Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.19488

What You Earn from What You Learn: Characterization and Complexity of the Value of Information

Ratip Emin Berker·Ioannis Anagnostides·Emanuel Tewolde·Brian Hu Zhang·Tuomas Sandholm·Vincent Conitzer
View original source ↗Read source document ↗Export metadata ↓

Abstract

We examine the value of information in extensive-form decision problems: the largest multiplicative gain that a decision maker can obtain from an information refinement, taken over all payoff environments. This measures the structural importance of information disentangled from any particular payoff specification, and generalizes the notion of value of recall recently introduced by Berker et al. (AAAI'25). We establish a unifying characterization of the value of information under any information refinement, uncovering an intriguing connection to the maximum fractional chromatic number over a certain family of conflict graphs. We then employ our characterization to elucidate the complexity of two central information refinements. First, for the value of perfect information in perfect-recall decision problems, we find that the relevant conflict graphs are cographs, so the fractional chromatic number collapses to the clique number. Even though the clique number is tractable for a given cograph, we show that the additional layer of optimization (over the family of graphs) makes computing the value of perfect information NP-complete. On the positive side, we prove fixed-parameter tractability in terms of the degree of imperfect information. Second, for the value of recall in imperfect-recall decision problems (with no absentmindedness), we first show that the value of recall can realize the fractional chromatic number of any graph. Interestingly, this implies that, unlike the value of perfect information, the value of recall can take fractional values. Building on this reduction, we then establish S2P-completeness. This addresses questions left open by Berker et al. (AAAI'25)---both on the characterization and the complexity of the value of recall---and shows that computing the value of recall is strictly harder than the value of perfect information.

Explore related subjects

cs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ratip Emin Berker, Ioannis Anagnostides, Emanuel Tewolde, Brian Hu Zhang, Tuomas Sandholm, Vincent Conitzer. 2026-10-14. What You Earn from What You Learn: Characterization and Complexity of the Value of Information. https://arxiv.org/abs/2610.19488

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Incentivize Contribution and Learn Parameters Too: Federated Learning with Strategic Data Owners

In federated learning (FL), a center trains a shared model from updates that clients compute on their private data. Collecting and training on data is costly, so a strategic client may contribute little data and free-ride on the model trained by the others. We study mechanisms that incentivize data contribution and learn the model at the same time. Our first mechanism, UPBReD, updates the clients ' contributions and the model jointly, and converges at a geometric rate to a Nash equilibrium of the contribution game together with the welfare-maximizing model for those contributions. This equilibrium can involve under-contribution, so our second mechanism, 2P-UPBReD, adds budget-balanced transfers that make full contribution a dominant strategy, after which training converges to the optimal model; we also give conditions under which every client prefers to participate. Both mechanisms trust what clients report about the data they use and the gradients they compute. We show that no payment rule can reward unverifiable contributions unless something the center observes depends on the data actually used. Building on this, T-2P-UPBReD checks each client's reported contribution against the other clients ' realized valuations of the trained model, and prices gradient reports with a budget-balanced charge. It elicits truthful contribution reports, makes gradient reports approximately truthful, still reaches full contribution and the optimal model, and never runs a deficit. Experiments on CIFAR-10, FEMNIST, and Twitter show that 2P-UPBReD matches the welfare of FedAvg trained on all data, while strategic clients without incentives lower the welfare of the learned model.

cs.GT↗
arXiv2026

Likes, Budgets, and Equilibria: Designing Contests for Socially Optimal Advertising

We study competitive advertising on a social network. Each of $m$ firms allocates a budget across consumers, and a platform decides, through a contest success function (CSF), what share of each consumer's attention every firm captures; awareness then spreads through the network. We model awareness and budgets on two timescales and bound how many fast steps awareness needs to settle between budget updates. On the slow timescale, best-response dynamics converge at a geometric rate to a Nash equilibrium whenever the firms' utilities are strongly concave and smooth, and a subclass of the standard ratio-form CSFs satisfies these conditions. Their equilibrium, however, need not maximize welfare: a firm's spending lowers its rivals' shares of attention, so individual and social optima differ, and a constant per-unit charge cannot close this gap in general. We give a sufficient condition for the equilibrium to coincide with the welfare optimum. To meet it, we multiply each firm's ratio share by a function of the total spending at the consumer, a class we call scaled ratio CSFs (SRCSFs), and show that within this class the condition holds exactly when this function is a power of the total spending, which gives the Power RCSF. The Power RCSF alone falls short in two ways. Its equilibrium is optimal only when firms exhaust their budgets, which we remove with a budget-balanced per-unit charge. Its curvature also becomes unbounded as spending at a consumer approaches zero, breaking convergence, which we restore by requiring every firm to spend a small minimum on each consumer. With both additions, best-response dynamics converge to a unique, symmetric equilibrium that maximizes $p$-mean social welfare for every $p \le 1$ simultaneously, so the Price of Anarchy is one.

cs.GT↗
arXiv2026

Fair Allocation with Dichotomous Preferences over Item Complements

We study the problem of fair allocation when agents have dichotomous submodular preferences over groups of, rather than individual, items. These preferences naturally extend existing models, and have a natural interpretation in settings such as course allocation. We show that this seemingly minor extension results in computational intractability barriers: computing a utilitarian or Nash-optimal allocation with item complements is NP-hard. However, when agents' complementary bundles have size at most $k$, there exist poly-time algorithms that compute $\frac1k$-$\texttt{maxUSW}$ allocations and approximate Nash-welfare-maximizing allocations. While PO+EF-1 allocations may not exist in the complementary preference setting, it is possible to compute $\frac1{k+1}$-approximately $\texttt{maxUSW}$ EF-X allocations in polynomial time; furthermore, these allocations offer each agent $i$ a utility of at least $\frac{\texttt{MMS}_i - k}{k+1 + \frac1n}$, where $\texttt{MMS}_i$ is agent $i$'s maximin share guarantee. While the standard dichotomous binary submodular setting admits simple sequential techniques for computing fair and efficient allocations, our results for the complements setting require more complex tools from combinatorial optimization.

cs.GT↗