Moreover, polarization arises quite organically in their model: in each time step, each agent updates opinions according to their correlation/response with an issue drawn at random. However, their techniques do not seem to extend beyond a set of special cases they identify, which benefit from fragile symmetry or contractiveness assumptions, leaving open how general this phenomenon really is. In this paper, we further the study of polarization in related geometric models. We show that the exact form of polarization in such models is quite nuanced: even when strong polarization does not hold, it is possible for weaker notions of polarization to nonetheless attain. We provide a concrete example where weak polarization holds, but strong polarization provably fails. However, we show that strong polarization provably holds in many variants of the HJMR model, which are also robust to a wider array of distributions of random issues -- this indicates that the form of polarization introduced by HJMR is more universal than suggested by their special cases. We also show that the weaker notions connect more readily to the theory of Markov chains on general state spaces.

cs.SI↗