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Solution concept in game theory
An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Set of strategies in game theory
In game theory an evolutionarily stable set (ES set), sometimes referred to as evolutionary stable sets, is a set of strategies, which score equally against
Evolutionarily_stable_set
Condition where selection restores genetic composition
A population can be described as being in an evolutionarily stable state when that population's "genetic composition is restored by selection after a
Evolutionarily_stable_state
Pairing where no unchosen pair prefers each other over their choice
and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering
Stable_matching_problem
Game where groups of players may enforce cooperative behaviour
unique vector. The core is contained in any stable set, and if the core is stable it is the unique stable set; see (Driessen 1988) for a proof. For simple
Cooperative_game_theory
Game theory model of aggression
model was originally formulated by John Maynard Smith; a mixed evolutionarily stable strategy (ESS) was determined by Bishop & Cannings. An example is
War_of_attrition_(game)
Complete plan on how a game player will behave in every possible game situation
and extended form games. Nash equilibrium Haven (graph theory) Evolutionarily stable strategy Ben Polak Game Theory: Lecture 1 Transcript ECON 159, 5
Strategy_(game_theory)
Logical paradox in decision-making theory
Studies: An Irish Quarterly Review, 86(344), 346–359. http://www.jstor.org/stable/30091841 Blumner, Robyn E. (August–September 2016). "Is My Intolerance of
Paradox_of_tolerance
Decision rule used for minimizing the possible loss for a worst-case scenario
worst possible result is then no payment. However, this solution is not stable, since if B believes A will choose A2 then B will choose B1 to gain 1; then
Minimax
Mathematical models of strategic interactions
that would be maintained by evolutionary forces. The best-known equilibrium in biology is known as the evolutionarily stable strategy (ESS), first introduced
Game_theory
Model of conflict for two players in game theory
strategies. Either the pure, or mixed, Nash equilibria will be evolutionarily stable strategies depending upon whether uncorrelated asymmetries exist
Chicken_(game)
Overuse of a shared resource
these classes and distinguish between psychological individual differences (stable personality traits) and situational factors (the environment). Situational
Tragedy_of_the_commons
Application of game theory to evolving populations in biology
Some attractors (all global asymptotically stable fixed points) of the equations are evolutionarily stable states. A strategy which can survive all "mutant"
Evolutionary_game_theory
Weakly optimal allocation of resources
solution sets) being incomparable Emmerich, M. T. M.; Deutz, A. H. (2018). "A tutorial on multiobjective optimization: fundamentals and evolutionary methods"
Pareto_efficiency
Situation where total gains match total losses
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Zero-sum_game
Problem in process of sharing surplus
sequential bargaining. A two-person bargain problem consists of: A feasibility set F {\displaystyle F} , a closed subset of R 2 {\displaystyle \mathbb {R} ^{2}}
Cooperative_bargaining
English saying meaning "equivalent retaliation"
ethologists and evolutionary psychologists to apply tit-for-tat strategies to explain why altruism evolves in many animal communities. Evolutionary game theory
Tit_for_tat
Standard example in game theory
shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade
Prisoner's_dilemma
Solution concept of a non-cooperative game
above there are both stable and unstable equilibria. The equilibria involving mixed strategies with 100% probabilities are stable. If either player changes
Nash_equilibrium
Paper-and-pencil game for two players
trying with the eyes shut to bring the pencil down on one of the numbers of a set, the number hit being scored". "Tic-tac-toe" may also derive from "tick-tack"
Tic-tac-toe
Hand game for two players or more
2012-01-14. Retrieved 2009-12-05. St. John, Kelly (2003-03-19). "Ready, set ... Roshambo! Contestants vie for $1,000 purse in Rock, Scissors, Paper contest"
Rock_paper_scissors
Israeli-American psychologist and economist (1934–2024)
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Daniel_Kahneman
Simultaneous game found in game theory
Unlike the pure Nash equilibria, the mixed equilibrium is not an evolutionarily stable strategy (ESS). The mixed Nash equilibrium is also Pareto dominated
Coordination_game
Search algorithm
function may return values (v) that exceed (v < α or v > β) the α and β bounds set by its function call arguments. In comparison, fail-hard alpha–beta limits
Alpha–beta_pruning
Hungarian and American mathematician and physicist (1903–1957)
Uchaikin, Vladimir V.; Zolotarev, Vladimir M. (1999). Chance and Stability: Stable Distributions and their Applications. De Gruyter. pp. xviii, 281, 424. doi:10
John_von_Neumann
Concept in game theory
task; such situations are often called coalitional games. For a coalition (set of players) S {\displaystyle S} , we define the payoff or value function
Shapley_value
Hand game for two or more players
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Chopsticks_(hand_game)
Game whose outcome can be correctly predicted
Playground". tromp.github.io. "UCI Machine Learning Repository: Connect-4 Data Set". archive.ics.uci.edu. "ChristopheSteininger/c4". github.com. Böck, Markus
Solved_game
Israeli psychologist (1937–1996)
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Amos_Tversky
Dynamical system
set of evolutionarily stable states of the population. In general nondegenerate cases, there can be at most one interior evolutionary stable state (ESS)
Replicator_equation
Concept in game theory
not know which one of them is which, then the mixed Nash is an evolutionarily stable strategy (ESS), as play is confined to the bottom left to top right
Best_response
