arXiv subjects

Ioannis Caragiannis

Publications and source records attributed to Ioannis Caragiannis.

At least 19 recordsLinked to original sources

arXiv2026

The Robotaxi Placement Problem: Minimizing Expected ETA for Stochastic Demand

Autonomous ride-hailing platforms must strategically position idle robotaxis to minimize the wait times of prospective riders. We formalize this as the robotaxi placement problem ($k$-RP). Given a finite metric space and a demand distribution over its points, the goal is to position $k$ robotaxis to minimize the expected total distance in a perfect matching between the robotaxis and $k$ random riders. We present several theoretical results for this stochastic optimization problem. First, we observe that sampling robotaxi locations independently according to the demand distribution yields a randomized $2$-approximation algorithm. Second, we present an explicit inapproximability bound via a novel gap-preserving reduction from the maximum coverage problem. Furthermore, while it is not even clear whether the exact expected cost of a placement can be computed efficiently on general metrics, we design an exact polynomial-time dynamic programming algorithm for $k$-RP in tree metrics by decoupling the stochastic matching dependencies. Finally, empirical evaluations on real-world ride-hailing data reveal that a variance-reduced random placement strategy is highly effective in practice, yielding expected wait times that are very close to those obtained by computationally heavy exact algorithms for the uniform capacitated $k$-median problem.

cs.DS↗

arXiv2026

Deterministic Stackelberg Strategies in Robotaxi Assignment Games

In autonomous mobility duopolies, platforms compete for riders based on vehicle proximity. A critical operational challenge---faced by an incumbent proactively defending against a market entrant---is how to dispatch fleets to minimize demand poached by a reactive competitor. We model this competition as a zero-sum robotaxi assignment game, focusing on computing optimal deterministic Stackelberg strategies for the leader. We formulate this problem as an exact single-level integer linear program and use its relaxation to design a polynomial-time approximation algorithm achieving an additive error from the optimum. We argue that this is not far from best possible by proving that deciding whether a strictly positive payoff is achievable is NP-complete, and that approximating the optimal payoff within an additive error scaling linearly with the number of riders is NP-hard. We also provide an exact polynomial-time dynamic programming algorithm for computing the optimal Stackelberg payoff when riders and vehicles are on the Euclidean line. Finally, we complement our theoretical findings with an empirical evaluation using real-world ride-hailing data. The experiments demonstrate that our LP-based algorithm significantly outperforms its worst-case guarantee in practice, while lightweight heuristics achieve highly competitive payoffs with negligible computational overhead, offering practical solutions for large-scale deployments.

cs.GT↗

arXiv2026

A Unified Framework for Uniform-Price Resource Allocation Mechanisms

Mechanisms for allocating a divisible resource among strategic agents have been widely studied. The prominent paradigm is the proportional (Kelly) mechanism, which elicits a scalar bid per agent, allocates the resource proportionally, and charges payments equal to the bids. Follow-up mechanisms improve social welfare, but sacrifice simplicity by introducing complex allocation rules or unintuitive payments. We introduce a unified framework for designing simple resource allocation mechanisms with proportional-style allocations and uniform pricing. Our framework yields a family of mechanisms that interpolate between the Kelly mechanism and the first-price auction. These mechanisms strictly improve upon Kelly's efficiency guarantees, even achieving full efficiency in equilibrium, while also providing revenue guarantees relative to the VCG mechanism.

cs.GT↗

arXiv2026

Quantile agent utility and implications to randomized social choice

We initiate a novel direction in randomized social choice by proposing a new definition of agent utility for randomized outcomes. Each agent has a preference over all outcomes and a {\em quantile} parameter. Given a {\em lottery} over the outcomes, an agent gets utility from a particular {\em representative}, defined as the least preferred outcome that can be realized so that the probability that any worse-ranked outcome can be realized is at most the agent's quantile value. In contrast to other utility models that have been considered in randomized social choice (e.g., stochastic dominance, expected utility), our {\em quantile agent utility} compares two lotteries for an agent by just comparing the representatives, as is done for deterministic outcomes. This yields a purely ordinal yet informative comparison of randomized outcomes. We revisit fundamental questions in randomized social choice using the new utility definition. We study the compatibility of efficiency and strategyproofness for randomized voting rules, and of efficiency, fairness, and strategyproofness for randomized one-sided matching mechanisms. In contrast to classical impossibility results, we show that under quantile agent utilities, these properties can often be satisfied simultaneously.

