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game theory
the study of strategic interactions where the outcome for each participant depends on the choices of others
strategic interdependence
a situation in which the best decision for one player depends on the decisions of others
players
the decision-makers in a game
strategies
the possible actions a player can take in a game
strategy set
the complete list of strategies available to a player
strategy pair
a combination of strategies chosen by two players in a two-player game
strategic reasoning
the process of anticipating other players’ moves and best responses
strategic behavior
actions taken by a player based on expectations of how others will behave
sincere behavior
acting according to one’s true preferences rather than strategically manipulating the outcome
strategic games
games in which players choose their strategies simultaneously without knowing the choices of others
extensive form
a representation of a game using a decision tree to show the order of moves and possible outcomes
strategic form
a representation of a game using a matrix that shows players’ payoffs for each strategy combination
payoff matrix
a table showing the outcomes (payoffs) for all possible strategy combinations in a game
decision tree
a graphical representation of sequential decision-making in a game
perfect information
a game setting where all players know the full history of moves before making a decision
information set
in extensive-form games, a collection of decision nodes where a player must make a move but cannot distinguish between them
imperfect information
a game setting where players do not know all past moves or the full state of the game
rationality
the assumption that players make decisions that maximize their expected payoff
knowledge
the information players have about the game, which may or may not be shared among all players
beliefs
a player’s expectations about what other players will do
other’s beliefs
the beliefs a player has about the beliefs of others
unilateral deviation
a situation where a player changes their strategy, assuming all other players keep theirs fixed
indifference
a scenario where a player values two or more outcomes equally and has no preference between them
iterated deletion of strictly dominated strategies (IDSDS)
the process of sequentially removing strategies that are strictly worse than another strategy
iterated deletion of weakly dominated strategies (IDWDS)
a refinement of IDSDS that removes weakly dominated strategies
strictly dominant strategies
strategies that always provide a higher payoff than any other strategy, regardless of what opponents do
weakly dominant strategies
strategies that are at least as good as any other and strictly better in some cases
strictly dominated strategies
strategies that always result in a lower payoff than some other strategies
weakly dominated strategies
strategies that never perform better than another and perform worse in some cases
Pareto dominance
a situation where one outcome is strictly better for at least one player without making anyone worse off
Pareto dominated strategies
strategies that result in outcomes worse than another option for all players
iterated deletion
the process of removing dominated strategies from consideration to simplify a game
Nash equilibrium
a situation where no player can improve their outcome by changing their strategy while others keep theirs unchanged
“group rational” outcomes
outcomes that maximize the collective benefit of all players
“individual rational” outcomes
outcomes that are beneficial for each player based on their own preferences
strategy n-tuple
a set of strategies where each player has chosen one strategy
coordination games
games where players benefit from choosing the same or compatible strategies
coordination and conflict games
games that involve both elements of cooperation and competition
cooperative game theory
the study of games where players can form binding agreements and negotiate outcomes
non-cooperative game theory
the study of games where players act independently and cannot make binding agreements
zero-sum games
games where one player’s gain is exactly balanced by another’s loss
matching-sum games
games where the total payoff can vary, and players’ gains are not necessarily balanced by others’ losses
pure conflict games
games where players’ interests are completely opposed
mutual interest games
games where all players benefit from cooperating
symmetric games
games where players have identical strategies and payoffs, meaning roles can be swapped without changing the outcome
auction theory
the study of bidding strategies and outcomes in different types of auctions
second-price auctions
auctions where the highest bidder wins but pays the second-highest bid
mechanism design
the branch of game theory that focuses on designing rules or institutions to achieve desired outcomes
mixed strategies
strategies where players randomize their choices to keep opponents uncertain
expected payoff
the weighted average of all possible payoffs, considering their probabilities
cardinal payoffs
payoffs that have meaningful numerical differences (e.g., a score of 10 is twice as good as a score of 5)
ordinal payoffs
payoffs that indicate preference rankings without numerical significance (e.g., ranking options as 1st, 2nd, 3rd)
risk-neutral players
players who only care about expected payoffs and are indifferent to risk
risk-averse players
players who prefer certainty over higher but riskier payoffs
learning
the process by which players adjust their strategies over time based on past experiences
John Forbes Nash
mathematician known for Nash equilibrium, a foundational concept in game theory.
Joseph E. Harrington Jr.
economist known for contributions to game theory and industrial organization – author of Games, Strategies, and Decision Making
evolution
the process by which populations change over generations through natural selection
population
a group of individuals of the same species that live and interact in a given area
speciation
the formation of new species through evolutionary processes
genotype
the genetic makeup of an organism, determining its characteristics
allele
a variant form of a gene that can lead to different traits
fictitious play
players repeatedly best respond to the opponent’s past average play, assuming it reflects their strategy
objective probability
true likelihood of an event based on empirical data or mathematical reasoning
subjective probability
personal belief about the likelihood of an event, based on individual judgment or information
probability distribution
a function that assigns probabilities to all possible outcomes of a random variable
credible threats
a threat a player can actually carry out because it’s in their best interest at the time they would have to act
incredible threats
a threat a player says they’ll make but wouldn’t actually follow through with because it wouldn’t benefit them when the moment comes
subgame perfection
refinement of Nash equilibrium where players’ strategies form a Nash equilibrium in every subgame of the larger game
subgame perfect equilibrium (SPE)
a strategy set where players make optimal decisions at every stage of the game, not just along the main path, eliminating incredible threats
Reinhard Selten
the game theorist who introduced the concept of subgame perfection and won the Nobel Prize for his work
rollback equilibrium
another name for subgame perfect equilibrium, found using backward induction to solve games step by step from the end
perfect recall
a player remembers all past information they observed and their own past choices
imperfect recall
a player forgets or loses access to some past information or past choices
simulated introspection
a method where players predict opponents’ strategies by reasoning about how those opponents model their own behavior
first-price auctions
an auction format where the highest bidder wins and pays their bid amount
