How to 'show your work' with game theoretic notation

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Everything I've read on game theory seems to describe the game in notation and solves it in natural language.

  1. How do you work with notation in game theory?
  2. Could you recommend a straight-forward introductory book to working with game theoretic notation.

Thank you.

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Yale has online materials for its Game Theory course, which are probably going to be useful. Here is the link: http://oyc.yale.edu/economics/econ-159

A lot of game theory notation is vector notation. You use vectors to denote strategies, as well as payoffs. Combinatorial games utilize graph theoretic and combinatorial notations. You will also find probability and statistics to be used in many games, and so familiarity with such notation will be useful.

Game Theory is really a diverse field, stretching into math, economics, and computer science. So a lot of the notation really depends on the field in which the game falls.