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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
Solution concept for non-cooperative games
Perfection: Each equilibrium in a stable set is perfect, and therefore admissible. Backward Induction and Forward Induction: A stable set includes a proper
Mertens-stable_equilibrium
Topics referred to by the same term
theory, a theory in mathematics Mertens-stable equilibrium in game theory Stochastically stable equilibrium in game theory This disambiguation page lists
Stable_equilibrium
Solution concept in game theory
terms, an ESS is an equilibrium refinement of the Nash equilibrium, being a Nash equilibrium that is also "evolutionarily stable." Thus, once fixed in
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Pairing where no unchosen pair prefers each other over their choice
mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements
Stable_matching_problem
Solution concept of a non-cooperative game
In game theory, a Nash equilibrium is a situation where no player could gain more by changing their own strategy (holding all other players' strategies
Nash_equilibrium
Game theory model of aggression
evolutionarily stable strategy coincides with the symmetric Nash equilibrium. This follows from the fact that any ESS must be a Nash equilibrium and the fact
War_of_attrition_(game)
Decision rule used for minimizing the possible loss for a worst-case scenario
two-player zero-sum games, the minimax solution is the same as the Nash equilibrium. In the context of zero-sum games, the minimax theorem is equivalent
Minimax
Concept in game theory
In this coordination game, any place and time in the city could be an equilibrium solution. Schelling asked a group of students this question and found
Focal_point_(game_theory)
Game theory concept
a recursive combination of the Bayesian Nash equilibrium and the Bellman optimality equation. Stochastic Bayesian games have been used to address diverse
Bayesian_game
Standard example in game theory
of strategies forms a stable equilibrium, and the system will always oscillate between bounds.[citation needed] In a stochastic iterated prisoner's dilemma
Prisoner's_dilemma
Mathematical models of strategic interactions
rules. The best-known equilibrium in biology is the evolutionarily stable strategy (ESS), which is equivalent to a Nash equilibrium in TGT. Another distinct
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
Situation where players have only a small incentive to change strategies
epsilon-equilibrium, or near-Nash equilibrium, is a strategy profile that approximately satisfies the condition of Nash equilibrium. In a Nash equilibrium, no
Epsilon-equilibrium
English saying meaning "equivalent retaliation"
disappear." Can be both Nash equilibrium and knife-edge equilibrium. Known as knife-edge equilibrium because the equilibrium "rests precariously on" the
Tit_for_tat
Formal rule for predicting how a game will be played
concept of Stable equilibrium, a refinement that satisfies forward induction. A counter-example was found where such a stable equilibrium did not satisfy
Solution_concept
Hungarian and American mathematician and physicist (1903–1957)
of an expanding economy, he proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem. Von Neumann's
John_von_Neumann
Paper-and-pencil game for two players
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Tic-tac-toe
Model of conflict for two players in game theory
strategy Nash equilibrium. Although there are three Nash equilibria in the Hawk–Dove game, the one which emerges as the evolutionarily stable strategy (ESS)
Chicken_(game)
Poker game developed by Harold Kuhn
other player). The game has a mixed-strategy Nash equilibrium; when both players play equilibrium strategies, the first player should expect to lose
Kuhn_poker
Game theory solution
In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician
Correlated_equilibrium
Simultaneous game found in game theory
equilibria, the mixed equilibrium is not an evolutionarily stable strategy (ESS). The mixed Nash equilibrium is also Pareto dominated by the two pure Nash equilibria
Coordination_game
Problem in process of sharing surplus
player 1 in equilibrium is 1/(1+d), while the payoff for player 2 is d/(1+d). In the limit as players become perfectly patient, the equilibrium division
Cooperative_bargaining
Refinement of Nash equilibrium
Sequential equilibrium is a refinement of Nash equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies
Sequential_equilibrium
Concept in game theory
Maskin. In extensive form games, and specifically in stochastic games, a Markov perfect equilibrium is a set of mixed strategies for each of the players
Markov_perfect_equilibrium
Condition where selection restores genetic composition
to an evolutionarily stable state, all of the strategies used within the population must have equal fitness. While the equilibrium may be disturbed by
Evolutionarily_stable_state
Type of perfect Bayesian equilibrium
In signaling games, a separating equilibrium is a type of perfect Bayesian equilibrium where agents with different characteristics choose different actions
Separating_equilibrium
Simple game studied in game theory
of mixed strategies and a mixed strategy Nash equilibrium. This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails)
Matching_pennies
Game theory concept
theory, a subgame perfect equilibrium (SPE), or subgame perfect Nash equilibrium (SPNE), is a refinement of the Nash equilibrium concept, specifically designed
Subgame_perfect_equilibrium
Concept in game theory
Whether every stochastic game with finitely many players, states, and actions, has a uniform equilibrium payoff, or a limiting-average equilibrium payoff, or
Stochastic_game
Type of stable matching problem
combinatorial game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching
Stable_roommates_problem
Economic model
residual demand, 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
Cournot_competition
Mathematical game
dominated strategies. There is a unique pure strategy Nash equilibrium. This equilibrium can be found by iterated elimination of weakly dominated strategies
