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Algorithm in game theory
the paranoid algorithm is a game tree search algorithm designed to analyze multi-player games using a two-player adversarial framework. The algorithm assumes
Paranoid_algorithm
Decision rule used for minimizing the possible loss for a worst-case scenario
combinatorial game theory, there is a minimax algorithm for game solutions. A simple version of the minimax algorithm, stated below, deals with games such as
Minimax
Game whose outcome can be correctly predicted
need not actually determine any details of the perfect play. Provide one algorithm for each of the two players, such that the player using it can achieve
Solved_game
Paper-and-pencil game for two players
that deals with the searching of game trees, most notably the minimax algorithm. It is straightforward to write a computer program to play tic-tac-toe
Tic-tac-toe
Search algorithm
Alpha–beta pruning is a tree search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an
Alpha–beta_pruning
Hungarian and American mathematician and physicist (1903–1957)
(1873), which was later popularized by Karmarkar's algorithm. Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision
John_von_Neumann
Logical paradox in decision-making theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Paradox_of_tolerance
Standard example in game theory
those with high scores reproduce (a genetic algorithm for finding an optimal strategy). The mix of algorithms in the final population generally depends
Prisoner's_dilemma
Israeli-American psychologist and economist (1934–2024)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Daniel_Kahneman
Overuse of a shared resource
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Tragedy_of_the_commons
Hand game for two players or more
that matches the last few moves in order to predict the next move of the algorithm. In frequency analysis, the program simply identifies the most frequently
Rock_paper_scissors
Israeli psychologist (1937–1996)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Amos_Tversky
Solution concept of a non-cooperative game
level. Shoham, Yoav; Leyton-Brown, Kevin (2009), Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, New York: Cambridge University
Nash_equilibrium
Problem in process of sharing surplus
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Cooperative_bargaining
Situation where total gains match total losses
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Zero-sum_game
Pairing where no unchosen pair prefers each other over their choice
stable. They presented an algorithm to do so. The Gale–Shapley algorithm (also known as the deferred acceptance algorithm) involves a number of "rounds"
Stable_matching_problem
Proof all ranked voting rules have spoilers
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Arrow's_impossibility_theorem
English saying meaning "equivalent retaliation"
Babak; Roberts, Stephen (2023). "Guidelines for Building a Realistic Algorithmic Trading Market Simulator for Backtesting While Incorporating Market Impact:
Tit_for_tat
Concept in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Focal_point_(game_theory)
Hand game for two or more players
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Chopsticks_(hand_game)
Concept in conflict studies
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Conflict_escalation
Model of conflict for two players in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Chicken_(game)
Military strategy during the Cold War with regard to the use of nuclear weapons
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Deterrence_theory
Two-player coordination game in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Situation where all parties are worse off
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
No-win_situation
Game theory case weighing own/others' sacrifice
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Volunteer's_dilemma
Conflict between safety and cooperation
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Stag_hunt
Notion in combinatorial game theory
a solution algorithm must work for every possible state of the game. It will be upper-bounded by the complexity of any particular algorithm that works
Game_complexity
Tendency to overestimate in auctions
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Winner's_curse
Concept in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Shapley_value
Model of humans as rational, self-interested agents
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Homo_economicus
Simple mathematical game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Pirate_game
Condition in economics and game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Perfect_information
Making of satisfactory, not optimal, decisions
has better algorithms and heuristics could make more rational (closer to optimal) decisions than one that has poorer heuristics and algorithms. And many
Bounded_rationality
Hungarian-American economist and philosopher (1920–2000)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
John_Harsanyi
Trigger strategy
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Grim_trigger
Mathematical models of strategic interactions
and information markets. Algorithmic game theory and within it algorithmic mechanism design combine computational algorithm design and analysis of complex
Game_theory
Game theory scenario
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Win–win_game
Application of game theory to evolving populations in biology
and one of the most successful of these is tit-for-tat with a simple algorithm. def tit_for_tat(last_move_by_opponent): """Defect if opponent defects
Evolutionary_game_theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
List_of_games_in_game_theory
Simultaneous game found in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Coordination_game
Resource distribution game
of the Colonel Blotto game. This solution, which includes a graphical algorithm for characterizing all the Nash equilibrium strategies, includes previously
Blotto_game
Game where groups of players may enforce cooperative behaviour
(vertex) of the core can be found in polynomial time using the greedy algorithm: Let π : N → N {\displaystyle \pi :N\to N} be a permutation of the players
Cooperative_game_theory
Facilitating a peaceful outcome to a dispute
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Conflict_resolution
Finding an optimal algorithm for playing chess
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Solving_chess
Branch of game theory about two-player sequential games with perfect information
distinction in emphasis: while economic game theory tends to focus on practical algorithms—such as the alpha–beta pruning strategy commonly taught in AI courses—combinatorial
Combinatorial_game_theory
Theorem in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Aumann's_agreement_theorem
