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Solution concept in game theory
somewhat rational, i.e. that they do not play dominated strategies. A strategy is rationalizable if there exists some possible set of beliefs both players
Rationalizable_strategy
Decision rule used for minimizing the possible loss for a worst-case scenario
with finitely many strategies, there exists a value V and a mixed strategy for each player, such that (a) Given Player 2's strategy, the best payoff possible
Minimax
Complete plan on how a game player will behave in every possible game situation
situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or
Strategy_(game_theory)
Solution concept of a non-cooperative game
where no player could gain more by changing their own strategy (holding all other players' strategies fixed) in a game. A Nash equilibrium is the most commonly
Nash_equilibrium
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
Standard example in game theory
probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit-for-tat strategy written as P = { 1 , 0 ,
Prisoner's_dilemma
Situation where total gains match total losses
point-loss independent of the opponent's strategy. This leads to a linear programming problem with the optimal strategies for each player. This minimax method
Zero-sum_game
Logical paradox in decision-making theory
which ban intolerant or extremist behavior are often ineffective against a strategy of a façade, which does not meet the legal criteria for a ban. Several
Paradox_of_tolerance
Game whose outcome can be correctly predicted
both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of
Solved_game
Search algorithm
Since the minimax algorithm and its variants are inherently depth-first, a strategy such as iterative deepening is usually used in conjunction with alpha–beta
Alpha–beta_pruning
Paper-and-pencil game for two players
often played by young children who may not have discovered the optimal strategy. Because of the simplicity of tic-tac-toe, it is often used as a pedagogical
Tic-tac-toe
Model of conflict for two players in game theory
one player chooses one strategy, the other player chooses the opposite strategy. The third Nash equilibrium is a mixed strategy which lies along the diagonal
Chicken_(game)
Quality of a strategy in game theory
In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some
Strategic_dominance
Hand game for two players or more
& Walker, Graham (2004) The Official Rock Paper Scissors Strategy Guide. Fireside. (strategy, tips and culture from the World Rock Paper Scissors Society)
Rock_paper_scissors
Conflict between safety and cooperation
two pure strategy Nash equilibria, that is, stable attractors where an individual player cannot improve their position with a different strategy if the
Stag_hunt
Israeli-American psychologist and economist (1934–2024)
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Daniel_Kahneman
Overuse of a shared resource
excess of resources, causes animal populations to have r reproduction strategies (many offspring, short gestation, less parental care, and a short time
Tragedy_of_the_commons
English saying meaning "equivalent retaliation"
recorded in 1558. It is also a highly effective strategy in game theory. An agent using this strategy will first cooperate, then subsequently replicate
Tit_for_tat
Concept in game theory
best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given. The concept
Best_response
Finding an optimal algorithm for playing chess
Solving chess consists of finding an optimal strategy for the game of chess; that is, one by which one of the players (White or Black) can always force
Solving_chess
Israeli psychologist (1937–1996)
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Amos_Tversky
Argument in combinatorial game theory
In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot
Strategy-stealing_argument
Two-player coordination game in game theory
pure strategy Nash equilibria, one where both players go to the prize fight, and another where both go to the ballet. There is also a mixed strategy Nash
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Facilitating a peaceful outcome to a dispute
resolution. The dual model identifies five group conflict resolution styles or strategies that individuals may use depending on their dispositions toward pro-self
Conflict_resolution
Concept in game theory
introduced by the American economist Thomas Schelling in his book The Strategy of Conflict (1960). Schelling states that "[p]eople can often concert their
Focal_point_(game_theory)
Mathematical models of strategic interactions
mathematics that models interactions between multiple agents as "games" of strategy between "players". It is a scientific method of describing, predicting
Game_theory
Problem in game theory
deterministic pure strategy which is symmetric (same strategy for all players), it is guaranteed to fail no matter what it is. If the strategy suggests it will
El_Farol_Bar_problem
Solution concept in game theory
which pure strategy to play. The probability of any particular strategy being chosen is positively related to the payoff from that strategy. In other words
Quantal_response_equilibrium
Problem in process of sharing surplus
neither player can increase their return by unilaterally changing their strategy. In Rubinstein's alternating offers bargaining game, players take turns
Cooperative_bargaining
Preference of known risks to unknown risks
the range 60-260. For some values of x, the safe strategy (option R) is dominated by a mixed strategy of L and M, and thus would not be played in a Nash
Ambiguity_aversion
Resource distribution game
optimal strategies can be explicitly found. In addition to military strategy applications, the Colonel Blotto game has applications to political strategy (resource
Blotto_game
Hungarian-American economist and philosopher (1920–2000)
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
John_Harsanyi
