Algorithmic Game Theory

Algorithmic Game Theory

• Game theory is a mathematical approach to analyzing strategic interactions between rational decision-makers.
• It's composed of players, actions, payoffs, and strategies.
• Cooperative games allow binding agreements, while non-cooperative do not (default assumption).
• Zero-sum games have a constant total payoff, unlike non-zero-sum games.
• Perfect information games reveal all previous actions; imperfect information games do not.

Algorithmic Game Theory

• A field combining computer science and game theory to examine strategic interactions in networked systems.
• Key areas include equilibrium computation, mechanism design, price of anarchy, and social choice.

Prisoner's Dilemma

• This example illustrates cooperation challenges with two suspects, each choosing to "Cooperate" or "Defect".
• Payoff Matrix:

• In this scenario the Nash Equilibrium is both players defecting, despite mutual cooperation being more beneficial.

Importance of AGT

• AGT enhances strategic interaction understanding in Internet, economics, political science, and computer science contexts.
• Includes applications to online advertising, network routing and social networks.
• It creates efficient and fair mechanisms for auctions and economies
• As well as robust algorithms and systems regarding political behavior.

Course Overview

• Composed of four parts:
  • Introduction to Game Theory and its applications.
  • Algorithmic mechanism design.
  • The price of anarchy.
  • Social choice.

Math/CS Prerequisites

• Basic probability theory
• Basic linear algebra
• Basic algorithm design and analysis
• Mathematical maturity

Game Theory Basics

• Normal-Form Games
  • Defined by a player set $N = {1, 2,..., n}$, action set $A_i$ for each player $i \in N$, and payoff function $u_i: A \rightarrow \mathbb{R}$ for each player $i \in N$.
  • $A = A_1 \times A_2 \times... \times A_n$ represents all action profiles.
• Example: Prisoner's Dilemma
  • $N = {1, 2}$
  • $A_1 = A_2 = {C, D}$ (Cooperate, Defect}
  • $u_1(C, C) = -1, u_1(C, D) = -3, u_1(D, C) = 0, u_1(D, D) = -2$
  • $u_2(C, C) = -1, u_2(C, D) = 0, u_2(D, C) = -3, u_2(D, D) = -2$

Strategies

• Pure Strategy
  • A pure strategy for player $i$ is simply an action $a_i \in A_i$.
• Mixed Strategy
  • A mixed strategy for player $i$ is a probability distribution over their actions.
  • Notation is $s_i: A_i \rightarrow [0, 1]$, with $\sum_{a_i \in A_i} s_i(a_i) = 1$.
• Strategy Profile
  • A strategy profile is a tuple of strategies, one for each player.
  • E.g., $s = (s_1, s_2,..., s_n)$
• Payoff with Mixed Strategies
  • Defined as $u_i(s) = \sum_{a \in A} (\prod_{j \in N} s_j(a_j)) u_i(a)$

Domination

• Strategy $s_i$ strictly dominates $s'i$ if $u_i(s_i, s{-i}) > u_i(s'i, s{-i})$ for all $s_{-i}$.
• Strategy $s_i$ weakly dominates $s'i$ if $u_i(s_i, s{-i}) \ge u_i(s'i, s{-i})$ for all $s_{-i}$, with at least one $s_{-i}$ such that $u_i(s_i, s_{-i}) > u_i(s'i, s{-i})$.
• In the Prisoner's Dilemma, Defect strictly dominates Cooperate for both players.

Nash Equilibrium

• A strategy profile where no player gains by unilaterally changing strategy.
• Formally, $u_i(s_i, s_{-i}) \ge u_i(s'i, s{-i})$ for all players $i \in N$ and strategies $s'_i$.
• In the Prisoner's Dilemma, (Defect, Defect) is the only Nash Equilibrium.
• Every finite game has at least one mixed-strategy Nash Equilibrium
• Finding a Nash Equilibrium is PPAD-complete.

Computing Nash Equilibria

• Two-Player Zero-Sum Games
  • Can be formulated as a linear program and is polynomially solvable
• Two-Player General-Sum Games
  • Solved using the Lemke-Howson Algorithm, which has exponential worst-case complexity.
• N-Player Games
  • Generally computationally hard; approximation algorithms and heuristics are used.

