arXiv subjects

Emmanouil Pountourakis

Publications and source records attributed to Emmanouil Pountourakis.

At least 19 recordsLinked to original sources

arXiv2026

Knapsack Secretary is not $1/e$-Competitive

We prove that no algorithm for the knapsack secretary problem can be $1/e$-competitive. The knapsack secretary problem was first introduced by Babaioff, Immorlica, Kempe, and Kleinberg (2007). There have been many improvements to the achievable competitive ratio since then, but the $1/e$ impossibility barrier has remained unchanged. Many combinatorial variants of the secretary problem, including knapsack secretary, inherit the $1/e$ impossibility by embedding the single-choice problem as a special case. We construct a family of hard instances for the $1$-$B$ knapsack secretary problem, which is a special case of the general knapsack secretary problem, to improve the existing impossibility result. We show in this special case that the competitive ratio is at most $0.36437 < \frac{1}{e} - 0.0035$. Our construction is similar to the one used by Abels, Ladewig, Schewior, and Stinzendörfer (2022), for which they show an impossibility of $1/(1+e)$ for ordinal algorithms, where only the relative ranks of the items are known. Our work resolves an open question of theirs by showing that $1/e$ cannot be achieved even in the cardinal case of the $1$-$B$ knapsack secretary problem. We complement our impossibility result with a simple algorithm for $1$-$B$ knapsack secretary that is $(1/5.10-o(1))$-competitive for every fixed $B \geq 2$. This improves the guarantee obtained by applying general-purpose random-order knapsack algorithms to this special case.

cs.DS↗

arXiv2025

Repeated Sales with Heterogeneous Buyer Sophistication

This paper considers behavior-based price discrimination in the repeated sale of a non-durable good to a single long-lived buyer, by a seller without commitment power. We assume that there is a mixed population of forward-looking ``sophisticated'' buyers and myopic ``naive'' buyers. We investigate the impact of these dynamics on the seller's ability to learn about the buyer and exploit this learning for revenue. We obtain conclusions that differ dramatically with the time horizon of the interactions. To understand short time horizons, we analyze a two-period model, and find that the strategic demand reduction observed with fully sophisticated buyers is robust to the introduction of naive types. In fact, despite the inability of naive buyers to game the pricing algorithm, their introduction can further harm the seller's revenue, due to more intense demand reduction overall. For long horizons, we consider an infinite-horizon model with time discounting. We find that the extreme demand reduction predicted by previous work does not survive the introduction of naive buyers. Instead, we observe equilibria where the seller learns meaningfully despite the sophisticated buyers' demand reduction. We prove that for a natural family of such equilibria, the seller's revenue is not just high, but approximates the revenue attainable with commitment power, even when the fraction of naive types is vanishingly small.

cs.GT↗

arXiv2025

Polynomial-Time Approximation Schemes via Utility Alignment: Unit-Demand Pricing and More

This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller optimizing with respect to a subsequent choice by an agent or buyer. These include posted pricing for a unit-demand buyer with independent values (Chawla et al., 2007, Cai and Daskalakis, 2011), assortment optimization with independent utilities (Talluri and van Ryzin, 2004), and delegated choice (Khodabakhsh et al., 2024). Our results advance the state of the art for each of these problems. For unit-demand pricing with discrete distributions, our multiplicative PTAS improves on the additive PTAS of Cai and Daskalakis, and we additionally give a PTAS for the unbounded regular case, improving on the latter paper's QPTAS. For assortment optimization, no constant approximation was previously known. For delegated choice, we improve on both the $3$-approximation for the case with no outside option and the super-constant-approximation with an outside option. A key technical insight driving our results is an economically meaningful property we term utility alignment. Informally, a problem is utility aligned if, at optimality, the principal derives most of their utility from realizations where the agent's utility is also high. Utility alignment allows the algorithm designer to focus on maximizing performance on realizations with high agent utility, which is often an algorithmically simpler task. We prove utility alignment results for all the problems mentioned above, including strong results for unit-demand pricing and delegation, as well as a weaker but very broad guarantee that holds for many other problems under very mild conditions.

cs.GT↗

arXiv2024

The Price of Pessimism for Automated Defense

The well-worn George Box aphorism ``all models are wrong, but some are useful'' is particularly salient in the cybersecurity domain, where the assumptions built into a model can have substantial financial or even national security impacts. Computer scientists are often asked to optimize for worst-case outcomes, and since security is largely focused on risk mitigation, preparing for the worst-case scenario appears rational. In this work, we demonstrate that preparing for the worst case rather than the most probable case may yield suboptimal outcomes for learning agents. Through the lens of stochastic Bayesian games, we first explore different attacker knowledge modeling assumptions that impact the usefulness of models to cybersecurity practitioners. By considering different models of attacker knowledge about the state of the game and a defender's hidden information, we find that there is a cost to the defender for optimizing against the worst case.

