Lecture 4 - Game Theory Flashcards
(21 cards)
What is game theory?
Mathematical models to study conflict and cooperation between rational decision-makers
What are the two main forms of games?
- Simultaneous-move (Normal/Strategic form) 2. Sequential-move (Extensive form)
What are the three essential components of any game?
Players, Strategies, Payoffs
How are simultaneous-move games represented?
Using payoff matrices (2 players) or tables (3+ players)
How are sequential-move games represented?
Using game trees with nodes, branches, and terminal payoffs
What is a strictly dominated strategy?
A strategy that always yields a lower payoff than another strategy, regardless of opponents’ choices
What is a dominant strategy equilibrium?
When each player has a dominant strategy (best regardless of others’ choices)
What is a Nash Equilibrium?
A strategy profile where no player can benefit by unilaterally changing their strategy
How do you find Nash Equilibria?
- Identify best responses for each player 2. Find where all players are playing best responses
What is subgame perfect equilibrium?
A refinement of NE that requires equilibrium play in every subgame (found via backward induction)
What is backward induction?
Solving sequential games by starting from final nodes and working backward to initial node
What is the Prisoner’s Dilemma’s dominant strategy equilibrium?
(Defect, Defect) even though (Cooperate, Cooperate) would be better for both
What is common knowledge in game theory?
All players know the rules, and know that others know, and know that others know they know, etc.
What is perfect recall?
Players remember all past moves (opposite of imperfect recall)
What is a zero-sum game?
One player’s gain equals another’s loss (e.g., Matching Pennies)
Why does the Centipede Game seem paradoxical?
Backward induction suggests stopping immediately (2,0) though mutual cooperation yields higher payoffs
What are the Nash Equilibria in this game?<br></br>┌───┬─────┬─────┐<br></br>│ │ A │ P │<br></br>├───┼─────┼─────┤<br></br>│ A │ 0,0 │ 7,2 │<br></br>│ P │ 2,7 │ 6,6 │<br></br>└───┴─────┴─────┘
(A,P) and (P,A)
What is the ultimatum game?
A sequential game where one player proposes how to split money and the other accepts/rejects
What does ‘extensive form’ mean?
Game representation showing sequence of moves (game trees) as opposed to normal form matrices
What is the key difference between normal and extensive form games?
Normal form hides timing of moves, extensive form shows sequence of moves explicitly
What is an incredible threat?
A threat in a sequential game that wouldn’t be rational to carry out (eliminated by subgame perfection)