cs.GT↗

arXiv2026

Existence and Computation of Fair Allocations under Constraints

We study fair division of divisible goods under generalized assignment constraints. Here, each good has an agent-specific value and size, and every agent has a budget constraint that limits the total size of the goods she can receive. Since it may not always be feasible to assign all goods to the agents while respecting the budget constraints, we use the construct of charity to accommodate the unassigned goods. In this constrained setting with charity, we obtain several new existential and computational results for feasible envy-freeness (FEF); this fairness notion requires that agents are envy-free, considering only budget-feasible subsets. First, we simplify and extend known existential results for FEF allocations. Then, we show that the space of FEF allocations has a non-convex structure. Next, using a fixed-point argument, we establish a novel guarantee that FEF can always be achieved with Pareto-optimality. Furthermore, we give an alternative proof of the fact that one cannot additionally obtain truthfulness in this context: There does not exist a mechanism that is simultaneously truthful, fair, and Pareto-optimal. On the positive side, we show that truthfulness is compatible with each of FEF and Pareto-optimality, individually.

cs.GT↗

arXiv2026

Revenue Guarantees in Autobidding Platforms

Motivated by autobidding systems in online advertising, we study revenue maximization in markets with divisible goods and budget-constrained buyers with linear valuations. Our aim is to compute a single price for each good and an allocation that maximizes total revenue. We show that the First-Price Pacing Equilibrium (FPPE) guarantees at least half of the optimal revenue, even when compared to the maximal revenue of buyer-specific prices. This guarantee is particularly striking in light of our hardness result: we prove that revenue maximization under individual rationality and single-price-per-good constraints is APX-hard. We further extend our analysis in two directions: first, we introduce an online analogue of FPPE and show that it achieves a constant-factor revenue guarantee, specifically a $1/4$-approximation; second, we consider buyers with concave valuation functions, characterizing an FPPE-type outcome as the solution to an Eisenberg-Gale-style convex program and showing that the revenue approximation degrades gracefully with the degree of nonlinearity of the valuations.

cs.GT↗

arXiv2026

The Distortion of Prior-Independent b-Matching Mechanisms

In a setting where $m$ items need to be partitioned among $n$ agents, we evaluate the performance of mechanisms that take as input each agent's \emph{ordinal preferences}, i.e., their ranking of the items from most- to least-preferred. The standard measure for evaluating ordinal mechanisms is the \emph{distortion}, and the vast majority of the literature on distortion has focused on worst-case analysis, leading to some overly pessimistic results. We instead evaluate the distortion of mechanisms with respect to their expected performance when the agents' preferences are generated stochastically. We first show that no ordinal mechanism can achieve a distortion better than $e/(e-1)\approx 1.582$, even if each agent needs to receive exactly one item (i.e., $m=n$) and every agent's values for different items are drawn i.i.d.\ from the same known distribution. We then complement this negative result by proposing an ordinal mechanism that achieves the optimal distortion of $e/(e-1)$ even if each agent's values are drawn from an agent-specific distribution that is unknown to the mechanism. To further refine our analysis, we also optimize the \emph{distortion gap}, i.e., the extent to which an ordinal mechanism approximates the optimal distortion possible for the instance at hand, and we propose a mechanism with a near-optimal distortion gap of $1.076$. Finally, we also evaluate the distortion and distortion gap of simple mechanisms that have a one-pass structure.

