Algorithmic Game Theory (AGT)

Algorithmic Game Theory (AGT)

• AGT sits at the intersection of algorithm design and analysis, game theory, and economics.

Traditional Algorithm Design

• It focuses on designing efficient algorithms for well-defined problems.
• It uses a model where a single entity is responsible for computation.
• Optimization is focused on computational resources like time and space.
• Assumptions include centralized control and full knowledge of input.

Traditional Game Theory

• It aims to model strategic interactions between rational agents.
• It uses a model with multiple agents having individual interests.
• Optimization is focused on agents' utility or payoff.
• Assumptions include that agents are rational with unlimited computational power.

AGT: Challenges with Strategic Behavior

• Strategic agents may manipulate the system for their own benefit.
• This can lead to unpredictability in system outcomes.
• The system may operate inefficiently, not in a socially optimal way.

Selfish Routing Example

• Involves n agents routing traffic from a source (s) to a destination (t) in a network.
• Each agent chooses a path to minimize their travel time.
• Congestion on a chosen path increases travel time for all agents using it.
• A key question is how inefficient the resulting equilibrium is compared to the optimal solution.

AGT: Challenges With Computational Limitations

• Agents may exhibit bounded rationality, unable to find optimal strategies.
• Computing optimal strategies might be intractable due to computational complexity.
• Agents may lack full knowledge of the game (incomplete information).

Automated Mechanism Design Example

• Focuses on designing mechanisms like auctions that are efficient and computationally feasible.
• Finding the optimal mechanism can be computationally hard.
• The goal is to design approximation algorithms for near-optimal mechanisms.

Key Topics in Algorithmic Game Theory

• Mechanism Design: Includes auctions, voting rules, and matching mechanisms.
• Equilibrium Computation: Covers Nash equilibrium, correlated equilibrium, and approximate equilibrium.
• Price of Anarchy: Involves measuring the inefficiency of equilibria, bounding the price of anarchy, and improving efficiency through mechanism design.
• Social Choice: Includes voting theory, fair division, and coalitional game theory.
• Learning in Games: Focuses on how agents learn in repeated games, convergence to equilibrium, and regret minimization.
• Network Games: Includes routing games, congestion games, and social networks.

Importance of AGT

• Internet Economics: Applications in sponsored search auctions, online advertising, and network routing.
• Social Networks: Relevant to information diffusion, community formation, and influence maximization.
• E-commerce: Used in recommendation systems, reputation systems, and pricing strategies.
• Cloud Computing: Applied to resource allocation, virtual machine placement, and load balancing.
• Political Science: Relevant to voting systems, coalition formation, and fair division.

Kidney Exchange Example

• Problem: Patients with kidney failure may have willing but incompatible donors.
• Solution: A central database matches patient-donor pairs for kidney exchange.
• Challenges: This includes addressing incentives, ensuring fairness, and dealing with computational complexity (NP-hard).

Kidney Exchange: AGT Perspective

• Involves designing incentive-compatible and computationally feasible mechanisms.
• Studies the trade-off between efficiency, fairness, and incentives.
• The presented diagram shows three patient-donor pairs (A1-A2, B1-B2, C1-C2) with compatibility indicated by arrows.
• The cycle arrangement (A2 -> B1, B2 -> C1, C2 -> A1) facilitates kidney exchange among the three pairs.