Game theory

Welcome to the seventh episode of Applied Mathematics. In this session, we delve into the fascinating world of Game Theory, the mathematical study of strategic decision-making. Building upon our understanding of mathematical modeling, we will explore how to represent situations of conflict and cooperation. You will learn about the core components of any 'game': players, strategies, and payoffs. We will dissect the famous 'Prisoner's Dilemma' to understand concepts like dominant strategies and the Nash Equilibrium. We will also classify different types of games—from zero-sum to cooperative—and discuss their wide-ranging applications in economics, political science, and even evolutionary biology. This episode will equip you with the foundational concepts to analyze strategic interactions all around you.

Check your understanding

These are the same multiple-choice questions you will see in the Quiz section after you listen to the episode. Use them here to preview or review the answers.

What are the three essential components that define a 'game' in the context of Game Theory?

  1. Players, Strategies, and Payoffs
  2. Rules, Boards, and Pieces
  3. Chance, Skill, and Outcome
  4. Cooperation, Competition, and Equilibrium
  5. Models, Algorithms, and Solutions

In the classic Prisoner's Dilemma, what is the outcome known as the Nash Equilibrium?

  1. Both prisoners remain silent.
  2. One prisoner confesses while the other remains silent.
  3. Both prisoners confess.
  4. Both prisoners are set free.
  5. The prisoners negotiate a deal.

Which of the following statements accurately describes a zero-sum game?

  1. All players can potentially win together.
  2. The total gains and losses of all players add up to zero.
  3. No player can improve their outcome by changing their strategy.
  4. Players must make their moves sequentially.
  5. One player's gain is always exactly equal to another player's loss.

Which of the following are examples of fields where Game Theory is applied?

  1. Economics
  2. Evolutionary Biology
  3. Political Science
  4. Topology
  5. Computer Science

A game where players make their decisions at the same time, without knowledge of the other players' choices, is called a:

  1. Sequential game
  2. Cooperative game
  3. Zero-sum game
  4. Simultaneous game
  5. Non-zero-sum game

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