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Game and Decision Theory
Explore strategic models; randomization and sequential games; uncertainty and collective decisions. Concepts and connections are available independently of video coverage.
Prerequisites and connections
Probability
A probability measure assigns nonnegative weights to events, with total weight one and countable additivity on disjoint events.
3 reviewed resources
Strategic models
Normal-form games
Players, strategies and payoff functions define a normal-form game.
Video explanations to be addedDominant strategies
A dominant strategy is at least as good against every opponent choice, with strength depending on the definition.
Video explanations to be addedBest responses
A best response maximizes a player's payoff given opponents' strategies.
Video explanations to be addedNash equilibrium
At equilibrium no player gains by unilateral deviation while others keep their strategies.
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Randomization and sequential games
Mixed strategies
A mixed strategy is a probability distribution over pure strategies.
Video explanations to be addedZero-sum games and minimax
For finite two-player zero-sum games, optimal mixed strategies equalize maximin and minimax values.
Video explanations to be addedExtensive-form games
A game tree represents the order of decisions, information and terminal payoffs.
Video explanations to be addedBackward induction
Reasoning backward from terminal choices solves finite perfect-information games under appropriate preferences.
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Uncertainty and collective decisions
Expected utility
Expected utility evaluates uncertain outcomes using probabilities and a utility function.
Video explanations to be addedBayesian games
Players' private types and beliefs extend strategic analysis to incomplete information.
Video explanations to be addedSocial choice
Voting rules aggregate individual preferences and face fairness tradeoffs.
Video explanations to be addedMechanism design
Rules are chosen to induce desired outcomes from strategic participants.
Video explanations to be added