cs.CR↗

arXiv2024

Simple Delegated Choice

This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a $3$-approximation. When the agent has an outside option the principal cannot rule out, the constant approximation fails, but we prove a $\log ρ/\log\log ρ$-approximation, where $ρ$ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new.

cs.GT↗

arXiv2024

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy, reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

cs.DS↗

arXiv2024

An impossibility result for strongly group-strategyproof multi-winner approval-based voting

Multi-winner approval-based voting has received considerable attention recently. A voting rule in this setting takes as input ballots in which each agent approves a subset of the available alternatives and outputs a committee of alternatives of given size $k$. We consider the scenario when a coalition of agents can act strategically and alter their ballots so that the new outcome is strictly better for a coalition member and at least as good for anyone else in the coalition. Voting rules that are robust against this strategic behaviour are called strongly group-strategyproof. We prove that, for $k\in \{1,2, ..., m-2\}$, strongly group-strategyproof multi-winner approval-based voting rules which furthermore satisfy the minimum efficiency requirement of unanimity do not exist, where $m$ is the number of available alternatives. Our proof builds a connection to single-winner voting with ranking-based ballots and exploits the infamous Gibbard-Satterthwaite theorem to reach the desired impossibility result. Our result has implications for paradigmatic problems from the area of approximate mechanism design without money and indicates that strongly group-strategyproof mechanisms for minimax approval voting, variants of facility location, and classification can only have an unbounded approximation ratio.

cs.GT↗

arXiv2022

Simulation of Attacker Defender Interaction in a Noisy Security Game

In the cybersecurity setting, defenders are often at the mercy of their detection technologies and subject to the information and experiences that individual analysts have. In order to give defenders an advantage, it is important to understand an attacker's motivation and their likely next best action. As a first step in modeling this behavior, we introduce a security game framework that simulates interplay between attackers and defenders in a noisy environment, focusing on the factors that drive decision making for attackers and defenders in the variants of the game with full knowledge and observability, knowledge of the parameters but no observability of the state (``partial knowledge''), and zero knowledge or observability (``zero knowledge''). We demonstrate the importance of making the right assumptions about attackers, given significant differences in outcomes. Furthermore, there is a measurable trade-off between false-positives and true-positives in terms of attacker outcomes, suggesting that a more false-positive prone environment may be acceptable under conditions where true-positives are also higher.

cs.CR↗

arXiv2022

Optimal Data Acquisition with Privacy-Aware Agents

We study the problem faced by a data analyst or platform that wishes to collect private data from privacy-aware agents. To incentivize participation, in exchange for this data, the platform provides a service to the agents in the form of a statistic computed using all agents' submitted data. The agents decide whether to join the platform (and truthfully reveal their data) or not participate by considering both the privacy costs of joining and the benefit they get from obtaining the statistic. The platform must ensure the statistic is computed differentially privately and chooses a central level of noise to add to the computation, but can also induce personalized privacy levels (or costs) by giving different weights to different agents in the computation as a function of their heterogeneous privacy preferences (which are known to the platform). We assume the platform aims to optimize the accuracy of the statistic, and must pick the privacy level of each agent to trade-off between i) incentivizing more participation and ii) adding less noise to the estimate. We provide a semi-closed form characterization of the optimal choice of agent weights for the platform in two variants of our model. In both of these models, we identify a common nontrivial structure in the platform's optimal solution: an instance-specific number of agents with the least stringent privacy requirements are pooled together and given the same weight, while the weights of the remaining agents decrease as a function of the strength of their privacy requirement. We also provide algorithmic results on how to find the optimal value of the noise parameter used by the platform and of the weights given to the agents.

cs.GT↗

arXiv2022

Eliciting Truthful Reports with Partial Signals in Repeated Games

We consider a repeated game where a player self-reports her usage of a service and is charged a payment accordingly by a center. The center observes a partial signal, representing part of the player's true consumption, which is generated from a publicly known distribution. The player can report any value that does not contradict the signal and the center issues a payment based on the reported information. Such problems find application in net metering billing in the electricity market, where a customer's actual consumption of the electricity network is masked and complete verification is impractical. When the underlying true value is relatively constant, we propose a penalty mechanism that elicits truthful self-reports. Namely, besides charging the player the reported value, the mechanism charges a penalty proportional to her inconsistent reports. We show how fear of the uncertainty in the future incentivizes the player to be truthful today. For Bernoulli distributions, we give the complete analysis and optimal strategies given any penalty. Since complete truthfulness is not possible for continuous distributions, we give approximate truthful results by a reduction from Bernoulli distributions. We also extend our mechanism to a multi-player cost sharing setting and give equilibrium results.