Field of economics and game theory
a θ {\displaystyle \theta } interval satisfying the condition above. Algorithmic mechanism design Alvin E. Roth – Nobel Prize, market design Assignment
Mechanism_design
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Conjectural_variation
Complete plan on how a game player will behave in every possible game situation
or battleship. The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation
Strategy_(game_theory)
Human behavior pattern in which the participant takes on increasing risk
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Escalation_of_commitment
Paradox of combining strategies
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Parrondo's_paradox
Weakly optimal allocation of resources
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Pareto_efficiency
Concept in economics and game theory
approximation algorithm or the 'competitive ratio' in an online algorithm. This is in the context of the current trend of analyzing games using algorithmic lenses
Price_of_anarchy
Variation of minimax game tree search
search that relies on the zero-sum property of a two-player game. This algorithm relies on the fact that min ( a , b ) = − max ( − b , − a ) {\displaystyle
Negamax
Field in social science
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Peace_and_conflict_studies
Poker game developed by Harold Kuhn
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Kuhn_poker
Game which can have any number of players
theorem that is the basis of tree searching for 2-player games. Other algorithms, like maxn, are required for traversing the game tree to optimize the
N-player_game
Quality of a strategy in game theory
Dominance Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University
Strategic_dominance
Game in economic experiments
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Ultimatum_game
Study of strategic decision making
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Mean-field_game_theory
Type of stable matching problem
science, particularly in the fields of combinatorial game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable
Stable_roommates_problem
Economic phenomenon
Externality Fabian strategy Fredkin's paradox Free rider problem Greedy algorithm Law of triviality Overexploitation Path dependence Price of anarchy Race
Tyranny_of_small_decisions
Political model of international conflict resolution
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Two-level_game_theory
Statement that players know and also know that other players know (ad infinitum)
Chapter 3. Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University
Common_knowledge_(logic)
Non-zero-sum game thought experiment
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Traveler's_dilemma
Level of information in economics and game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Complete_information
Diplomatic policy of concessions
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Appeasement
Academic discipline
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Quantum_game_theory
Solution concept in game theory
Oxford. Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Outcome_(game_theory)
Israeli-American mathematician (born 1930)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Robert_Aumann
Mathematical modelling of phenotypic evolution
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Evolutionary invasion analysis
Evolutionary_invasion_analysis
Game illustrating paradox in rational choice theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Dollar_auction
Game that repeats a base game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Repeated_game
Iterated game for peace and conflict studies
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Peace_war_game
Mathematical game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Guess_2/3_of_the_average
Class of strategies employed in a repeated non-cooperative game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Trigger_strategy
Situation where players have only a small incentive to change strategies
PTAS remains an open problem. For constant values of ε, polynomial-time algorithms for approximate equilibria are known for lower values of ε than are known
Epsilon-equilibrium
Canadian computer scientist and mathematician
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Donald_B._Gillies
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Transferable_utility
Italian economist (born 1961)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Pierpaolo_Battigalli
Cooperation between firms to limit competition
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Collusion
Experimental economics game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Public_goods_game
English mathematician and game theorist (born 1940)
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Kenneth_Binmore
When a decision-maker's future preferences can contradict earlier preferences
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Dynamic_inconsistency
Game theory solution
level) Shoham, Yoav; Leyton-Brown, Kevin (2009), Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, New York: Cambridge University
Correlated_equilibrium
American computer scientist and mathematician
structural and dynamical properties of self-engineered networks, and algorithmic game theory. She is considered one of the world's experts in the modeling
Jennifer_Tour_Chayes
Dynamical system
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Replicator_equation
Simple game studied in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Matching_pennies
Game whose payoffs depend on strategies as opposed to players
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Symmetric_game
Aspect of game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Self-confirming_equilibrium
Decrease in severity of conflicts
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
De-escalation
Incomplete-information coordination game
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Electronic_mail_game
Neologism for cooperative competition
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Coopetition
Game theory concept
for an extensive form game from gametheory.net. Kaminski, M.M. Generalized Backward Induction: Justification for a Folk Algorithm. Games 2019, 10, 34.
Subgame_perfect_equilibrium
Economic Model
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Bertrand–Edgeworth_model
Class of theorems about Nash equilibrium payoff profiles in repeated games
practical consequence of this is that no efficient (polynomial-time) algorithm is known that computes the strategies required by folk theorems in the
Folk_theorem_(game_theory)
Subset of a game; used in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Subgame
Game class in game theory
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Signaling_game
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