cs.GT↗

arXiv2025

Selling an Item Among a Strategic Bidder and a Profiled Agent

We consider the fundamental scenario where a single item is to be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. The other agent is profiled, i.e., the mechanism receives a prediction for her valuation, which can be true or false. Our goal is to design mechanisms for selling the item that make as much revenue as possible in cases of a correct or incorrect prediction. As a benchmark for proving our revenue-approximation guarantees, we use the maximum expected revenue that can be obtained by a strategic and an honest bidder. We study two mechanisms. The first one yields optimal revenue when the prediction is guaranteed to be correct and a constant revenue approximation when the prediction is incorrect, assuming that the agent valuations are drawn from a monotone hazard rate (MHR) distribution. The second mechanism ignores the prediction for the second agent and simulates the revenue-optimal mechanism when no bid information for the bidders is available. We prove, again assuming that valuations are drawn from MHR distributions, that this mechanism achieves a constant revenue approximation guarantee compared to our revenue benchmark. The MHR assumption is necessary; we show that there are non-MHR but regular probability distributions for which no constant approximation of our revenue benchmark is possible.

cs.GT↗

arXiv2025

Computing Approximately Proportional Allocations of Indivisible Goods: Beyond Additive and Monotone Valuations

Although approximate notions of envy-freeness-such as envy-freeness up to one good (EF1)-have been extensively studied for indivisible goods, the seemingly simpler fairness concept of proportionality up to one good (PROP1) has received far less attention. For additive valuations, every EF1 allocation is PROP1, and well-known algorithms such as Round-Robin and Envy-Cycle Elimination compute such allocations in polynomial time. PROP1 is also compatible with Pareto efficiency, as maximum Nash welfare allocations are EF1 and hence PROP1. We ask whether these favorable properties extend to non-additive valuations. We study a broad class of allocation instances with {\em satiating goods}, where agents have non-negative valuation functions that need not be monotone, allowing for negative marginal values. We present the following results: - EF1 implies PROP1 for submodular valuations over satiating goods, ensuring existence and efficient computation via Envy-Cycle Elimination for monotone submodular valuations; - Round-robin computes a partial PROP1 allocation after the second-to-last round for satiating submodular goods and a complete PROP1 for monotone submodular valuations; - PROP1 allocations for satiating subadditive goods can be computed in polynomial-time; - Maximum Nash welfare allocations are PROP1 for monotone submodular goods, revealing yet another facet of their ``unreasonable fairness.''

cs.GT↗

arXiv2025

Rethinking Pricing in Energy Markets: Pay-as-Bid vs Pay-as-Clear

The design of energy markets is a subject of ongoing debate, particularly concerning the choice between the widely adopted Pay-as-Clear (PC) pricing mechanism and the alternative Pay-as-Bid (PB). These mechanisms determine how energy producers are compensated: under PC, all selected producers are paid the market-clearing price (i.e., the highest accepted bid), while under PB, each selected producer is paid their own submitted bid. The overarching objective is to meet the total demand for energy at minimal cost in the presence of strategic behavior. We present two key theoretical results. First, no mechanism can uniformly dominate PC or PB. This means that for any mechanism $\mathcal{M}$, there exists a market configuration and a mixed-strategy Nash equilibrium of PC (respectively for PB) that yields strictly lower total energy costs than under $\mathcal{M}$. Second, in terms of worst-case equilibrium outcomes, PB consistently outperforms PC: across all market instances, the highest possible equilibrium price under PB is strictly lower than that under PC. This suggests a structural robustness of PB to strategic manipulation. These theoretical insights are further supported by extensive simulations based on no-regret learning dynamics, which consistently yield lower average market prices in several energy market settings.