cs.GT↗

arXiv2021

Single-Sample Prophet Inequalities Revisited

The study of the prophet inequality problem in the limited information regime was initiated by Azar et al. [SODA'14] in the pursuit of prior-independent posted-price mechanisms. As they show, $O(1)$-competitive policies are achievable using only a single sample from the distribution of each agent. A notable portion of their results relies on reducing the design of single-sample prophet inequalities (SSPIs) to that of order-oblivious secretary (OOS) policies. The above reduction comes at the cost of not fully utilizing the available samples. However, to date, this is essentially the only method for proving SSPIs for many combinatorial sets. Very recently, Rubinstein et al. [ITCS'20] give a surprisingly simple algorithm which achieves the optimal competitive ratio for the single-choice SSPI problem $-$ a result which is unobtainable going through the reduction to secretary problems. Motivated by this discrepancy, we study the competitiveness of simple SSPI policies directly, without appealing to results from OOS literature. In this direction, we first develop a framework for analyzing policies against a greedy-like prophet solution. Using this framework, we obtain the first SSPI for general (non-bipartite) matching environments, as well as improved competitive ratios for transversal and truncated partition matroids. Second, motivated by the observation that many OOS policies for matroids decompose the problem into independent rank-$1$ instances, we provide a meta-theorem which applies to any matroid satisfying this partition property. Leveraging the recent results by Rubinstein et al., we obtain improved competitive guarantees (most by a factor of $2$) for a number of matroids captured by the reduction of Azar et al. Finally, we discuss applications of our SSPIs to the design of mechanisms for multi-dimensional limited information settings with improved revenue and welfare guarantees.

cs.GT↗

arXiv2021

Prior-Free Clock Auctions for Bidders with Interdependent Values

We study the problem of selling a good to a group of bidders with interdependent values in a prior-free setting. Each bidder has a signal that can take one of $k$ different values, and her value for the good is a weakly increasing function of all the bidders' signals. The bidders are partitioned into $\ell$ expertise-groups, based on how their signal can impact the values for the good, and we prove upper and lower bounds regarding the approximability of social welfare and revenue for a variety of settings, parameterized by $k$ and $\ell$. Our lower bounds apply to all ex-post incentive compatible mechanisms and our upper bounds are all within a small constant of the lower bounds. Our main results take the appealing form of ascending clock auctions and provide strong incentives by admitting the desired outcomes as obvious ex-post equilibria.

cs.GT↗

arXiv2021

Resource-Aware Cost-Sharing Mechanisms with Priors

In a decentralized system with $m$ machines, we study the selfish scheduling problem where each user strategically chooses which machine to use. Each machine incurs a cost, which is a function of the total load assigned to it, and some cost-sharing mechanism distributes this cost among the machine's users. The users choose a machine aiming to minimize their own share of the cost, so the cost-sharing mechanism induces a game among them. We approach this problem from the perspective of a designer who can select which cost-sharing mechanism to use, aiming to minimize the price of anarchy (PoA) of the induced games. Recent work introduced the class of \emph{resource-aware} cost-sharing mechanisms, whose decisions can depend on the set of machines in the system, but are oblivious to the total number of users. These mechanisms can guarantee low PoA bounds for instances where the cost functions of the machines are all convex or concave, but can suffer from very high PoA for cost functions that deviate from these families. In this paper we show that if we enhance the class of resource-aware mechanisms with some prior information regarding the users, then they can achieve low PoA for a much more general family of cost functions. We first show that, as long as the mechanism knows just two of the participating users, then it can assign special roles to them and ensure a constant PoA. We then extend this idea to settings where the mechanism has access to the probability with which each user is present in the system. For all these instances, we provide a mechanism that achieves an expected PoA that is logarithmic in the expected number of users.

cs.GT↗

arXiv2018

Electric Vehicle Valet

We propose a novel way to use Electric Vehicles (EVs) as dynamic mobile energy storage with the goal to support grid balancing during peak load times. EVs seeking parking in a busy/expensive inner city area, can get free parking with a valet company in exchange for being utilized for grid support. The valet company would have an agreement with the local utility company to receive varying rewards for discharging EVs at designated times and locations of need (say, where power lines are congested). Given vehicle availabilities, the valet company would compute an optimal schedule of which vehicle to utilize where and when so as to maximize rewards collected. Our contributions are a detailed description of this new concept along with supporting theory to bring it to fruition. On the theory side, we provide new hardness results, as well as efficient algorithms with provable performance guarantees that we also test empirically.

