arXiv subjects

Maya Schlesinger

Publications and source records attributed to Maya Schlesinger.

6 recordsLinked to original sources

arXiv2026

Combinatorial Contracts Through Demand Types

In the combinatorial action model of contract design, a principal delegates a complex project to an agent, incentivizing a subset of actions from a ground set of $n$ actions, via a linear contract. Computing the optimal contract is a challenging problem that generally hinges on two factors: (i) the number of "critical values" - values of the linear contract parameter at which the agent's best response changes from one set to another, and (ii) the complexity of the agent's best-response problem (demand query). Prior work has used this approach to devise polynomial-time algorithms for the optimal contract problem under specific reward functions: gross substitutes, supermodular, and ultra. We develop a unified geometric framework for algorithmic contract design by establishing a fundamental link to the theory of demand types from consumer theory. Under this geometric view, bounding the number of critical values reduces to counting the best-response regions which the "contract ray" pierces. Leveraging this connection, we introduce the class of All Substitutes and Complements (ASC) functions, and show that it admits at most $O(n^2)$ critical values, strictly generalizing and unifying all previously known classes admitting poly-many critical values. We conjecture that, under some mild assumptions, ASC is the maximal such class. Turning to the demand query aspect, we develop a new technique for efficiently computing a demand query using value queries, which works in general for "succinct" demand types. Combining these structural and algorithmic results, we obtain polynomial-time algorithms for new classes of reward functions that exhibit substitutes and complements simultaneously.

cs.GT↗

arXiv2026

Equal-Pay Contracts

We study multi-agent contract design, where a principal incentivizes a team of agents to take costly actions that jointly determine the project success via a combinatorial reward function. While prior work largely focuses on unconstrained contracts that allow heterogeneous payments across agents, many real-world environments limit payment dispersion. Motivated by this, we study equal-pay contracts, where all agents receive identical payments. Our results also extend to nearly-equal-pay contracts where any two payments are identical up to a constant factor. We provide both algorithmic and hardness results across a broad hierarchy of reward functions, under both binary and combinatorial action models. While we focus on equal-pay contracts, our analysis also yields new insights into unconstrained contract design, and resolves two important open problems. On the positive side, we design polynomial-time O(1)-approximation algorithms for (i) submodular rewards under combinatorial actions, and (ii) XOS rewards under binary actions. These guarantees are tight: We rule out the existence of (i) a PTAS for combinatorial actions, even for gross substitutes rewards (unless P = NP), and (ii) any O(1)-approximation for XOS rewards with combinatorial actions. Crucially, our hardness results hold even for unconstrained contracts, thereby settling the corresponding open problems in this setting. Finally, we quantify the loss induced by fairness via the price of equality, defined as the worst-case ratio between the optimal principal's utility achievable by unconstrained contracts and that achievable by equal-pay contracts. We obtain a bound of $\Theta(\log n/ \log \log n)$, where $n$ is the number of agents. This gap is tight in a strong sense: the upper bound applies even for XOS rewards with combinatorial actions, while the lower bound arises already for additive rewards with binary actions.

cs.GT↗

arXiv2025

One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts

We study multi-agent contract design with combinatorial actions, under budget constraints, and for a broad class of objective functions, including profit (principal's utility), reward, and welfare. Our first result is a strong impossibility: For submodular reward functions, no randomized poly-time algorithm can approximate the optimal budget-feasible value within \textit{any finite factor}, even with demand-oracle access. This result rules out extending known constant-factor guarantees from either (i) unbudgeted settings with combinatorial actions or (ii) budgeted settings with binary actions, to their combination. The hardness is tight: It holds even when all but one agent have binary actions and the remaining agent has just one additional action. On the positive side, we show that gross substitutes rewards (a well-studied strict subclass of submodular functions) admit a deterministic poly-time $O(1)$-approximation, using only value queries. Our results thus draw the first sharp separation between budgeted and unbudgeted settings in combinatorial contracts, and identifies gross substitutes as a tractable frontier for budgeted combinatorial contracts. Finally, we present an FPTAS for additive rewards, demonstrating that arbitrary approximation is tractable under any budget. This constitutes the first FPTAS for the multi-agent combinatorial-actions setting, even in the absence of budget constraints.