Paradox of combining strategies
in game theory, describes how a combination of losing strategies can become a winning strategy. It is named after its creator, Juan Parrondo, who discovered
Parrondo's_paradox
Game theory scenario
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Win–win_game
Human behavior pattern in which the participant takes on increasing risk
decision and prospect theories Martingale (betting system) – Gambling strategy where the amount is raised until a person wins or becomes insolvent Mission
Escalation_of_commitment
Subfield of set theory
the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy"
Determinacy
Game theory concept
(non-Bayesian) game, a strategy profile is a Nash equilibrium if every player's strategy is a best response to the other players' strategies. In this situation
Bayesian_game
Hungarian and American mathematician and physicist (1903–1957)
Poker Is Applied to Business Problems; GAMING STRATEGY USED IN ECONOMICS Big Potentialities Seen Strategies Analyzed Practical Use in Games". The New York
John_von_Neumann
Type of perfect Bayesian equilibrium
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Separating_equilibrium
Variation of minimax game tree search
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Negamax
Game in economic experiments
can adopt a strategy that rejects unfair splits often enough to induce the proposer to always make a fair offer. Any change in strategy by the proposer
Ultimatum_game
unilaterally change their strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a game can have any
List_of_games_in_game_theory
Trigger strategy
In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game. Initially, a player using grim trigger
Grim_trigger
Strategy which only depends on the current state of a game
In game theory, a Markov strategy is a strategy that depends only on the current state of the game, rather than the full history of past actions. The state
Markov_strategy
Game theory case weighing own/others' sacrifice
seen by the payoff matrix, there is no dominant strategy in the volunteer's dilemma. In a mixed-strategy Nash equilibrium, an increase in N players will
Volunteer's_dilemma
Military strategy during the Cold War with regard to the use of nuclear weapons
military superiority. The topic gained increased prominence as a military strategy during the Cold War with regard to the use of nuclear weapons. It is related
Deterrence_theory
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
Matching_pennies
Variant of Nash equilibrium in game theory
restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy in an n {\displaystyle n} -player
Trembling hand perfect equilibrium
Trembling_hand_perfect_equilibrium
Condition in economics and game theory
implies common knowledge of each agent's utility functions, payoffs, strategies and "types". A system with perfect information may or may not have complete
Perfect_information
Economic model of competition
{\displaystyle p^{m}=argmax_{p}(p-c)D(p)} . This is the largest rationalizable strategy. Even without price competition, no firm has an incentive to raise
Bertrand_competition
Tendency to overestimate in auctions
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Winner's_curse
Model of humans as rational, self-interested agents
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Homo_economicus
Class of theorems about Nash equilibrium payoff profiles in repeated games
players' choices in the prior iterations. A choice of strategy for each of the players is a strategy profile, and it leads to a payout profile for the repeated
Folk_theorem_(game_theory)
Subset of a game; used in game theory
trivially call an equilibrium subgame perfect by ignoring playable strategies to which a strategy was not a best response. Furthermore, if subgames cut across
Subgame
Formal rule for predicting how a game will be played
played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The
Solution_concept
Solution concept in game theory
likely they will choose the strategy corresponding to it. The payoff matrix in Figure 1 provides a simple two-player, two-strategy example of a game with two
Risk_dominance
Poker game developed by Harold Kuhn
the 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
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Contingent_cooperator
Game where groups of players may enforce cooperative behaviour
David Gaddis (2018-08-01). "Using cooperative game theory to contribute to strategy research". Strategic Management Journal. 39 (11): 2859–2876. doi:10.1002/smj
Cooperative_game_theory
Game theory concept
designed for dynamic games where players make sequential decisions. A strategy profile is an SPE if it represents a Nash equilibrium in every possible
Subgame_perfect_equilibrium
Academic discipline
initial states, Quantum entanglement of initial states, Superposition of strategies to be used on the initial states. This theory is based on the physics
Quantum_game_theory
Weakly optimal allocation of resources
way possible. In terms of game theory, a strategy profile s is Pareto efficient when there is no other strategy profile s′ such that ui(s′) ≥ ui(s) for
Pareto_efficiency
Situation where all parties are worse off
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
No-win_situation
mechanism dominant strategy is dominant-strategy implementable. "A social choice rule is dominant strategy incentive compatible, or strategy-proof, if the
Implementation_theory
Transactional view of violent conflict in international relations theory
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Bargaining_model_of_war
Representation of a game in game theory
players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, whereas a strategy is a
Normal-form_game
Class of strategies employed in a repeated non-cooperative game
theory, a trigger strategy is any of a class of strategies employed in a repeated non-cooperative game. A player using a trigger strategy initially cooperates
