Algorithmic Game Theory

Undergraduate course, University of Giresun, Department of Computer Engineering, 2023

algorithmic game theory Algorithmic Game Theory is an interdisciplinary field that blends the mathematical rigor of game theory with the practical, problem-solving techniques of computer science. This area of study focuses on designing and analyzing algorithms for solving games and game-like scenarios, where multiple players with potentially conflicting interests interact. It encompasses a wide range of topics, including the computation of equilibria, the efficiency and fairness of various algorithmic mechanisms, and the strategic behavior of rational agents in competitive environments. By leveraging computational methods, algorithmic game theory provides valuable insights into complex systems, from economic markets to networked environments, thereby bridging the gap between theoretical foundations and real-world applications.

The resources:

  • Toronto CSC304 [website]

  • Michael Dinitz 601.436/636 [website]

  • Game Theory, Alive [pdf]
  • Algorithmic Game Theory [pdf]

  • Networks, Crowds, and Markets [pdf]

  • Cambridge CS 364 [notes]

  • CMU 15-896 [notes]

  • GAMUT is a suite of game generators designated for testing game-theoretic algorithms. [website]
  • Gambit is an open-source collection of tools for doing computation in game theory. [website]

Chapter 1: Game Theory Fundamentals

Game theory is a mathematical framework used to analyze and understand strategic interactions between rational decision-makers. It provides a systematic way of studying situations where the outcome of one person’s decision depends on the actions of others.

Chapter 2: Introduction to Algorithmic Game Theory

Algorithmic game theory is an interdisciplinary field that combines concepts from game theory and computer science. It focuses on the study of strategic interactions in computational settings and aims to design efficient algorithms and computational models for analyzing and solving games.

Chapter 3: Nash Equilibrium and Strategic Behavior

Nash equilibrium is a central concept in game theory that captures the notion of strategic behavior and stable outcomes in games. It refers to a set of strategies, one for each player, where no player has an incentive to unilaterally deviate from their chosen strategy, assuming all other players stick to their strategies.

Chapter 4: Mechanism Design and Incentives

Mechanism design is a field of study within game theory and economics that focuses on designing rules or mechanisms to achieve desired outcomes in strategic settings. It involves designing incentive-compatible mechanisms that align the self-interests of individual participants with the desired collective goals.

Chapter 5: Auctions and Market Design

Auctions and market design are closely related fields that utilize principles from economics, game theory, and mechanism design to study the allocation of goods, resources, and services in various settings. Both areas aim to create efficient and fair mechanisms for matching buyers and sellers, determining prices, and optimizing resource allocation.

Chapter 6: Social Choice and Voting Systems

Social choice theory is a branch of economics and political science that studies methods for aggregating individual preferences or opinions into a collective choice. It explores the challenges and possibilities of making decisions on behalf of a group or society based on the preferences of its members. Voting systems are one of the key tools analyzed in social choice theory.

Chapter 7: Algorithmic Fairness and Ethics

Algorithmic fairness and ethics play a crucial role in algorithmic game theory by addressing the potential biases, discrimination, and ethical implications that may arise in the design and deployment of algorithms within game-theoretic frameworks.

Chapter 8: Network Design and Routing

In algorithmic game theory, network design and routing are studied with a focus on understanding the strategic behavior of self-interested agents and optimizing network efficiency and fairness.

Chapter 9: Price of Anarchy and Efficiency

Price of Anarchy (PoA) is a measure that quantifies the loss of efficiency in a system due to the selfish behavior of individual agents. It evaluates the impact of strategic decision-making on the overall performance or welfare of a system.

Chapter 10: Learning and Adaptation

Learning and adaptation play a significant role in algorithmic game theory by addressing how self-interested agents can improve their decision-making strategies over time and adapt to changing environments.

Chapter 11: Online Platforms

In algorithmic game theory, online platforms are studied as environments where self-interested agents interact and make decisions in the pursuit of their own objectives. Online platforms encompass various digital platforms, such as e-commerce platforms, social media platforms, ride-sharing platforms, and online auctions.

Chapter 12: Decision-Making

Decision-making is a central concept that focuses on how self-interested agents make choices or decisions in strategic situations. Decision-making in algorithmic game theory involves analyzing the strategic interactions among agents, understanding their preferences and objectives, and designing mechanisms and algorithms to optimize outcomes.

Chapter 13: Multi-Agent Systems

Multi-agent systems refer to scenarios where multiple self-interested agents interact and make decisions in a shared environment. Multi-agent systems are analyzed to understand the strategic behavior of agents, optimize outcomes, and design mechanisms that align individual incentives with system objectives.

Chapter 14: Future Directions

Algorithmic game theory is a rapidly evolving field that continues to explore new directions and address emerging challenges.