Game in economic experiments
proposer can choose from many different splits. A Nash equilibrium is a set of strategies (one for the proposer and one for the responder in this case)
Ultimatum_game
Finding an optimal algorithm for playing chess
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Solving_chess
Theorem in game theory
which also introduced the formal, set-theoretic definition of common knowledge. The model of Aumann considers a finite set of states S {\displaystyle S} drawn
Aumann's_agreement_theorem
Field of economics and game theory
{u}}(\theta )\ \forall \theta } The principal here is a monopolist trying to set a profit-maximizing price scheme in which it cannot identify the type of
Mechanism_design
Proof all ranked voting rules have spoilers
to occur in practice. Holliday, Wesley H.; Pacuit, Eric (2023-03-14). "Stable Voting". Constitutional Political Economy. 34 (3): 421–433. arXiv:2108.00542
Arrow's_impossibility_theorem
Modelling evolution using differential equations
evolutionary biology. An important concept of evolutionary game theory as applied in biology is the evolutionarily stable strategy or ESS. This is important because
Evolutionary_dynamics
Level of information in economics and game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Complete_information
Making of satisfactory, not optimal, decisions
the optimum (best possible) payoff as U ∗ {\displaystyle U^{*}} , then the set of epsilon-optimizing options S ( ϵ ) {\textstyle S(\epsilon )} can be defined
Bounded_rationality
Mathematical modelling of phenotypic evolution
function where finite evolutionary steps lead past the local 'flatness'. Second, a fitness maximum which is known as an evolutionarily stable strategy (ESS)
Evolutionary invasion analysis
Evolutionary_invasion_analysis
Type of stable matching problem
algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint
Stable_roommates_problem
Diplomatic policy of concessions
Nations and the failure of collective security. The League of Nations was set up in the aftermath of World War I in the hope that international co-operation
Appeasement
Condition in economics and game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Perfect_information
Statement that players know and also know that other players know (ad infinitum)
knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an
Common_knowledge_(logic)
Facilitating a peaceful outcome to a dispute
necessary for survival, giving it a strong evolutionary value. A further focus of this is among species that have stable social units, individual relationships
Conflict_resolution
Model of humans as rational, self-interested agents
discussion. In its standard formulation, the model assumes that individuals have stable preferences, access to relevant information, and seek to maximize utility
Homo_economicus
Concept in game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Focal_point_(game_theory)
Economic phenomenon
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Tyranny_of_small_decisions
Situation where all parties are worse off
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
No-win_situation
Human behavior pattern in which the participant takes on increasing risk
when subjects view current issues as having unstable reasoning rather than stable reasoning, or when the individual is unwilling to admit mistakes. They then
Escalation_of_commitment
Simple mathematical game
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Pirate_game
Poker game developed by Harold Kuhn
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Kuhn_poker
Tendency to overestimate in auctions
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Winner's_curse
Set in game theory
coalition having at least (n+1)/2 members has an empty core. That is, no stable coalition exists. Consider a group of n miners, who have discovered large
Core_(game_theory)
Hungarian-American economist and philosopher (1920–2000)
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
John_Harsanyi
Notion in combinatorial game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Game_complexity
Game theory scenario
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Win–win_game
Political model of international conflict resolution
are smaller. The perceived win-set size, however, is just as important as the actual win-set size. If a state's win-set size is perceived to be large,
Two-level_game_theory
Branch of game theory about two-player sequential games with perfect information
information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical
Combinatorial_game_theory
Two-player coordination game in game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Cooperation between firms to limit competition
incentive for firms to compete on product differentiation Stable demand and/or excess capacity: Stable demand and capacity implies predictability and therefore
Collusion
a crucial role in determining which Nash equilibria qualify as evolutionarily stable strategies (ESS) in coordination games and discoordination games
Uncorrelated_asymmetry
Game where a certain player can force a win with perfect play
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
First-player and second-player win
First-player_and_second-player_win
In game theory, a stochastically stable equilibrium is a refinement of the evolutionarily stable state in evolutionary game theory, proposed by Dean Foster
Stochastically stable equilibrium
Stochastically_stable_equilibrium
Field in social science
do not only seek for the profits in a near future that might violate the stable state of peace. For a sustainable peace, nurturing, empowerment, and communications
Peace_and_conflict_studies
Formal rule for predicting how a game will be played
ISBN 978-0-521-89943-7. Thomas, B. (1985a) On evolutionary stable sets. J. Math. Biol. 22:105–115. Thomas, B. (1985b) Evolutionary stable sets in mixed-strategist models
Solution_concept
Israeli-American mathematician (born 1930)
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Robert_Aumann