Guess_2/3_of_the_average
Situation where total gains match total losses
the game always has at least one equilibrium solution. The different game theoretic solution concepts of Nash equilibrium, minimax, and maximin all give
Zero-sum_game
Conflict between safety and cooperation
mixed strategy Nash equilibrium, that is, one in which the players choose either option with some probability. This equilibrium depends on the payoffs
Stag_hunt
Complete plan on how a game player will behave in every possible game situation
impact on normal and extended form games. Nash equilibrium Haven (graph theory) Evolutionarily stable strategy Ben Polak Game Theory: Lecture 1 Transcript
Strategy_(game_theory)
Two-player extensive form game
also called a centipede game. The unique subgame perfect equilibrium (and every Nash equilibrium) of these games results in the first player taking the
Centipede_game
Two-player coordination game in game theory
favored pure strategy equilibrium). It remains unclear how expectations would form that would result in a particular equilibrium being played out. One
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Game theory case weighing own/others' sacrifice
dominant strategy in the volunteer's dilemma. In a mixed-strategy Nash equilibrium, an increase in N players will decrease the likelihood that at least
Volunteer's_dilemma
Solution concept in game theory
response equilibrium (QRE) is a solution concept in game theory. First introduced by Richard McKelvey and Thomas Palfrey, it provides an equilibrium notion
Quantal_response_equilibrium
Dynamical system
incorporates population structure is used in evolutionary graph theory. Nash equilibrium computation Hofbauer, Josef; Sigmund, Karl (2003). "Evolutionary game
Replicator_equation
Academic discipline
choosing to betray each other is still an equilibrium, however, there can also exist multiple Nash equilibriums that vary based on the entanglement of the
Quantum_game_theory
Hand game for two players or more
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Rock_paper_scissors
Quality of a strategy in game theory
game has only one unique Nash equilibrium, referred to as a "dominant strategy equilibrium". However, that Nash equilibrium is not necessarily "efficient"
Strategic_dominance
Weakly optimal allocation of resources
Nash equilibrium Pareto-efficient envy-free division Proctor optimum water content Social Choice and Individual Values by Kenneth Arrow Stable marriage
Pareto_efficiency
Condition in economics and game theory
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Perfect_information
State of balance between external forces on a fluid and internal pressure gradient
In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which
Hydrostatic_equilibrium
Variant of Nash equilibrium in game theory
theory, trembling hand perfect equilibrium, or simply perfect equilibrium, is a type of refinement of a Nash equilibrium that was first proposed by Reinhard
Trembling hand perfect equilibrium
Trembling_hand_perfect_equilibrium
Overuse of a shared resource
organization Jevons paradox – Efficiency leads to increased demand Nash equilibrium – Solution concept of a non-cooperative game Overfishing – Removal of
Tragedy_of_the_commons
Facilitating a peaceful outcome to a dispute
meeting the needs of others and have a general concern for maintaining stable, positive social relationships. When faced with conflict, individuals with
Conflict_resolution
Solution concept in game theory
mutation, predicts that the risk dominant state is the only stochastically stable equilibrium. Both models assume that multiple two-player games are played
Risk_dominance
Solution concept in game theory
Equilibrium (PBE) is a solution with Bayesian probability to a turn-based game with incomplete information. More specifically, it is an equilibrium concept
Perfect_Bayesian_equilibrium
Israeli-American psychologist and economist (1934–2024)
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Daniel_Kahneman
Israeli economist
Laureates Robert Aumann and Lloyd Shapley, Rubinstein analyzed perfect equilibrium in repeated game models with players using "limit of means" or "overtaking"
Ariel_Rubinstein
The concept of coalition-proof Nash equilibrium applies to certain "noncooperative" environments in which players can freely discuss their strategies
Coalition-proof Nash equilibrium
Coalition-proof_Nash_equilibrium
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
Finding an optimal algorithm for playing chess
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Solving_chess
Wide-ranging representation of a game in game theory
Bayesian equilibrium; i.e. an equilibrium in which different types do different things. If both types play the same action (pooling), an equilibrium cannot
Extensive-form_game
Situation where all parties are worse off
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
No-win_situation
Concept in game theory
response is central to John Nash's best-known contribution, the Nash equilibrium, the point at which each player in a game has selected the best response
Best_response
Game that repeats a base game
deviation. In other words, in the pricing competition game, the only Nash equilibrium is inefficient (for gas stations) that both charge p = c. This is more
Repeated_game
Solution concept capturing altruism in game theory
Berge equilibrium is a game theory solution concept named after the mathematician Claude Berge. It is similar to the standard Nash equilibrium, except
Berge_equilibrium
Solution Concept for Noncooperative games
was first used to refer to the stable point of a dynamic interaction between players that are learning an equilibrium by taking actions and observing
Satisfaction_equilibrium
Economic model
Stackelberg who published Marktform und Gleichgewicht (Market Structure and Equilibrium) in 1934, which described the model. In game theory terms, the players
Stackelberg_competition
Game class in game theory
signal. The equilibrium concept relevant to signaling games is the "perfect Bayesian equilibrium," a refinement of the Bayesian Nash equilibrium. Nature chooses
