Algorithmic Game Theory introduction

• Algorithmic Game Theory (AGT) combines algorithm design and analysis with game theory and economics.

Traditional Algorithm Design

• Focuses on efficient algorithms for well-defined problems.
• Assumes a single entity controls computation.
• Focuses on optimizing computational resources like time and space.
• Operates under centralized control and full knowledge of input.

Traditional Game Theory

• Models strategic interactions between rational agents.
• Involves multiple agents with individual interests.
• Focuses on optimizing agents' utility (payoff).
• Assumes agents are rational with unlimited computational power.

AGT: Coping with Strategic Behavior

• Addresses challenges from strategic agents who might manipulate the system for their own benefit, leading to unpredictability and inefficiency.
• Selfish Routing illustrates this, where agents choose paths to minimize travel time, causing congestion and raising questions about equilibrium inefficiency.

AGT: Coping with Computational Limitations

• Deals with challenges when agents have limited computational resources, leading to bounded rationality, computational complexity, and incomplete information.
• Automated Mechanism Design is an example, aiming to create efficient and computationally feasible mechanisms (e.g., auctions), using approximation algorithms to handle computational hardness.

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: measures inefficiency of equilibria, setting bounds and designing mechanisms to improve efficiency.
• Social Choice: covers voting theory, fair division, and coalitional game theory.
• Learning in Games: examines 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

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

Example: Kidney Exchange

• The Problem: Patients with kidney failure need transplants, but willing donors are often incompatible with their intended recipients.
• The Solution includes kidney exchange where Pairs of patients and donors register in a central database to exchange kidneys between compatible pairs, increasing successful transplants.

Challenges in Kidney Exchange

• Incentives for patients to reveal their true preferences.
• Fairness in finding a matching that is equitable for all patients.
• Computational Complexity with the optimal matching being NP-hard.

AGT Perspective on Kidney Exchange

• Focuses on designing incentive-compatible and computationally feasible mechanisms.
• Aims to balance efficiency, fairness, and incentives.

Kidney Exchange Diagram Description

• Kidney exchange diagram illustrates a Kidney Exchange scenario with three patient-donor pairs (A1-A2, B1-B2, C1-C2).
• An arrow from one donor to another indicates compatibility, meaning the first donor's kidney is suitable for the second patient.
• The current cycle arrangements show that A2 can donate to B1; B2 can donate to C1; and C2 can donate to A1.
• This arrangement facilitates kidney exchange between the three pairs.