Game Theory

  1. Game theory: Game theory is like studying how people make decisions when their choices affect each other. Imagine you and your friend deciding where to eat - your happiness depends not just on your choice, but also on what your friend chooses.

  2. What makes a game?
    • Players: Players are the people (or companies, countries, etc.) making decisions
    • Choices: Each player has different options they can pick from
    • Results: What each player gets based on everyone’s choices combined

    Think of it like playing rock-paper-scissors - you’re a player, you have three choices, and whether you win depends on what both you and your opponent choose.

  3. What is rational behavior? In game theory, we assume everyone tries to get the best outcome for themselves. It’s like shopping for a good deal - you want to get the most value for your money, and you assume other shoppers are doing the same.

  4. Different types of games:
    1. Cooperative vs. non-cooperative:
      • Cooperative: Players can work together and make deals (like teammates in sports).
      • Non-cooperative: Everyone acts alone (like competing businesses).
    2. Zero-sum vs. non-zero-sum:
      • Zero-sum: One person’s win is another’s loss (like splitting a pie).
      • Non-zero-sum: Everyone can win or lose to different degrees (like a group project where everyone can get a good grade).
    3. Simultaneous vs. sequential:
      • Simultaneous: Everyone decides at the same time (like rock-paper-scissors).
      • Sequential: Players take turns (like chess).

  5. Nash equilibrium: Nash equilibrium is when everyone’s happy enough with their choice that they wouldn’t change it, assuming others stick to their choices too. It’s like when everyone at a four-way stop sign follows the rules - nobody gains by breaking them if others follow them.

  6. Dominant and dominated strategies:
    • Dominant strategy: The best choice no matter what others do (like using an umbrella on a rainy day)
    • Dominated strategy: A choice that’s always worse than another option (like paying more for the exact same product)

  7. Payoff matrix: Payoff matrix is just a chart showing what each player gets based on everyone’s choices. Think of it like a menu showing prices for different meal combinations.

  8. The prisoner’s dilemma: This famous example shows how two people might not help each other even when it’s best for both. Imagine two suspects being questioned separately:
    • If both stay quiet, they get light sentences.
    • If one talks and one stays quiet, the talker goes free while the other gets a harsh sentence.
    • If both talk, they both get medium sentences. Usually, both end up talking because they’re afraid of getting the worst outcome.
  9. Repeated games and evolution: When games are played multiple times:
    • Players can learn from past experiences.
    • They might develop strategies like “I’ll be nice if you’re nice.”
    • Successful strategies become more common over time, like popular trends catching on.

In summary, game theory looks at how people make choices when their success depends not just on what they do, but also on what others around them decide to do.