Trigger_strategy
player. The term was coined by Thomas Schelling in his 1960 book, The Strategy of Conflict, and has gained wide currency in political science and industrial
Strategic_move
Application of game theory to evolving populations in biology
contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies. Evolutionary game theory
Evolutionary_game_theory
Israeli-American mathematician (born 1930)
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Robert_Aumann
Game that repeats a base game
preferred strategy is not to play a Nash strategy of the stage game, but to cooperate and play a socially optimum strategy. An essential part of strategies in
Repeated_game
Solution concept in Game Theory
"average away" the information regarding other players' types' mixed strategies. The solution concept was first introduced by Erik Eyster and Matthew
Cursed_equilibrium
Branch of game theory about two-player sequential games with perfect information
analysis of game complexity and the existence of optimal strategies through methods like the strategy-stealing argument. Combinatorial game theory arose in
Combinatorial_game_theory
Positional game strategy
In a positional game, a pairing strategy is a strategy that a player can use to guarantee victory, or at least force a draw. It is based on dividing the
Pairing_strategy
Italian economist (born 1961)
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Pierpaolo_Battigalli
Concept in game theory
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Shapley_value
Combinatorial game theory theorem
has a winning strategy for A + G + H {\displaystyle A+G+H} : respond to moves in A {\displaystyle A} according to their winning strategy for A {\displaystyle
Sprague–Grundy_theorem
Term in game theory
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Move_by_nature
Game theory solution
signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from their strategy (assuming
Correlated_equilibrium
Hand game for two or more players
combinatorial game, and is solved in the sense that, with perfect play, an optimal strategy from any point is known. In Chopsticks, players tally points using the
Chopsticks_(hand_game)
Zero-sum game where competitions between strategies contain a cycle
game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation
Intransitive_game
Making of satisfactory, not optimal, decisions
seen when comparing the cognitive strategies utilised in simple situations (e.g. tic-tac-toe), in comparison to strategies utilised in difficult situations
Bounded_rationality
Game class in game theory
specific order of play. However, in simultaneous games, all players select strategies without observing the choices of their rivals and players choose at exactly
Simultaneous_game
Dynamical system
system used in evolutionary game theory to model how the frequency of strategies in a population changes over time. It is a deterministic, monotone, non-linear
Replicator_equation
Algorithm in game theory
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Paranoid_algorithm
Pairing where no unchosen pair prefers each other over their choice
misrepresenting his preferences. Moreover, the GS algorithm is even group-strategy proof for men, i.e., no coalition of men can coordinate a misrepresentation
Stable_matching_problem
Game theory model of aggression
originally formulated by John Maynard Smith; a mixed evolutionarily stable strategy (ESS) was determined by Bishop & Cannings. An example is a second price
War_of_attrition_(game)
Game whose payoffs depend on strategies as opposed to players
any strategy set. That is, the payoff for playing strategy a against strategy b receives the same payoff as playing strategy b against strategy a. Only
Symmetric_game
Neologism for cooperative competition
term is a portmanteau of "cooperation" and "competition". In business strategy, coopetition can involve companies collaborating in areas like research
Coopetition
Game theory concept
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Game_form
American economist (born 1948)
Technology, Strategy and Organization". American Economic Review. 80 (3): 511–28. JSTOR 2006681. Milgrom, Paul; Roberts, John (1990c). "Rationalizability, Learning
Paul_Milgrom
Problem about bus travel
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Wait/walk_dilemma
Political model of international conflict resolution
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Two-level_game_theory
rather than in fixed, simultaneous turns, leading to unpredictable timing strategies and outcomes. Abraham, I., Alvisi, L., & Halpern, J. Y. (2011). Distributed
Asynchrony_(game_theory)
Solution concept in Game Theory
thought of a as BCE, where the recommended joint strategy is simply the equilibrium joint strategy. Formally, let Γ = ( G , S ) {\displaystyle \Gamma
Bayes_correlated_equilibrium
Level of information in economics and game theory
participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information
Complete_information
Incomplete-information coordination game
\}} and then must choose an action { A , B } {\displaystyle \{A,B\}} . A strategy in the electronic mail game is thus defined as a function from N ∋ T i
Electronic_mail_game
American computer scientist and mathematician
dominated strategies Open-loop model Pareto efficiency Payoff dominance Price of anarchy Rational agent Rationalizable strategy Shapley value Strategies Appeasement
Jennifer_Tour_Chayes
Condition where selection restores genetic composition
stable strategy (ESS), evolutionarily stable states are not identical and the two terms cannot be used interchangeably. An ESS is a strategy that, if
Evolutionarily_stable_state
factors affect it. A strategy is a set of actions that a player can take in response to the actions of others. Each player’s strategy is based on their expectation
Outcome_(game_theory)
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