cs.GT↗

arXiv2025

A new lower bound for multi-color discrepancy with applications to fair division

A classical problem in combinatorics seeks colorings of low discrepancy. More concretely, the goal is to color the elements of a set system so that the number of appearances of any color among the elements in each set is as balanced as possible. We present a new lower bound for multi-color discrepancy, showing that there is a set system with $n$ subsets over a set of elements in which any $k$-coloring of the elements has discrepancy at least $Ω\left(\sqrt{\frac{n}{\ln{k}}}\right)$. This result improves the previously best-known lower bound of $Ω\left(\sqrt{\frac{n}{k}}\right)$ of Doerr and Srivastav [2003] and may have several applications. Here, we explore its implications on the feasibility of fair division concepts for instances with $n$ agents having valuations for a set of indivisible items. The first such concept is known as consensus $1/k$-division up to $d$ items (\cd$d$) and aims to allocate the items into $k$ bundles so that no matter which bundle each agent is assigned to, the allocation is envy-free up to $d$ items. The above lower bound implies that \cd$d$ can be infeasible for $d\in Ω\left(\sqrt{\frac{n}{\ln{k}}}\right)$. We furthermore extend our proof technique to show that there exist instances of the problem of allocating indivisible items to $k$ groups of $n$ agents in total so that envy-freeness and proportionality up to $d$ items are infeasible for $d\in Ω\left(\sqrt{\frac{n}{k\ln{k}}}\right)$ and $d\in Ω\left(\sqrt{\frac{n}{k^3\ln{k}}}\right)$, respectively. The lower bounds for fair division improve the currently best-known ones by Manurangsi and Suksompong [2022].

cs.GT↗

arXiv2025

Bounds on the revenue gap of linear posted pricing for selling a divisible item

Selling a perfectly divisible item to potential buyers is a fundamental task with apparent applications to pricing communication bandwidth and cloud computing services. Surprisingly, despite the rich literature on single-item auctions, revenue maximization when selling a divisible item is a much less understood objective. We introduce a Bayesian setting, in which the potential buyers have concave valuation functions (defined for each possible item fraction) that are randomly chosen according to known probability distributions. Extending the sequential posted pricing paradigm, we focus on mechanisms that use linear pricing, charging a fixed price for the whole item and proportional prices for fractions of it. Our goal is to understand the power of such mechanisms by bounding the gap between the expected revenue that can be achieved by the best among these mechanisms and the maximum expected revenue that can be achieved by any mechanism assuming mild restrictions on the behavior of the buyers. Under regularity assumptions for the probability distributions, we show that this revenue gap depends only logarithmically on a natural parameter characterizing the valuation functions and the number of agents. Our results follow by bounding the objective value of a mathematical program that maximizes the ex-ante relaxation of optimal revenue under linear pricing revenue constraints.

cs.GT↗

arXiv2025

New Fairness Concepts for Allocating Indivisible Items

For the fundamental problem of fairly dividing a set of indivisible items among agents, envy-freeness up to any item (EFX) and maximin fairness (MMS) are arguably the most compelling fairness concepts proposed until now. Unfortunately, despite significant efforts over the past few years, whether EFX allocations always exist is still an enigmatic open problem, let alone their efficient computation. Furthermore, today we know that MMS allocations are not always guaranteed to exist. These facts weaken the usefulness of both EFX and MMS, albeit their appealing conceptual characteristics. We propose two alternative fairness concepts, called epistemic EFX (EEFX) and minimum EFX share fairness (MXS), inspired by EFX and MMS. For both, we explore their relationships to well-studied fairness notions and, more importantly, prove that EEFX and MXS allocations always exist and can be computed efficiently for additive valuations. Our results justify that the new fairness concepts can be excellent alternatives to EFX and MMS.

cs.GT↗

arXiv2024

On Interim Envy-Free Allocation Lotteries

With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too stringent notion of ex-post envy-freeness and the very weak notion of ex-ante envy-freeness. Our analysis relates iEF to other fairness notions as well, and reveals tradeoffs between iEF and efficiency. Even though several of our results apply to general fair division problems, we are particularly interested in instances with equal numbers of agents and items where allocations are perfect matchings of the items to the agents. We show how to compute iEF allocations in matching allocation instances in polynomial time, while also maximizing several efficiency objectives, even though this proves to be considerably more challenging than computing envy-free allocations. Our algorithms use efficient solutions to a novel variant of the bipartite matching problem. We also study the extension of iEF when payments to or from the agents are allowed. We present a series of results on two optimization problems, including a generalization of the classical rent division problem to random allocations.

cs.GT↗

arXiv2024

On the satisfiability of random $3$-SAT formulas with $k$-wise independent clauses