Point in evolutionary space where selection always leads
selection, such as an evolutionarily stable strategy, other possibilities are available. Because identification of an evolutionary attractor on its own
Evolutionary_attractor
Decrease in severity of conflicts
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
De-escalation
Concept in conflict studies
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Conflict_escalation
Problem of sharing resources
Fair division is an optimisation problem in game theory of dividing a set of resources among several parties who have an entitlement to them so that each
Fair_division
Class of theorems about Nash equilibrium payoff profiles in repeated games
requirement is needed because of the last step. In the last step, the only stable outcome is a Nash-equilibrium in the basic game. Suppose a player i gains
Folk_theorem_(game_theory)
Representation of a game in game theory
cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or
Normal-form_game
Neologism for cooperative competition
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Coopetition
Military strategy during the Cold War with regard to the use of nuclear weapons
deterrence has succeeded. Furthermore, as Jentleson et al. argue, two key sets of factors for successful deterrence are important: a defending state strategy
Deterrence_theory
Solution concept for non-cooperative games
and Player Splitting. The stable sets of the product of two independent games are the products of their stable sets. Stable sets are not affected by splitting
Mertens-stable_equilibrium
Conflict between safety and cooperation
a stag hunt is a game with two pure strategy Nash equilibria, that is, stable attractors where an individual player can't improve their position with
Stag_hunt
Trigger strategy
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Grim_trigger
Economic model
and then behaves as a monopoly. The state of equilibrium... is therefore stable; i.e., if either of the producers, misled as to his true interest, leaves
Cournot_competition
Wide-ranging representation of a game in game theory
edges of any two nodes of the same information set—thus the set of all outgoing edges of an information set is partitioned in equivalence classes, each class
Extensive-form_game
Concept in game theory involving long-term strategic planning
stable configurations. Evolutionary game theory Cooperative game theory Hedonic games Subgame perfect equilibrium Repeated game Evolutionarily stable
Farsightedness_(game_theory)
In board games that cannot end in a draw, one of the two players has a winning strategy
certain set, containing all possible sequences of moves such that a player wins independently of how the other player plays. But should this set be empty
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Quality of a strategy in game theory
dominated by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, while all other sets of opponents' actions give B the
Strategic_dominance
is a player. Strategies per player: In a game each player chooses from a set of possible actions, known as pure strategies. If the number is the same
List_of_games_in_game_theory
Experimental tool
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Dictator_game
Two-player extensive form game
coins for himself. In the centipede game, a pure strategy consists of a set of actions (one for each choice point in the game, even though some of these
Centipede_game
Game illustrating paradox in rational choice theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Dollar_auction
Game-theoretic concept
costly for the sender depending on the state of the world. This basic setting set by Vincent Crawford and Joel Sobel has given rise to a variety of variants
Cheap_talk
Search heuristic for combinatorial games
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Aspiration_window
Game theory concept
consists of the following elements: Set of players, N The set of players within the game Action sets, ai The set of actions available to Player i. An
Bayesian_game
Study of strategic decision making
Du)m)=0&(2)\\m(0)=m_{0}&(3)\\u(x,T)=G(x,m(T))&(4)\end{cases}}} The basic dynamics of this set of Equations can be explained by an average agent's optimal control problem
Mean-field_game_theory
Concept in game theory
stochastic game are: a finite set of players I {\displaystyle I} ; a state space S {\displaystyle S} (either a finite set or a measurable space ( S , S
Stochastic_game
English mathematician and game theorist born 1940
contributions to the foundations of game theory, experimental economics, evolutionary game theory and analytical philosophy. He took up economics after holding
Kenneth_Binmore
Game theory case weighing own/others' sacrifice
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Volunteer's_dilemma
Mathematical game
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Guess_2/3_of_the_average
Combinatorial game theory theorem
move loses). At any given point in the game, a player's position is the set of moves they are allowed to make. As an example, we can define the zero
Sprague–Grundy_theorem
American computer scientist and mathematician
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Jennifer_Tour_Chayes
Simple game studied in game theory
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Matching_pennies
American economist (born 1939)
Neumann Evolutionary game theory Core concepts Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state
Samuel_Bowles_(economist)
the Evolutionarily stable strategy or ESS. As the authors argued, "Beliefs determine Behavior. Behavior determines payoff. From an evolutionary perspective
Conjectural_variation
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
Surname or Lastname
English
English : byname from Middle English staley ‘resolute’, ‘reliable’, a reduced form of Stallard.Belgian French : from Old French estalee ‘fish trap’, hence possibly a metonymic occupational name for a fisherman, or topographic name for someone who lived near where fish traps were set.
