Game Theory & Behavioral: Cheat Sheet
Based on Varian’s Microeconomics
1. Game Theory Basics 4. Sequential Games
Strategic interaction where outcome depends on choices of Players move in turns.
all players.
• Game Tree: Nodes represent decision points.
• Normal Form: Payoff matrix (Simultaneous). • Backward Induction: Start at the end, solve for
• Extensive Form: Game tree (Sequential). the best move, and work backward.
• Subgame Perfect NE: An equilibrium that is ratio-
Dominant Strategy nal in every sub-part of the tree. It eliminates non-
credible threats.
A strategy that yields a higher payoff than any other, re-
gardless of what the opponent plays.
5. Behavioral Economics
• If both have one: Dominant Strategy Equilib-
rium. Combines psychology and economics.
Nash Equilibrium (NE) Time Inconsistency
A set of strategies where no player has an incentive to Standard (Exponential): δ t . Consistent preferences
deviate, taking the other’s strategy as given. over time. Behavioral (Hyperbolic): Impatient now,
patient later.
Mutual Best Response: Action a1 is best for P1
given P2 plays a2 . Action a2 is best for P2 given P1 1
D(t) =
plays a1 . 1 + kt
Leads to procrastination and the need for Commitment
2. Classic Games Devices.
Prisoner’s Dilemma Prospect Theory (Kahneman & Tversky)
C D • Reference Dependence: We value changes relative
C (-3,-3) (0,-6)
D (-6,0) (-1,-1)
to a status quo, not absolute wealth.
• Loss Aversion: The pain of losing $X is greater than
• Dominant Strategy: Defect (D). the joy of gaining $X. Value function is steeper in the
• NE: (Defect, Defect). loss domain.
• Framing: ”90% survival rate” vs ”10% mortality
• Pareto Efficient: (Cooperate, Cooperate).
rate” changes decisions.
• Conclusion: Individual rationality ̸= Group rational-
ity. Social Norms
Battle of the Sexes Ultimatum Game: Proposer offers split. Responder ac-
cepts or rejects (both get 0).
Coordination game with conflict.
• Rational Prediction: Offer $0.01, Accept.
• 2 Pure Nash Equilibria (Doing the same thing). • Reality: Offers < 30% are often rejected to punish
unfairness.
• 1 Mixed Nash Equilibrium.
Biases
3. Mixed Strategies
• Anchoring: Relying too heavily on the first piece of
When there is no Pure Strategy NE (e.g., Matching Pen- information (e.g., sticker price).
nies), players randomize.
• Sunk Cost Fallacy: ”I must finish this bad movie
because I paid for the ticket.” (Rational: Ignore sunk
• Method: Find probability p that makes the oppo-
costs).
nent indifferent between their choices.
• Endowment Effect: Overvaluing what you own.
E[Choice A] = E[Choice B]
1
Based on Varian’s Microeconomics
1. Game Theory Basics 4. Sequential Games
Strategic interaction where outcome depends on choices of Players move in turns.
all players.
• Game Tree: Nodes represent decision points.
• Normal Form: Payoff matrix (Simultaneous). • Backward Induction: Start at the end, solve for
• Extensive Form: Game tree (Sequential). the best move, and work backward.
• Subgame Perfect NE: An equilibrium that is ratio-
Dominant Strategy nal in every sub-part of the tree. It eliminates non-
credible threats.
A strategy that yields a higher payoff than any other, re-
gardless of what the opponent plays.
5. Behavioral Economics
• If both have one: Dominant Strategy Equilib-
rium. Combines psychology and economics.
Nash Equilibrium (NE) Time Inconsistency
A set of strategies where no player has an incentive to Standard (Exponential): δ t . Consistent preferences
deviate, taking the other’s strategy as given. over time. Behavioral (Hyperbolic): Impatient now,
patient later.
Mutual Best Response: Action a1 is best for P1
given P2 plays a2 . Action a2 is best for P2 given P1 1
D(t) =
plays a1 . 1 + kt
Leads to procrastination and the need for Commitment
2. Classic Games Devices.
Prisoner’s Dilemma Prospect Theory (Kahneman & Tversky)
C D • Reference Dependence: We value changes relative
C (-3,-3) (0,-6)
D (-6,0) (-1,-1)
to a status quo, not absolute wealth.
• Loss Aversion: The pain of losing $X is greater than
• Dominant Strategy: Defect (D). the joy of gaining $X. Value function is steeper in the
• NE: (Defect, Defect). loss domain.
• Framing: ”90% survival rate” vs ”10% mortality
• Pareto Efficient: (Cooperate, Cooperate).
rate” changes decisions.
• Conclusion: Individual rationality ̸= Group rational-
ity. Social Norms
Battle of the Sexes Ultimatum Game: Proposer offers split. Responder ac-
cepts or rejects (both get 0).
Coordination game with conflict.
• Rational Prediction: Offer $0.01, Accept.
• 2 Pure Nash Equilibria (Doing the same thing). • Reality: Offers < 30% are often rejected to punish
unfairness.
• 1 Mixed Nash Equilibrium.
Biases
3. Mixed Strategies
• Anchoring: Relying too heavily on the first piece of
When there is no Pure Strategy NE (e.g., Matching Pen- information (e.g., sticker price).
nies), players randomize.
• Sunk Cost Fallacy: ”I must finish this bad movie
because I paid for the ticket.” (Rational: Ignore sunk
• Method: Find probability p that makes the oppo-
costs).
nent indifferent between their choices.
• Endowment Effect: Overvaluing what you own.
E[Choice A] = E[Choice B]
1
