What is a Game?
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A game is a mathematical model of a strategic interaction, with the following elements:
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Players: Games must have participants. Players can be people, busiensses, teams, political parties, countries, etc.
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Choices: Players have to make a choice, or multiple choices between different actions. A strategy is a rule for choosing actions.
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Outcomes: When the players are done choosing, an outcome occurs and the game ends. The outcome also must depend on the choices.
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Preferences: Players have preferences over outcomes.
Two features are required to make a game strategic:
- Outcomes are determined by everyone’s actions
- Players have different preferences.
Games differ in a few aspects:
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Timing: Do players choose once? (Rps) Or over and over again? (Chess) Does the game eventually end? Does it continue forever? Do they choose simultaneously, or in turns?
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Observations: Can players observe each other’s choices?
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Uncertainty: Is the outcome rnadom, or is it a deterministic function of the player’s actions? Do some players have more or less information than others?