[ECON 246] Evolutionary Game Theory

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