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Mathematics Illuminated

Game Theory

We've all heard it said that life is like a game. Most games have well defined rules, with clear benefits for winning and costs for losing. And that makes them something we can think about logically and mathematically. But what about life? Can mathematics tell us anything about the competitions and collaborations that happen every day? From the social sciences to biology, robotics and beyond, the answer is yes.

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Hawks & Doves

John Maynard Smith

Competition and cooperation can be studied mathematically, an idea that first arose in the analysis of games like chess and checkers, but soon showed its relevance to economics and geopolitical strategy. This unit shows how conflict and strategies can be thought about mathematically, and in doing so, reveal important insights about human and even animal behaviors.

Unit Goals

  • Game theory is the mathematical study of social interactions as games that have payoffs for the players.
  • Traditional game theory assumes that players are rational actors, always acting in ways that maximize their benefits. Real people are not necessarily like this.
  • The payoff matrix is the essential way to express a game mathematically.
  • In zero-sum games, a winner’s gains come at a loser’s expense.
  • Non-zero-sum games can include both win-win and lose-lose situations.
  • Strategies are the actions that players take in a game.
  • Payoffs are often frequency dependent; that is, they depend on how many people are playing a particular strategy as well as how often a game is played.
  • Equilibrium is reached when each player has no incentive to play differently.
  • Game analysis changes when games are played repeatedly. This gives rise to mixed strategies.
  • Game theory can provide insight into many situations, phenomena, and subjects, including biology, sociology, and linguistics.




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