A textbook · SIAM Press, to appear 2027

Lectures on Static and Dynamic Game Theory

Foundations for Multi-Agent Systems and Control

Tamer Başar (University of Illinois Urbana-Champaign) and Quanyan Zhu (New York University)

Game theory is the mathematical study of strategic interactions among rational decision-makers. Where classical decision theory models an agent as an isolated optimizer in a fixed environment, game theory begins from interdependence: each player forms expectations about others who are reasoning about them in turn. These lectures develop that theory from matrix games to mean-field and learning games, with the multi-agent systems, control, and security problems that motivate it.

Read Part I free (PDF) Solve a 2×2 game Full contents
30chapters
7parts
~950pages
262pages in the free sample
Cover of Lectures on Static and Dynamic Game Theory by Tamer Başar and Quanyan Zhu
Interactive · Chapters 2–4

Solve a 2×2 game

Edit any payoff and the equilibria are recomputed. P1 chooses a row and P2 chooses a column; both maximize. Underlined payoffs are best responses, and a cell where both are underlined is a pure-strategy Nash equilibrium.

P2 (column)
P1 (row)LR
T , ,
B , ,

Each cell reads (u₁, u₂).

Equilibria

In a zero-sum game the mixed equilibrium is the saddle point, and the equilibrium payoff is the value of the game: what each player can guarantee with a security strategy, whatever the other does (§2.1.2, §2.2).

Contents

Thirty chapters in seven parts

Part I is available now as a free sample: fundamentals through correlated equilibrium, 262 pages. Every chapter ends with further notes, reading, and exercises; two appendices review optimal control and the mathematical background.

IFundamentals of Game Theoryin sample
  1. 1Introduction to Game Theory
  2. 2Matrix Games
  3. 3Nash Equilibrium: Concepts and Definition
  4. 4Nash Equilibrium: Properties and Computation
  5. 5Extensive-Form Games
  6. 6Stackelberg (Leader-Follower) Games
  7. 7Equilibrium Refinement
  8. 8Correlated Equilibrium
IIContinuous-Kernel Nash and Stackelberg Games
  1. 9Infinite and Continuous-Kernel Games
  2. 10Continuous-Kernel Stackelberg Games
  3. 11Quadratic and Network Games
IIIGames with Incomplete Information
  1. 12Bayesian Games
  2. 13Auction Games
  3. 14Revenue-Optimal Auction Design
  4. 15Mechanism Design Theory
IVDynamic and Repeated Games
  1. 16Extensive-Form Dynamic Games
  2. 17Principal-Agent Games
  3. 18Repeated Games
  4. 19Markov Games
  5. 20Dynamic Infinite Games
VDifferential and Stochastic Games
  1. 21Differential Games
  2. 22Dynamic Stackelberg Games
  3. 23Stochastic Differential Games
  4. 24Mean-Field Games
VICooperative and Matching Games
  1. 25Nash Bargaining
  2. 26Coalition Games
  3. 27Matching Games
VIIAdvanced Topics
  1. 28Routing Games
  2. 29Evolutionary Games
  3. 30Learning in Games
A·BAppendices
  1. AElements of Optimal Control Theory
  2. BMathematical Background
Download Part I (PDF, 4.4 MB)
Research

Game theory at NYU

The theory in the book is the working language of my group: designing systems whose participants, human or artificial, pursue their own objectives, and proving what those systems will do.

Games and control of socio-technical systems

Game-theoretic control as a design discipline for systems where people, institutions, and machines interact.

  • Revisiting Game-Theoretic Control in Socio-Technical Networks · Zhu and Başar, IEEE L-CSS 2025 · DOI
  • Disentangling Resilience from Robustness · Zhu and Başar, IEEE Control Systems Magazine 2024 · DOI
  • Cooperative and Noncooperative Paradigms for Game-Theoretic Control · Başar, Hayakawa, Ishii, and Zhu · arXiv

Security games and deception

Attacker–defender games, defensive deception, and automated penetration testing.

  • MEGA-PT: A Meta-Game Framework for Agile Penetration Testing · Ge and Zhu, GameSec 2024, Best Paper · DOI
  • Bilateral Cognitive Security Games under Stealthy Injection Attacks · Nguyen, Zhu, and Teixeira, CDC 2025 · DOI
  • More on the deception project site

Learning, conjectures, and misspecification

What agents converge to when their models of the world, and of each other, are wrong.

  • Adaptive Security Response Strategies Through Conjectural Online Learning · Hammar, Li, Stadler, and Zhu, IEEE TIFS 2025 · DOI
  • Computing and Learning Berk–Nash Equilibria in Infinite-Horizon MDPs · Zhu and Han · arXiv
  • Calibrated Learning of Sequential Equilibrium in Signaling Games · Zhu, CDC 2026

Coalitions, bargaining, and mean-field limits

Cooperative game theory for large populations of agents that join, leave, split, and merge.

  • Continuum Aumann–Drèze Value and Exit-and-Join Coalition Dynamics · Zhu, CDC 2026
  • Split-Merge Dynamics for Shapley-Fair Coalition Formation · Zhu and Han, MTNS 2026 · arXiv
  • Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games · Zhu · arXiv

Mechanism and information design

Designing the rules, the contracts, and the signals rather than the actions.

  • Stackelberg Risk Preference Design · Liu and Zhu, Mathematical Programming 2025 · DOI
  • Transparent Tagging for Strategic Social Nudges on Misinformation · Yang, Li, and Zhu, IEEE TNSE 2025 · DOI
  • Herd Accountability of Privacy-Preserving Algorithms: A Stackelberg Game Approach · Yang, Zhang, and Zhu, IEEE TIFS 2025 · DOI

Games for agentic AI

Language models and AI agents as strategic players: reasoning, pricing, and coordination.

  • Reasoning and Behavioral Equilibria in LLM-Nash Games · Zhu · arXiv
  • PACT: A Contract-Theoretic Framework for Pricing Agentic AI Services · Yang and Zhu, GLOBECOM 2025 · DOI
  • More on the Agentic AI and AI Tokenomics sites
All publications → Cognitive Security →
Teaching and community

Where this material is taught and discussed

ECE-GY 6263 Game Theory

The graduate course at NYU Tandon from which these lectures grew. The sample doubles as the course's opening chapters.

Dynamic games community

Executive Board of the International Society of Dynamic Games; Associate Editor of Dynamic Games and Applications.

GameSec

Chair of the 15th Conference on Decision and Game Theory for Security (New York, 2024), and program chair and organizer in earlier years.