Signaling_game
Concept in game theory
In game theory, a strong Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively
Strong_Nash_equilibrium
Game in economic experiments
case where the proposer can choose from many different splits. A Nash equilibrium is a set of strategies (one for the proposer and one for the responder
Ultimatum_game
Political model of international conflict resolution
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Two-level_game_theory
Making of satisfactory, not optimal, decisions
maximization and profit maximization as used in conventional general equilibrium models. Stock-flow consistent models (SFC) and agent-based models (ABM)
Bounded_rationality
Search algorithm
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Alpha–beta_pruning
Game-theoretic concept
choose in equilibrium not to do so. Cheap talk can, in general, be added to any game and has the potential to enhance the set of possible equilibrium outcomes
Cheap_talk
Simple mathematical game
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Pirate_game
Incomplete-information coordination game
sent n + 1 {\displaystyle n+1} emails The equilibrium concept to be used is that of a Bayesian Nash Equilibrium (BNE). Rubinstein showed that, no matter
Electronic_mail_game
Concept in mechanism design
probabilities that an agent receives by being truthful is not first-order-stochastically-dominated by the vector of probabilities he gets by misreporting. Universal
Strategyproofness
Concept in game theory
theory, where the different methods of equilibrium selection respond to different ideas of what equilibria will be stable and persistent for one player to play
Equilibrium_selection
Preference of known risks to unknown risks
a mixed strategy of L and M, and thus would not be played in a Nash equilibrium. For some higher values of x the game is dominance solvable. The effect
Ambiguity_aversion
Resource distribution game
algorithm for characterizing all the Nash equilibrium strategies, includes previously unidentified Nash equilibrium strategies as well as helps identify what
Blotto_game
Israeli-American mathematician (born 1930)
correlated equilibrium in game theory, which is a type of equilibrium in non-cooperative games that is more flexible than the classical Nash equilibrium. Furthermore
Robert_Aumann
Trigger strategy
is the cooperative profile while playing (D, D), also the unique Nash equilibrium in this game, is the punishment profile. In the grim trigger strategy
Grim_trigger
Game whose outcome can be correctly predicted
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Solved_game
Class of games where players choose their actions sequentially
Simultaneous game Subgame perfect equilibrium Sequential auction Brocas; Carrillo; Sachdeva (2018). "The Path to Equilibrium in Sequential and Simultaneous
Sequential_game
Subfield of set theory
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Determinacy
Game theory dilemma
that the expensive meal is strictly dominant and thus the unique Nash equilibrium. If everyone orders the expensive meal all of the diners pay k and the
Unscrupulous_diner's_dilemma
Hungarian-American economist and philosopher (1920–2000)
(specifically utilitarian ethics) as well as contributing to the study of equilibrium selection. For his work, he was a co-recipient along with John Nash and
John_Harsanyi
Tendency to overestimate in auctions
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Winner's_curse
Application of game theory to evolving populations in biology
evolutionarily stable strategy (ESS) is akin to the Nash equilibrium in classical game theory, but with mathematically extended criteria. Nash equilibrium is a
Evolutionary_game_theory
Game theory scenario
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Win–win_game
Level of information in economics and game theory
with static, complete information, the approach to solve is to use Nash equilibrium to find viable strategies. In dynamic games with complete information
Complete_information
Concept in game theory
Conklin M (2001). "Analysis of regression in game theory approach". Applied Stochastic Models in Business and Industry. 17 (4): 319–330. doi:10.1002/asmb.446
Shapley_value
Process of reasoning backwards in sequence
extensive-form representation of a game. In order to solve for a subgame perfect equilibrium with backwards induction, the game should be written out in extensive
Backward_induction
Solution concept in Game Theory
cursed equilibrium is a solution concept for static games of incomplete information. It is a generalization of the usual Bayesian Nash equilibrium, allowing
Cursed_equilibrium
Concept in conflict studies
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Conflict_escalation
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
Military strategy during the Cold War with regard to the use of nuclear weapons
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Deterrence_theory
Problem of sharing resources
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Fair_division
Concept in economics and game theory
Different concepts of equilibrium can be used to model the selfish behavior of the agents, among which the most common is the Nash equilibrium. Different flavors
Price_of_anarchy
Diplomatic policy of concessions
Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily
Appeasement
Solution concept in game theory
Proper equilibrium in game theory is a refinement of Nash Equilibrium by Roger B. Myerson. Proper equilibrium further refines Reinhard Selten's notion
Proper_equilibrium
Field of economics and game theory
information), and if it is well-behaved the game has a Bayesian Nash equilibrium. At equilibrium agents choose their reports strategically as a function of type
Mechanism_design
it is listed here. Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the
List_of_games_in_game_theory
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STOCHASTICALLY STABLE-EQUILIBRIUM
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STOCHASTICALLY STABLE-EQUILIBRIUM
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