Algorithmic Game Theory

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Questions and Answers

Which of the following describes a physical change in matter?

  • A change that alters the substance's identity, forming a new substance.
  • Any change that involves burning or combustion.
  • A process always accompanied by changes in temperature.
  • A transformation where the substance's nature remains unchanged; no new substances appear. (correct)

What is the key difference between a physical and chemical change?

  • Physical changes always involve energy, while chemical changes do not.
  • Physical changes alter the state of matter, while chemical changes only alter the appearance.
  • Chemical changes are reversible; physical changes are irreversible.
  • Physical changes do not change the substance's chemical identity, while chemical changes do. (correct)

Which of the following is always true about the chemical formula of a substance after it undergoes a physical change?

  • The chemical formula changes to represent a new compound.
  • The chemical formula may change depending on the energy involved.
  • The substance no longer has a chemical formula.
  • The chemical formula remains the same. (correct)

How does temperature affect the viscosity of honey or oil?

<p>Higher temperature reduces viscosity. (A)</p> Signup and view all the answers

What happens to a metal ring when heated, and how does this relate to physical change?

<p>It expands; the substance remains the same. (A)</p> Signup and view all the answers

Why is dissolving sugar in water considered a physical change?

<p>The sugar molecules remain chemically unchanged. (D)</p> Signup and view all the answers

When iron and sulfur are heated together, they form iron sulfide ($FeS$), a new substance with different properties. What type of change is this?

<p>Chemical change, because a new substance is formed. (D)</p> Signup and view all the answers

Electrolysis of water ($H_2O$) produces hydrogen ($H_2$) and oxygen ($O_2$). What type of change is electrolysis?

<p>Chemical change, because new substances with different properties are formed. (B)</p> Signup and view all the answers

In factories, aluminum is obtained from bauxite through electrolysis. How would you classify this process?

<p>Chemical change, producing the metal. (C)</p> Signup and view all the answers

Aluminum scraps are melted down for recycling. What kind of change is this?

<p>Physical change. (A)</p> Signup and view all the answers

Flashcards

Temperature Changes

Changes in temperature affect the properties of some substances, like viscosity of honey or oil.

Changes of state

Changes in state also can happen.

Dilations and compressions

The substances don't change.

Mixtures

When substances are mixed.

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Physical changes

Transformations of matter that do not change its nature; no new ones appear.

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Chemical Changes

In chemical changes, new substances are formed.

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Chemical Formulas

Substances are represented with chemical formulas before and after, and their properties change.

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Study Notes

  • Algorithmic Game Theory (AGT) is the application of algorithmic design techniques to game-theoretic problems, considering players with computational limitations

Game Theory

  • Examines interactions among rational, self-interested agents
  • Has applications in economics, politics, biology, and computer science

Algorithm Design

  • Focuses on creating efficient problem-solving algorithms
  • Operates within constraints of limited computational resources

Selfish Routing Model

  • Involves a network where each road has latency, $l_e(x)$, based on traffic fraction $x$
  • Users aim to minimize travel time from point A to B by choosing routes
  • Explores user behavior when acting selfishly and compares equilibrium to optimal route assignment

Braess's Paradox

  • Illustrates how adding a road to a network can increase travel time for all users

Social Cost

  • Is the sum of all players' costs
  • Increases in the Braess's Paradox when a road is added

Mechanism Design

  • Is the process of designing game rules to achieve a desirable outcome
  • Includes auctions, voting rules, and matching markets

Key Questions in Mechanism Design

  • Focus on creating mechanisms that are efficient and incentive-compatible
  • Investigates the complexity of these mechanisms

AGT Overview

  • Is an evolving field with many unanswered questions
  • Integrates computer science, economics, and game theory
  • Has potential to influence network design and online advertising, among other applications

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