ICM 2026 Invited Section Lecture - Michal Feldman

ICM 2026 Invited Section Lecture - Michal Feldman

Formal & Physical Sciences Mathematics PBUOptimizationPBUDGame theory
🎙 Michal Feldman 👥 60K 📅 September 14, 2026 ⏱ 56 min 👁 4 📄 literature review 🧭 2026-09-14
Available in: English (current) Français

Keywords

contract theoryalgorithmic mechanism designmoral hazardgross substitutesapproximation algorithms

Summary

This invited lecture at ICM 2026 by Michal Feldman surveys the emerging field of combinatorial contract design, where a principal incentivizes agents whose actions are hidden and combinatorial. After motivating with examples such as influencer marketing, Feldman formalizes the setting: a single principal, agents with sets of actions, and contracts specifying payments based on observed outcomes. He introduces two sources of complexity: a single agent selecting multiple actions, and multiple interacting agents. The core results revolve around tractability of computing optimal contracts under different classes of reward functions, notably gross substitutes, for which he sketches a proof using three ingredients: poly many critical values, efficient best-response computation via greedy algorithms, and recursive enumeration of critical points. He also presents hardness results for submodular functions, extensions to supermodular and more general classes, and discusses the multi-agent extension where contracts induce a game. The talk concludes with open questions about the tractability frontier and the role of oracle access.

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Critical Evaluation

Value of the Information & Strength of the Argument

The lecture provides a comprehensive and up-to-date overview of algorithmic contract design, emphasizing computational complexity and approximation. The argumentation is rigorous, proceeding from a clear model to theorems and proof sketches. Feldman connects the area to classical contract theory, algorithmic mechanism design, and combinatorial markets, giving it strong intellectual context. He clearly distinguishes algorithmic tractability from impossibility, and highlights the importance of oracle models. The talk is interactive, though the core value lies in the precise statements and relationships between function classes.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is evident: results are attributed to specific papers (e.g., the 2006 combinatorial agency paper, works by Dutting, Roughgarden, Talgam-Cohen, and the speaker’s own collaborations). References to Gul and Stacchetti for gross substitutes and to Baldwin and Klemperer for demand types demonstrate command of the literature. The title accurately reflects the content; no discrepancies were noted. As an invited lecture at a major mathematics congress, the source is authoritative. Public comments are not available for analysis.

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Title / Content Match

The video title accurately describes the content: an invited lecture at ICM 2026 by Michal Feldman. The specific topic (combinatorial contract design) is provided in the description.

Quality & Reliability

9/10

The lecture is given by an expert researcher at an ICM invited section, based on published papers and rigorous theoretical work. The reasoning is formal and well-supported.

Key Moments

Cited Sources

  • Combinatorial agency (2006) - Babaioff, Feldman, Nisan — Referenced as the starting point for the speaker's research on incentivizing teams with combinatorial interactions.
  • Simple versus optimal contracts (Dutting, Roughgarden, Talgam-Cohen) — Cited as important recent work that revived interest in algorithmic contract design around 2019-2020.
  • Gul and Stacchetti (1999) - on gross substitutes — Used to compute agent best response via greedy algorithm, a key step in the proof for gross substitutes.
  • Baldwin and Klemperer - Demand types — Their geometric characterization of set functions is used to extend tractability to larger classes like ASC.
  • Sun and Yang - Gross substitutes and complements — Their class is shown to be included in the ASC class for which polynomial critical values exist.

Concurring Sources

Contribution & Novelties

The lecture synthesizes recent work by the speaker and collaborators, presenting a coherent landscape for computing optimal contracts under combinatorial action sets. The key novelty is the identification of tractability boundaries (e.g., gross substitutes vs. submodular) and the use of oracle models to refine algorithmic results. The multi-agent extension, where contracts induce games, is a fresh perspective combining contract theory with game theory.

Pour aller plus loin :

109 words

Radar Profile

The scores are uniformly high, reflecting a dense theoretical lecture with strong quantitative and qualitative content, high technical level, and reliable sourcing. The slight dip in adventure/tractability is compensated by the depth of formal analysis.

Reliability 9/10