Algorithmic Game Theory: Introduction

Lecture 1: Introduction to Algorithmic Game Theory

• Game theory studies mathematical models of strategic interactions among rational agents.
• It offers tools to model and analyze strategic interactions, predict agent behavior, and design mechanisms for desired outcomes.
• The core components of a game include a set of players, their possible actions, and their preferences.

Selfish Routing

• In selfish routing, players aim to travel from a source to a destination through a network with varying travel times dependent on usage.
• The key question is how players behave in such a network.

Braess's Paradox

• Adding a road to a network can counterintuitively increase travel time for all players.
• In a network with 2000 players choosing between paths A->X->B and A->Y->B with travel times dependent on road usage, the equilibrium travel time is 65.
• Introducing a new road from Y to X (A->Y->X->B) can lead to all players using this route, resulting in a travel time of 75, worse than the original equilibrium.
• This paradox arises because players become uncoordinated and act solely in their self-interest.

Fundamental Questions in Algorithmic Game Theory

• Does an equilibrium always exist?
• How efficient or inefficient are the equilibrium states?
• How can an equilibrium be reached?
• Can we design games to ensure desirable equilibrium outcomes?

Course Outline

• Basics: Games in normal form, solution concepts (Nash equilibrium), and extensive form games.
• Mechanism Design: Social choice theory and mechanism design with and without money, including auctions.
• Selfish Routing: Examines the price of anarchy, Braess's paradox, and Stackelberg routing.
• Advanced Topics: Covers fair division, coalitional game theory, and online mechanism design.

Organizational Matters

• Resources include the course website on StudIP.
• Grading is based 50% on an exam and 50% on exercises.

Games in Normal Form

• A game in normal form involves a set of players, their actions, and a utility function that maps action profiles to real numbers.
• The Prisoner's Dilemma illustrates this with players choosing to cooperate or defect, affecting their utilities based on both players' choices.

Algorithmic Trading

• Algorithmic trading is the execution of orders using automated, pre-programmed instructions.
• It accounts for variables like price, timing, and volume to optimize trades.
• It has other names, including automated trading and black-box trading.

How Algorithmic Trading Functions

• A trader creates an algorithm with a set of rules.
• The algorithm undergoes testing with historical data, known as backtesting.
• The algorithm is deployed for live trading.
• The system automatically places orders when the pre-defined criteria are met.

Types of Algorithmic Trading Strategies

• Trend Following: Algorithms capitalize on existing market trends.
• Mean Reversion: Algorithms profit from prices returning to their average value.
• Arbitrage: Algorithms exploit price differences in different markets.
• Market Making: Algorithms place orders to profit from the bid-ask spread.
• Execution Algorithms: Designed to execute larger orders without impacting asset prices.
• Volume-Weighted Average Price (VWAP)
• Time-Weighted Average Price (TWAP)
• Percentage of Volume (POV)

Advantages of Algorithmic Trading

• Trades are executed at the best possible prices.
• Reduced transaction costs.
• Trades occur instantly and accurately.
• Fewer manual errors.
• Backtesting optimizes strategies.

Disadvantages of Algorithmic Trading

• Requires technical skills for coding and maintenance.
• Potential for unexpected losses due to glitches.
• Needs constant monitoring.
• Over-optimization can yield unexpected results.

Important Considerations for Algorithmic Trading

• Past performance isn't indicative of future results.
• Constant monitoring and maintenance are necessary.
• Regulatory oversight is involved.

Introduction to Optimization

• Optimization aims to find the best solution to a problem given certain restraints.
• An example is maximizing a rectangle's area while maintaining a fixed perimeter.

Reasons to Study Optimization

• Efficient decision-making.
• Performance improvement in various fields.
• Modeling and solving complex problems.

Types of Optimization Problems

• Linear Optimization: Objective function and constraints are linear.
• Non-Linear Optimization: Objective functions or constraints are non-linear.
• Integer Optimization: Variables must be integers.
• Dynamic Optimization: Optimization problems change over time.

Optimization Methods

• Analytical Methods: Calculus is used to find optimal solutions.
• Numerical Methods: Algorithms are used to approximate solutions. This includes gradient descent and Newton's method.
• Genetic Algorithms: Inspired by evolution to find solutions.
• Particle Swarm Optimization (PSO): Inspired by animal behavior to find solutions.

Applications of Optimization

• Engineering: Structural design.
• Economics: Resource allocation.
• Computer Science: Machine learning.
• Logistics: Vehicle routing.

Optimization Tools

• MATLAB.
• Python with libraries like SciPy.
• Gurobi.
• AMPL modeling language.

Conclusion on Optimization

• Optimization is a tool for problem-solving in different areas.
• Understanding problem types and methods is essential for making decisions and improving performance.

Algorithmic Trading Components

• Trading strategies involve several steps.

Strategy Identification

• Data Collection: Gathering both historical and real-time market data for analysis.
• Backtesting: Assessing the strategy's viability by testing it on historical data.
• Risk Management: Implementing measures to limit possible losses.

Algorithmic Development

• Coding: Translating the trading strategy into an algorithm
• Testing: Ensuring the functionality and efficiency of the algorithm.
• Optimization: Refining the algorithm to improve its performance.

Infrastructure Setup

• Hardware: Server and network equipment selection.
• Software: Selecting trading platforms and programming languages.
• Connectivity: Establishing reliable data feeds and exchange connections.

Execution and Monitoring

• Deployment: Executing algorithm in a live trading atmosphere.
• Monitoring: Tracking algorithm performance and finding issues.
• Maintenance: Updating and improving the algorithm as needed.

Advantages of Algorithmic Trading

• Faster trade execution than humans.
• Automating repetitive actions.
• Reducing human emotion.
• Reduce costs through automation.

Disadvantages of Algorithmic Trading

• Requires specialized knowledge for use.
• Can be expensive to develop and maintain.
• Algorithms may not perform well in unexpected market conditions.
• Over-optimization risk.

Example Algorithmic Trading Strategies

• Mean Reversion: Trading price fluctuations around an average value.
• Trend Following: Capturing income from assets moving with clear direction.
• Arbitrage: Exploiting price variations across multiple markets.
• Market Making: Providing liquidity to markets by placing orders.

Algorithmic Trading Risk Management

• Stop-Loss Orders: Automatically exit trades when prices bottom out.
• Position Sizing: Identifying appropriate amount allocated.
• Diversification: Spreading investments throughout various assets.
• Stress Testing: Simulating harsh conditions to measure the algorithm.

Future Trends

• Applying machine learning can improve trading strategies.
• Cloud-based scaling can improve cost efficiency.
• Analyzing is good for big trading opportunities.
• Adapting can help comply with evolving rules.