cs.GT↗

arXiv2025

Budget-Feasible Contracts

The problem of computing near-optimal contracts in combinatorial settings has recently attracted significant interest in the computer science community. Previous work has provided a rich body of structural and algorithmic insights into this problem. However, most of these results rely on the assumption that the principal has an unlimited budget for incentivizing agents, an assumption that is often unrealistic in practice. This motivates the study of the optimal contract problem under budget constraints. In this work, we study multi-agent contracts with binary actions under budget constraints. Our contribution is threefold. First, we show that all previously known approximation guarantees on the principal's utility extend (asymptotically) to budgeted settings. Second, through the lens of budget constraints, we uncover insightful connections between the standard objective of maximizing the principal's utility and other relevant objectives. Specifically, we identify a broad class of objectives, which we term BEST (BEyond STandard) objectives, including reward, social welfare, and principal's utility, and show that they are all equivalent (up to a constant factor), leading to approximation guarantees for all BEST objectives. Third, we introduce the price of frugality, which quantifies the loss due to budget constraints, and establish near-tight bounds on this measure, providing deeper insights into the tradeoffs between budgets and incentives.

cs.GT↗

arXiv2024

Contract Design for Sequential Actions

We introduce a novel model of contracts with combinatorial actions that accounts for sequential and adaptive agent behavior. As in the standard model, a principal delegates the execution of a costly project to an agent. There are $n$ actions, each one incurring a cost to the agent and inducing a probability distribution over $m$ outcomes; each outcome generates some reward for the principal. The principal incentivizes the agent through a contract that specifies a payment for each potential outcome. Unlike the standard model, the agent chooses actions sequentially. Following each action, the agent observes the realized outcome, and decides whether to stop or continue with another action. Upon halting, the agent chooses one of the realized outcomes, which determines both his payment and the principal's reward. This model captures common scenarios where the agent can make multiple attempts in the course of executing a project. We study the optimal contract problem in this new setting, namely the contract that maximizes the principal's utility. We first observe that the agent's problem - (adaptively) finding the sequence of actions that maximizes his utility for a given contract - is equivalent to the well-known Pandora's Box problem. Using this insight, we provide algorithms and hardness results for the optimal contract problem, under both independent and correlated actions, and for both linear and general contracts. For independent actions, we provide a poly-time algorithm for the optimal linear contract, and establish that finding the optimal general contract is NP-hard. In cases where the number of outcomes is constant, we devise a poly-time algorithm even for the optimal general contract. For correlated actions, we find that, for both linear and general contracts, approximating the optimal contract within any constant ratio is NP-hard.

cs.GT↗

arXiv2023

On the (In)approximability of Combinatorial Contracts

We study two combinatorial contract design models -- multi-agent and multi-action -- where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project's outcome (success or failure), and incentivizes the agent(s) using a contract, which is a payment scheme that specifies the payment to the agent(s) upon a project's success. In the multi-agent setting, the project is delegated to a team of agents, and every agent chooses whether or not to exert effort. A success probability function specifies the probability of success for every subset of agents exerting effort. For the family of submodular success probability functions, Duetting et al. [2023] established a poly-time constant-factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We show that no poly-time algorithm guarantees a better than $0.7$-approximation to the optimal contract. For XOS functions, Duetting et al. [2023] give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function specifies the probability of success for any subset of actions. Duetting et al. [2021a] devised a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and established NP-hardness with respect to submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant approximation either. For the broader class of XOS functions, we establish the hardness of obtaining a $n^{-1/2+\varepsilon}$-approximation for any $\varepsilon > 0$.

cs.GT↗