The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The classical assumption in this line of research is that, for a given set of $n$ Boolean variables, each clause is drawn uniformly at random among all sets of three literals from these variables, independently from other clauses. Here, we keep the uniform distribution of each clause, but deviate significantly from the independence assumption and consider richer families of probability distributions. For integer parameters $n$, $m$, and $k$, we denote by $\DistFamily_k(n,m)$ the family of probability distributions that produce formulas with $m$ clauses, each selected uniformly at random from all sets of three literals from the $n$ variables, so that the clauses are $k$-wise independent. Our aim is to make general statements about the satisfiability or unsatisfiability of formulas produced by distributions in $\DistFamily_k(n,m)$ for different values of the parameters $n$, $m$, and $k$.

math.CO↗

arXiv2024

Proportional Fairness in Non-Centroid Clustering

We revisit the recently developed framework of proportionally fair clustering, where the goal is to provide group fairness guarantees that become stronger for groups of data points (agents) that are large and cohesive. Prior work applies this framework to centroid clustering, where the loss of an agent is its distance to the centroid assigned to its cluster. We expand the framework to non-centroid clustering, where the loss of an agent is a function of the other agents in its cluster, by adapting two proportional fairness criteria -- the core and its relaxation, fully justified representation (FJR) -- to this setting. We show that the core can be approximated only under structured loss functions, and even then, the best approximation we are able to establish, using an adaptation of the GreedyCapture algorithm developed for centroid clustering [Chen et al., 2019; Micha and Shah, 2020], is unappealing for a natural loss function. In contrast, we design a new (inefficient) algorithm, GreedyCohesiveClustering, which achieves the relaxation FJR exactly under arbitrary loss functions, and show that the efficient GreedyCapture algorithm achieves a constant approximation of FJR. We also design an efficient auditing algorithm, which estimates the FJR approximation of any given clustering solution up to a constant factor. Our experiments on real data suggest that traditional clustering algorithms are highly unfair, whereas GreedyCapture is considerably fairer and incurs only a modest loss in common clustering objectives.

cs.LG↗

arXiv2024

Beyond the worst case: Distortion in impartial culture electorates

{\em Distortion} is a well-established notion for quantifying the loss of social welfare that may occur in voting. As voting rules take as input only ordinal information, they are essentially forced to neglect the exact values the agents have for the alternatives. Thus, in worst-case electorates, voting rules may return low social welfare alternatives and have high distortion. Accompanying voting rules with a small number of cardinal queries per agent may reduce distortion considerably. To explore distortion beyond worst-case conditions, we use a simple stochastic model according to which the values the agents have for the alternatives are drawn independently from a common probability distribution. This gives rise to so-called {\em impartial culture electorates}. We refine the definition of distortion so that it is suitable for this stochastic setting and show that, rather surprisingly, all voting rules have high distortion {\em on average}. On the positive side, for the fundamental case where the agents have random {\em binary} values for the alternatives, we present a mechanism that achieves approximately optimal average distortion by making a {\em single} cardinal query per agent. This enables us to obtain slightly suboptimal average distortion bounds for general distributions using a simple randomized mechanism that makes one query per agent. We complement these results by presenting new tradeoffs between the distortion and the number of queries per agent in the traditional worst-case setting.

cs.GT↗

arXiv2024

Welfare-Optimal Serial Dictatorships have Polynomial Query Complexity

Serial dictatorship is a simple mechanism for coordinating agents in solving combinatorial optimization problems according to their preferences. The most representative such problem is one-sided matching, in which a set of n agents have values for a set of n items, and the objective is to compute a matching of the agents to the items of maximum total value (a.k.a., social welfare). Following the recent framework of Caragiannis and Rathi [10], we consider a model in which the agent-item values are not available upfront but become known by querying agent sequences. In particular, when the agents are asked to act in a sequence, they respond by picking their favorite item that has not been picked by agents who acted before and reveal their value for it. Can we compute an agent sequence that induces a social welfare-optimal matching? We answer this question affirmatively and present an algorithm that uses polynomial number (n^5) of queries. This solves the main open problem stated by Caragiannis and Rathi [CR23]. Our analysis uses a potential function argument that measures progress towards learning the underlying edge-weight information. Furthermore, the algorithm has a truthful implementation by adapting the paradigm of VCG payments.

cs.GT↗