Chapter 14: Government

Section 1: The Nature of Government and Politics

• Government refers to the institutions and processes for creating public policies.
• Governments maintain order, provide services, and enforce decisions.
• Politics defines selecting leaders and the policies produced.
• Harold Lasswell described politics "Who gets what, when, and how."

What Governments Do

• They provide national defense
• As well as public services (roads, schools, etc.)
• Preserve order via police force
• Socialize young people
• They collect taxes; about a third of Americans earnings go to taxes.

Section 2: How Should We Govern?

Democracy

• This is a system where policymakers are selected via public preferences.

Principles of Traditional Democratic Theory

• “One person, one vote” equality in voting.
• Where citizens participate effectively.
• Civic understanding through free press and speech
• Citizen Control of the Agenda in government
• Inclusion for all subject to governmental laws.

Three Contemporary Theories of American Democracy

• Pluralist Theory is a competition among groups for preferred policies.
• Elite and Class Theory states societies are divided along class lines, where upper-class elite rule.
• Hyperpluralism is where groups are too strong and weaken the government.

Challenges to Democracy

• Decisions are being made increasingly by specialists rather than citizens.
• Low voter turnout exemplifies limited governmental involvement.
• Escalating Campaign Costs result in members of congress spending more raising money.
• Political gridlock is a result of diverse Political Interests.

Section 3: What Should Government Do?

Individualism

• The belief individuals should operate independently of government.

Evolving Role of the Government

• With Americans ideologically conservative, but operationally liberal.

Political Culture and Ideologies

• Political Culture indicates shared societal values.

American Political Culture

• Entails the freedom expression and religion through liberty.
• There is equality of opportunity in the absence of aristocracy, demonstrated through Egalitarianism.
• Belief that people should get ahead on their own via Individualism.
• Freedom for free markets and limited government shown in Laissez-faire.
• The rights of average citizens against privileged elites are Populism.

A Culture War?

• Includes different views between: America drifting from moral roots, and America making progress.

Political Ideologies

• This is a set of coherent beliefs about policy, politics and public purpose.

Liberals

• They believe in broader governmental roles in society.

Conservatives

• Favor less active governmental roles.

Section 4: Government and Public Policy

Public Policy

• The choice a government makes to address political issues.

How Policymaking Works

1. People
2. Linkage Institutions: Parties elections media interest groups
3. Policy Agenda
4. Policymaking Institutions: Legislature executive courts bureaucracy
5. Policy
6. People

Effects on Government

• Policies via government affect people.
• Democracy depends on informed citizens in public policies.

Algorithmic Trading

Types of automated trading strategies

• Execution Algorithms
  • VWAP: Executes orders to match volume-weighted average price.
  • TWAP: Match time-weighted average price.
  • POV: Percentage of volume completion.
  • Implementation shortfall: Minimize the difference between actual and price.
• Statistical Arbitrage
  • Pairs trading: Exploits temporary price differences between correlated assets.
  • Index arbitrage: Exploits differences between index and stock prices.
  • Triangular arbitrage: Exploits differences in currency exchange rates.
• Trend Following
  • Moving averages: Identify trends.
  • Breakout strategies: When prices reach support levels.
  • Channel strategies: Identifying overbought or oversold conditions.

Backtesting

• Backtesting evaluates strategy performance on historical data.
• Determines a trading strategy's viability before live execution.
• Considerations include data quality, costs, overfitting, and look-ahead bias.

Order Placement

• Market orders executed at the best price. Limit orders are handled at a specific price.
• After reaching levels, stop orders are executed. Stop-limit does both.
• Displayed in order book are hidden orders.
• Larger orders broken up into smaller orders (iceberg order).

Guía de estudio para el examen CCNA

Capítulo 7: Seguridad de la LAN

Amenazas a la seguridad de la LAN

• Amenazas Internas: Originan dentro de la red
• Amenazas Externas: Originan fuera de la red
• Tipos comunes de ataques: reconocimiento, acceso, denegación de servicio, manipulación de datos.

