Paper Citation Record · LEDGER

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method

As of 9 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 3 inbound Pith citation observations for arXiv:2509.08161.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.08161 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:22:14.195148Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T14:21:43.409685Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-03T13:38:19.160441Z

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy26
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 09749d3d-4b6f-4fe6-b6b7-61bfb44332e0 · outbound

This paper cites Differentiable convex optimization layers.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Differentiable convex optimization layers

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.027819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 066e6031-7b78-4cd2-8baf-93c3684c098c · outbound

This paper cites Optnet: Differentiable optimization as a layer in neural networks.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Optnet: Differentiable optimization as a layer in neural networks

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.032836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13c4458f-d679-4134-b431-9ea337e83f06 · outbound

This paper cites Stackelberg security games (ssg) basics and application overview.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Stackelberg security games (ssg) basics and application overview

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.952028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 51a823f3-4667-466a-b1c5-7f5698f4d599 · outbound

This paper cites Sample-efficient learning of stackelberg equilibria in general-sum games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Sample-efficient learning of stackelberg equilibria in general-sum games

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.936339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b668cb3f-e675-4de7-be50-ed10faa8f5b3 · outbound

This paper cites Ba s ar and R.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Ba s ar and R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.920840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 321475d3-3d66-41e9-9295-1ad2bfc4b25d · outbound

This paper cites On Stackelberg--Nash Equilibria in Bilevel Optimization Games, pages 27--51.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method On Stackelberg--Nash Equilibria in Bilevel Optimization Games, pages 27--51

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.903311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fd49172d-7cbb-409e-a943-a827a1d34ad1 · outbound

This paper cites Doubly optimal no-regret learning in monotone games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Doubly optimal no-regret learning in monotone games

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.888468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3fcc6500-6262-4423-9c00-d85034c6566c · outbound

This paper cites Near-optimal nonconvex-strongly-convex bilevel optimization with fully first-order oracles.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Near-optimal nonconvex-strongly-convex bilevel optimization with fully first-order oracles

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.873381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b811e213-238c-495d-b210-ae68ce815790 · outbound

This paper cites Finite--Dimensional Variational Inequalities and Complementarity Problems, volume 1 of Springer Series in Operations Research and Financial Engineering.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Finite--Dimensional Variational Inequalities and Complementarity Problems, volume 1 of Springer Series in Operations Research and Financial Engineering

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.857926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2782d914-a3d3-4fc8-9b2b-3e640db6e1b0 · outbound

This paper cites Convergence of Learning Dynamics in Stackelberg Games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Convergence of Learning Dynamics in Stackelberg Games

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.071688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f09e040-5266-4ed0-a950-5292ea3590f3 · outbound

This paper cites Implicit learning dynamics in stackelberg games: Equilibria and convergence.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Implicit learning dynamics in stackelberg games: Equilibria and convergence

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.840395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7f02feea-687f-451e-b559-b74738d75a22 · outbound

This paper cites Continuous-time convergence rates in potential and monotone games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Continuous-time convergence rates in potential and monotone games

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.825234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5a0a139b-bb74-459e-a93d-1abfcfcc4c0e · outbound

This paper cites Oracles & followers: Stackelberg equilibria in deep multi-agent reinforcement learning.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Oracles & followers: Stackelberg equilibria in deep multi-agent reinforcement learning

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.808150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f4735e7d-c00e-4d40-92d6-f36937e9f3ed · outbound

This paper cites Approximation Methods for Bilevel Programming.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Approximation Methods for Bilevel Programming

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.091678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09782ba1-63a8-4187-ab3f-3ba3ae3daa30 · outbound

This paper cites Zero-sum stochastic stackelberg games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Zero-sum stochastic stackelberg games

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.665572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 966bcaf6-5fa3-4d34-99fb-aed3dfe2940a · outbound

This paper cites Convex-concave zero-sum markov stackelberg games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Convex-concave zero-sum markov stackelberg games

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.648512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2260012b-723f-490b-9697-61af16293b35 · outbound

This paper cites Tight last-iterate convergence rates for no-regret learning in multi-player games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Tight last-iterate convergence rates for no-regret learning in multi-player games

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.632648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9932f43c-9949-4582-999e-fc6c09a67785 · outbound

This paper cites Hierarchical game theory for system-optimal control: Applications of reverse stackelberg games in regulating marketing channels and traffic routing.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Hierarchical game theory for system-optimal control: Applications of reverse stackelberg games in regulating marketing channels and traffic routing

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.615784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ca02500b-c203-4896-82ba-aacc36c326ca · outbound

This paper cites A double oracle algorithm for zero-sum security games on graphs.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method A double oracle algorithm for zero-sum security games on graphs