Boy/Male
Shakespearean American English
Henry VI, Part 2' Sir John Stanley. 'King Henry the Sixth, Part III' Sir William Stanley. 'King...
Surname or Lastname
English, Dutch, North German, and Danish
English, Dutch, North German, and Danish : variant of Stubbe.
Boy/Male
Hindu
Stable
Boy/Male
Indian, Punjabi, Sikh
Stable
Surname or Lastname
English
English : occupational name for someone who looked after horses or cattle, from an agent derivative of Middle English stable ‘stable’.German (Stäbler) : occupational name for an official who carried a staff as a symbol of office, Middle High German stebelære.
Surname or Lastname
English
English : variant of Staple.
Boy/Male
Indian, Sanskrit
Stable
Boy/Male
Tamil
Stable
Boy/Male
Vietnamese
Stable.
Surname or Lastname
English
English : topographic name for someone who lived near a boundary post, from Middle English stapel ‘post’ + the suffix -er, denoting an inhabitant.
Female
English
Elaborated form of English Star, STARLA means "star."
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
Female
English
Feminine variant spelling of English unisex Stacey, STACEE means "resurrection."
Male
French
French name derived from Latin amabilis, AMABLE means "lovable."
Surname or Lastname
English
English : from Middle English stapel ‘post’, hence a topographic name for someone who lived near a boundary post, or a habitational name from some place named with this word (Old English stapel), as for example Staple in Kent or Staple Fitzpaine in Somerset.Americanized spelling of German Stapel.
Female
English
Feminine variant spelling of English unisex Stacey, STACIE means "resurrection."
Surname or Lastname
English
English : topographic name for someone who lived by a stable, or an occupational name for someone employed in one, from Middle English stable, plural stables (via Old French from Latin stabulum, a derivative of stare ‘to stand’). In Middle English the term was used of the quarters occupied by cattle as well as those reserved for horses.
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : habitational name from Scoble in Devon.
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
Surname or Lastname
German
German : unexplained.English : variant of Hicks.
Girl/Female
Hindu, Indian
Giving
Female
African
angel.
Girl/Female
Indian, Sanskrit
Braid of Flowers
Girl/Female
Hindu, Indian
A Light that Shines Very Bright
Boy/Male
Hindu
Protector in kaliyug
Female
English
Elaborated form of English Joanne, JOANDRA means "God is gracious."
Boy/Male
Indian
Main Person in a Yagna
Female
English
Variant spelling of English Kayley, KAILEE means "slender."
Boy/Male
Arabic, Australian, Biblical, Farsi, French, German, Iranian, Turkish
Abbreviated Form of Abdul; My Servant
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
EVOLUTIONARILY STABLE-SET
v. i.
Firmly established; not easily moved, shaken, or overthrown; fixed; as, a stable government.
a.
Being of reasonable or suitable size; as, sizable timber; sizable bulk.
imp. & p. p.
of Stable
v. t.
To sort according to its staple; as, to staple cotton.
v. t.
To put or keep in a stable.
a.
Pertaining to, or being market of staple for, commodities; as, a staple town.
v. i.
A house, shed, or building, for beasts to lodge and feed in; esp., a building or apartment with stalls, for horses; as, a horse stable; a cow stable.
n.
The fur of the sable.
a.
Established in commerce; occupying the markets; settled; as, a staple trade.
n.
Hence, food placed on a table to be partaken of; fare; entertainment; as, to set a good table.
imp. & p. p.
of Sable
n.
A stable keeper.
a.
Relating to evolution; as, evolutionary discussions.
a.
Liable to, or subjected by law to, taxation; as, ratable estate.
v. t.
To form into a table or catalogue; to tabulate; as, to table fines.
v. i.
To dwell or lodge in a stable; to dwell in an inclosed place; to kennel.
adv.
In a stable manner; firmly; fixedly; steadily; as, a government stably settled.
n.
The fiber of wool, cotton, flax, or the like; as, a coarse staple; a fine staple; a long or short staple.
a.
Not stable; not standing fast or firm; unstable; prone to change or recede from a purpose; mutable; inconstant.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.