Protección de la LAN

• Medidas Físicas
• Medidas Técnicas
• Medidas Administrativas

Seguridad de los endpoints

• Antivirus
• Firewall Personal
• Network Access Control(NAC)

Seguridad de la WLAN

• Wired Equivalent Privacy (WEP)
• Wi-Fi Protected Access(WPA)
• Wi-Fi Protected Access 2 (WPA2)
• Wi-Fi Protected Access 3 (WPA3)

Autenticación

• Pre-Shared Key (PSK)
• Autenticación se basa en servidor

Seguridad de los switches

• Port Security
• DHCP Snooping
• ARP Inspection
• Storm Control
• VLAN

Herramientas de seguridad

• Nmap
• Analizador de paquetes(Wireshark)
• Metasploit

Conceptos clave

• AAA (Authentication, Authorization, Accounting)
• Firewall
• IDS/IPS (Intrusion Detection System/Intrusion Prevention System)
• VPN (Virtual Private Network)

Resumen

• La seguridad de la LAN es crucial para proteger los recursos de la red contra amenazas internas y externas
• Se deben implementar medidas físicas, técnicas y administrativas para garantizar la seguridad de la red
• También es importante proteger los endpoints y la WLAN
• Los switches también deben estar protegidos contra ataques
• Existen varias herramientas de seguridad disponibles para ayudar a proteger la red.

Chapter 14: Factorial ANOVA

14.1 Introduction

• More than one independent variable is a factorial design.
• It allows us to investigate interaction effects.

14.2 Theory

14.2.1 Partitioning Variance

• Same logic as one-way ANOVA
• More complicated formulas due to independent variables
• Example: Two Independent variables (A & B).

$$ \begin{aligned} S S_{\text {Total }} &=S S_{\text {A }}+S S_{\text {B }}+S S_{\text {A x B }}+S S_{\text {Residual }} \ d f_{\text {Total }} &=d f_{\text {A }}+d f_{\text {B }}+d f_{\text {A x B }}+d f_{\text {Residual }} \end{aligned} $$

• Interaction effect ($A \times B$):
• $SS_{Residual}$:
• Variability not explained by the model.

Hypotheses

• Main Effect of A: $H_0: \mu_{A1} = \mu_{A2} = \dots = \mu_{Ak}$
• Main Effect of B: $H_0: \mu_{B1} = \mu_{B2} = \dots = \mu_{Bk}$
• Interaction effect of A and B: $H_0$: No interaction between A and B.

F Ratios

• Each Effect has its own F Ratio.

$$ F_{\text {A }}=\frac{M S_{\text {A }}}{M S_{\text {Residual }}} $$

$$ F_{\mathrm{B}}=\frac{M S_{\mathrm{B}}}{M S_{\text {Residual }}} $$

$$ F_{\mathrm{A} \times \mathrm{B}}=\frac{M S_{\mathrm{A} \times \mathrm{B}}}{M S_{\text {Residual }}} $$

• $MS = SS/df$
• Appropriate degrees for freedom ($df_{effect}, df_{residual}$)

14.3 Example

• Example: Playing video games and doing homework
  • Independent variable A: Video game playing (0 hours vs. 2 hours).
  • Independent variable B: Doing homework (1 hour vs. 3 hours).
  • Dependent variable: Exam score
• Assumptions: normally distributed data and homogeneity of variance.

14.4 Running Factorial ANOVA

• Using statistical software.
• Specify variables, independent and dependent.
• Software calculates F-ratios and p-values.

14.5 Interpreting Output

• p-values for each effect.

14.5.1 Interaction Effects

• There will be a significant analysis and effect of independent variables.
• Simple effects analysis:
• Investigate effect of on independent variables at each level of the other independent variable.
• Visualization:
• Interaction plots can help understand interaction effects.

14.6 Writing it Up

14.6.1 APA style

• Report F-ratios degrees of freedom, p-values for each effect.

Summary

Economía

1. Introducción a la Economía

1.1. Concepto de Economía

La economía es una ciencia social que estudia cómo las sociedades administran los recursos escasos para distribuir entre los individuos.

• Escasez
• Elección
• Eficiencia

1.2. Microeconomía y Macroeconomía

• Microeconomía
• Macroeconomía

1.3. Factores de Producción

• Tierra
• Trabajo
• Capital
• Tecnología

2. El Mercado

2.1. Demanda

• Definición
• Ley de la Demanda
• Factores que afectan la demanda
  • Precio del bien
  • Ingreso de los consumidores
  • Precios de bienes relacionados (sustitutos y complementarios)
  • Gustos y preferencias
  • Expectativas

2.2. Oferta

• Definición
• Ley de la Oferta
• Factores que afectan la oferta
  • Precio del bien
  • Costos de producción
  • Tecnología
  • Expectativas
  • Número de vendedores