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.596965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 58d5f3b1-8b85-4e0d-87c3-4dcc944073e5 · outbound

This paper cites Bilevel optimization: Convergence analysis and enhanced design.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Bilevel optimization: Convergence analysis and enhanced design

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.122426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7be1a25e-04bb-4c2c-8cb5-9c75f42f3a28 · outbound

This paper cites A fully first-order method for stochastic bilevel optimization.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method A fully first-order method for stochastic bilevel optimization

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.567605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4c8dc0ad-d610-4526-8219-6a84d0d6bd7e · outbound

This paper cites End-to-end learning and intervention in games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method End-to-end learning and intervention in games

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.549607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3a45d4a0-4dfd-4a5c-a284-480cb2fa5043 · outbound

This paper cites A review of dynamic stackelberg game models.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method A review of dynamic stackelberg game models

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.531213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fc7c2e1b-2c0c-460f-af97-24a7c5a582d8 · outbound

This paper cites Solving Structured Hierarchical Games Using Differential Backward Induction.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Solving Structured Hierarchical Games Using Differential Backward Induction

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:22:14.318044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3b8b70b6-03de-45e0-b7fd-3bc83fb0e0d8 · outbound

This paper cites Finite-time last-iterate convergence for multi-agent learning in games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Finite-time last-iterate convergence for multi-agent learning in games

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.514581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 51b334ca-f8b5-41de-93c7-2748a2800105 · outbound

This paper cites Bome! bilevel optimization made easy: A simple first-order approach.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Bome! bilevel optimization made easy: A simple first-order approach

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.497346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 959c249a-8a4e-4318-81da-de67f5f7447d · outbound

This paper cites First-order penalty methods for bilevel optimization.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method First-order penalty methods for bilevel optimization

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.479124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 46f61541-d176-4da4-bd70-0e3390cea36a · outbound

This paper cites Follower Agnostic Methods for Stackelberg Games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Follower Agnostic Methods for Stackelberg Games

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.158126Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a0cb2b8-9c6a-4483-88d9-74c8a1e3fb07 · outbound

This paper cites Learning in games with continuous action sets and unknown payoff functions.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Learning in games with continuous action sets and unknown payoff functions

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.162895Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ecbed37-c2ad-4147-9afb-e06c1626c6a8 · outbound

This paper cites Learning nash equilibria in monotone games.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Learning nash equilibria in monotone games

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.448203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bafeb654-92c2-4b6f-8ea7-fc30f56068be · outbound

This paper cites Reiter, and Milind Tambe.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Reiter, and Milind Tambe

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.431464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e709d45b-946b-41d5-8ae8-9cd03bbea116 · outbound

This paper cites Alternating projected sgd for equality-constrained bilevel optimization.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Alternating projected sgd for equality-constrained bilevel optimization

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.414061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0028a5f7-ede8-4324-a3ae-d2f792ae89bd · outbound

This paper cites A one-leader multi-follower bayesian-stackelberg game for anti-jamming transmission in uav communication networks.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method A one-leader multi-follower bayesian-stackelberg game for anti-jamming transmission in uav communication networks

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.397499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b0f3ca7-1b23-47c6-9f5e-3d53a4b91603 · outbound

This paper cites Accelerating Inexact HyperGradient Descent for Bilevel Optimization.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Accelerating Inexact HyperGradient Descent for Bilevel Optimization

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.185484Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9de132d5-e62c-4090-a733-4393837c8a6c · outbound

This paper cites Multi-agent reinforcement learning: A selective overview of theories and algorithms.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method Multi-agent reinforcement learning: A selective overview of theories and algorithms

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:22:14.379152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b8b2e3c-fd41-43d3-b82b-4cba562abeee · outbound

This paper cites An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning.

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T21:22:14.195148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 85af0787-279b-45df-8279-ad77cb0ca59c · inbound

Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games cites this paper.

Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-10T22:30:50.049355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f7e64261-61c4-4cdd-a8f1-78c602250fe3 · inbound

Continuity of VaR and Continuous Differentiability of CVaR under Decision-Dependent Losses cites this paper.

Continuity of VaR and Continuous Differentiability of CVaR under Decision-Dependent Losses Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method

Reference 83

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T03:57:38.626266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 568ce321-3347-459a-a74c-d92d6d8bd634 · inbound

Shared Infrastructure Investment and Pricing: Stackelberg Equilibria in Risk-Aware Take-or-Pay Contracts cites this paper.

Shared Infrastructure Investment and Pricing: Stackelberg Equilibria in Risk-Aware Take-or-Pay Contracts Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method

Reference 58

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T13:38:19.162524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.