Lecture 5- Game theory Flashcards
What is Game Theory?
A technique used to study interactive decision making where the outcome of each player depends on the actions of all other players in the game
What are the three basic elements of a game?
- The players, 2. The rules of the game/strategies, 3. The available payoffs
What is a game of perfect information?
A game where when any player makes a move, they know all the prior choices made by the other players
What is a game of imperfect information?
A game where when a player reaches a decision point, they don’t know all the choices of the other players who preceded them
What is a zero-sum game?
A game where the gains of one player equal the losses of other players, making the sum of payoffs always equal to zero
What is a non-cooperative game?
A game where players must make strategy choices in isolation without consulting other players, with no possibility of formal binding cooperation
What is a dominant strategy?
A strategy that is best for a player no matter what strategy the other player uses
What is a Nash equilibrium?
A state where no player wishes to change their behavior given the behavior of other players - each player’s choice is optimal given the other players’ choices
What are the three problems with Nash equilibrium?
- A game may have multiple Nash equilibria, 2. Some games have no Nash equilibrium, 3. Nash equilibrium may not lead to Pareto-optimal choices
What is a credible threat?
A threat that a player would actually carry out if the game progressed to that point, making it rational and believable
What is a non-credible threat?
A threat that a player would not actually carry out if the game reached that point, making it irrational and unbelievable
What is a sub-game perfect equilibrium?
A set of strategies where the actions prescribed for players in any sub-game constitute Nash equilibrium for that sub-game
What is backward induction?
A process of solving a game by starting at its end and working backward to figure out what each player will do along the way
What is the Prisoner’s Dilemma?
A game showing how individual rational choices can lead to collectively sub-optimal outcomes, where two prisoners must decide whether to confess or remain silent
Why is cooperation difficult in the Prisoner’s Dilemma?
Because cooperation is individually irrational - each prisoner has a dominant strategy to confess regardless of what the other does
What is an extensive form of a game?
A detailed description of the game rules shown through a game tree diagram, showing all possible moves and their sequence
What is a normal form of a game?
The presentation of game strategies in matrix form, showing payoffs for each combination of player strategies
What’s the difference between extensive and normal form?
Extensive form shows the sequence of moves through a tree diagram, while normal form presents all strategies and payoffs in a matrix
What determines if a game is classified as ‘perfect information’?
Whether players know all prior choices made by other players when making their own moves
How do you identify a dominant strategy equilibrium?
When each player has a strategy that dominates all others regardless of what other players do
What makes the Nash equilibrium different from dominant strategy equilibrium?
Nash equilibrium requires each player’s choice to be optimal given others’ choices, while dominant strategy is optimal regardless of others’ choices
What is the purpose of backward induction?
To find sub-game perfect equilibria by working backwards from end payoffs to determine rational choices at each decision point
What is a pure strategy?
A complete plan of action that tells a player what choice to make at any node of the game tree or in any situation that might arise
What happens in a cooperative game that’s different from non-cooperative?
In cooperative games, players can communicate and make binding agreements, while in non-cooperative games they must act independently
What makes a threat ‘credible’ in game theory?
A threat is credible if it would be rational for the player to actually carry it out if the game reached that point, rather than just threatening to do so