2.3. Equilibrio de Mercado

• Definición
• Precio de Equilibrio
• Cantidad de Equilibrio
• Exceso de Demanda
• Exceso de Oferta

3. Estructuras de Mercado

3.1. Competencia Perfecta

• Características
  • Gran número de compradores y vendedores
  • Productos homogéneos
  • Libre entrada y salida del mercado
  • Información perfecta
  • Las empresas son precio-aceptantes
• Ejemplo

3.2. Monopolio

• Características
  • Un único vendedor
  • Producto único sin sustitutos cercanos
  • Barreras a la entrada
  • La empresa es precio-decisora
• Causas
  • Control exclusivo de un recurso
  • Patentes
  • Monopolios naturales (altos costos fijos)
• Ejemplo

3.3. Oligopolio

• Características
  • Pocos vendedores
  • Productos homogéneos o diferenciados
  • Barreras a la entrada
  • Interdependencia entre las empresas
• Ejemplo

3.4. Competencia Monopolística

• Características
  • Gran número de vendedores
  • Productos diferenciados
  • Libre entrada y salida del mercado
  • Las empresas tienen cierto poder de mercado
• Ejemplo

4. Macroeconomía

4.1. Producto Interno Bruto (PIB)

• Definición
• Formas de calcular el PIB
  • Gasto: $PIB = C + I + G + (X - M)$
  • Ingreso
  • Valor Agregado
• PIB Nominal
• PIB Real

4.2. Inflación

• Definición
• Causas
  • Aumento de la demanda agregada
  • Aumento de los costos de producción
  • Aumento de la oferta monetaria
• Consecuencias
  • Pérdida del poder adquisitivo
  • Incertidumbre
  • Dificultad para planificar
  • Redistribución de la riqueza
• Medición: Índice de Precios al Consumidor (IPC)

4.3. Desempleo

• Definición
• Tasa de Desempleo: $Tasa \ de \ Desempleo = \frac{Número \ de \ Desempleados}{Población \ Activa} * 100$
• Tipos de Desempleo
  • Friccional
  • Estructural
  • Cíclico
  • Estacional

4.4. Política Fiscal

• Definición
• Instrumentos
  • Gasto Público
  • Impuestos
• Tipos de Política Fiscal
  • Expansiva
• -Contractiva

4.5. Política Monetaria

• Definición
• Instrumentos
  • Tasas de Interés
  • Operaciones de Mercado Abierto
  • Encaje Bancario
• Tipos de Política Monetaria.

Guía para la detección de noticias falsas

Noticias falsas

• Son noticias inventadas que se parecen a noticias reales
  • Intentan influir en opiniones causan confusión.

¿Cómo detectar noticias falsas?

• Sospecha de los titulares
• Investiga la fuente, ya que los enlaces pueden parecer muy similares
• Verifica las fechas de publicación
• Consulta los hechos
• Piensa antes de compartir información.

Algorithmic Trading and Order Execution

Topic 1: Introduction to Algorithmic Trading

• Algorithmic trading uses programs to automate trade decisions.
• Execution algorithms aim to optimally place orders.
• Various factors like timing are considered.
• It aims to maximize profits and minimize cost.

Topic 2: Order Book and Market Microstructure

Order Book

• Display of buy/sell orders for a security.

Market Microstructure

• Considers how the market operates.
  • Market microstructure affects the price discovery process.

Topic 3: VWAP and TWAP Algorithms

VWAP (Volume Weighted Average Price)

• Aims to execute an order at the average price weighted by volume.
• Formula for VWAP
  • $VWAP = \frac{\sum_{i=1}^{n} P_i * V_i}{\sum_{i=1}^{n} V_i}$

TWAP (Time Weighted Average Price)

• Aims to execute an order evenly.
• Formula for TWAP $TWAP = \frac{\sum_{i=1}^{n} P_i}{n}$

Topic 4: Implementation Shortfall

• Measure the difference between the actual execution price and the benchmark price.
• Formula for Implementation Shortfall (IS):
  • $IS = (P_e - P_b) * Q$

Topic 5: Smart Order Routing

• Smart order routing (SOR) aims to route to the available market
• Aims to minimize transaction cost

Topic 6: High-Frequency Trading (HFT)

• High-frequency trading uses technology to trade at high speeds.
• HFT firms provide market liquidity.
• HFT strategies can be controversial due to its market stability

Further Reading

• "Algorithmic Trading" by Earnie Chen