math.OC↗

arXiv2018

Optimal Mechanism Design with Risk-loving Agents

One of the most celebrated results in mechanism design is Myerson's characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In this paper we investigate the case where the buyers are risk-loving, i.e. they prefer gambling to being rewarded deterministically. We use the standard model for risk from expected utility theory, where risk-loving behavior is represented by a convex utility function. We focus our attention on the special case of exponential utility functions. We characterize the optimal auction and show that randomization can be used to extract more revenue than when buyers are risk-neutral. Most importantly, we show that the optimal auction is simple: the optimal revenue can be extracted using a randomized take-it-or-leave-it price for a single buyer and using a loser-pay auction, a variant of the all-pay auction, for multiple buyers. Finally, we show that these results no longer hold for convex utility functions beyond exponential.

cs.GT↗

arXiv2018

Revenue Maximization with an Uncertainty-Averse Buyer

Most work in mechanism design assumes that buyers are risk neutral; some considers risk aversion arising due to a non-linear utility for money. Yet behavioral studies have established that real agents exhibit risk attitudes which cannot be captured by any expected utility model. We initiate the study of revenue-optimal mechanisms under buyer behavioral models beyond expected utility theory. We adopt a model from prospect theory which arose to explain these discrepancies and incorporates agents under-weighting uncertain outcomes. In our model, an event occurring with probability $x < 1$ is worth strictly less to the agent than $x$ times the value of the event when it occurs with certainty. In contrast to the risk-neutral setting, the optimal mechanism may be randomized and appears challenging to find, even for a single buyer and a single item for sale. Nevertheless, we give a characterization of the optimal mechanism which enables positive approximation results. In particular, we show that under a reasonable bounded-risk-aversion assumption, posted pricing obtains a constant approximation. Notably, this result is "risk-robust" in that it does not depend on the details of the buyer's risk attitude. Finally, we examine a dynamic setting in which the buyer is uncertain about his future value. In contrast to positive results for a risk-neutral buyer, we show that the buyer's risk aversion may prevent the seller from approximating the optimal revenue in a risk-robust manner.

cs.GT↗

arXiv2017

A Submodular Approach for Electricity Distribution Network Reconfiguration

Distribution network reconfiguration (DNR) is a tool used by operators to balance line load flows and mitigate losses. As distributed generation and flexible load adoption increases, the impact of DNR on the security, efficiency, and reliability of the grid will increase as well. Today, heuristic-based actions like branch exchange are routinely taken, with no theoretical guarantee of their optimality. This paper considers loss minimization via DNR, which changes the on/off status of switches in the network. The goal is to ensure a radial final configuration (called a spanning tree in the algorithms literature) that spans all network buses and connects them to the substation (called the root of the tree) through a single path. We prove that the associated combinatorial optimization problem is strongly NP-hard and thus likely cannot be solved efficiently. We formulate the loss minimization problem as a supermodular function minimization under a single matroid basis constraint, and use existing algorithms to propose a polynomial time local search algorithm for the DNR problem at hand and derive performance bounds. We show that our algorithm is equivalent to the extensively used branch exchange algorithm, for which, to the best of our knowledge, we pioneer in proposing a theoretical performance bound. Finally, we use a 33-bus network to compare our algorithm's performance to several algorithms published in the literature.

math.OC↗

arXiv2016

Procrastination with variable present bias

Individuals working towards a goal often exhibit time inconsistent behavior, making plans and then failing to follow through. One well-known model of such behavioral anomalies is present-bias discounting: individuals over-weight present costs by a bias factor. This model explains many time-inconsistent behaviors, but can make stark predictions in many settings: individuals either follow the most efficient plan for reaching their goal or procrastinate indefinitely. We propose a modification in which the present-bias parameter can vary over time, drawn independently each step from a fixed distribution. Following Kleinberg and Oren (2014), we use a weighted task graph to model task planning, and measure the cost of procrastination as the relative expected cost of the chosen path versus the optimal path. We use a novel connection to optimal pricing theory to describe the structure of the worst-case task graph for any present-bias distribution. We then leverage this structure to derive conditions on the bias distribution under which the worst-case ratio is exponential (in time) or constant. We also examine conditions on the task graph that lead to improved procrastination ratios: graphs with a uniformly bounded distance to the goal, and graphs in which the distance to the goal monotonically decreases on any path.

cs.GT↗