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Notion in combinatorial game theory
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position) Game tree
Game_complexity
American professional electronic sports organization
Complexity Gaming, formerly stylized as compLexity, is an American esports franchise headquartered in Frisco, Texas. The franchise was founded in 2003
Complexity_Gaming
Feature of systems that defy description
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity
Complexity
Mathematical models of strategic interactions
Hex. A related field of study, drawing from computational complexity theory, is game complexity, which is concerned with estimating the computational difficulty
Game_theory
Game whose outcome can be correctly predicted
Jin Lim (2007). The game is a draw. Chess Fully solving chess remains elusive, and it is speculated that the complexity of the game may preclude it ever
Solved_game
Situation where total gains match total losses
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result
Zero-sum_game
Model of conflict for two players in game theory
game of chicken, also known as the hawk-dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game
Chicken_(game)
Abstract strategy board game for two players
to be considered at each stage of the game (game-tree complexity) can be estimated with bd, where b is the game's breadth (number of legal moves per position)
Go_(game)
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
Combinatorial_game_theory
Design of the content and rules of video games
the job of the game designer became separate from the lead programmer. Soon, game complexity demanded team members focused on game design. A number
Video_game_design
Problem in process of sharing surplus
the bargaining procedure is modeled as a non-cooperative game. The most common form of such game is called sequential bargaining. A two-person bargain problem
Cooperative_bargaining
Combinatorial game theory concept to represent all possible game states
A game tree can be used to measure the complexity of a game, as it represents all the possible ways that the game can pan out. Due to the large game trees
Game_tree
Logical paradox in decision-making theory
Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game tree Impartial
Paradox_of_tolerance
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Concept in game theory
In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication in order to avoid
Focal_point_(game_theory)
Standard example in game theory
In game theory, the prisoner's dilemma is a thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray
Prisoner's_dilemma
Hand game for two or more players
(sometimes called Splits, Calculator, or just Sticks)[citation needed] is a hand game for two or more players, in which players extend a number of fingers from
Chopsticks_(hand_game)
Estimate of number of possible chess games
mathematician Claude Shannon, is a conservative lower bound of the game-tree complexity of chess of 10120, based on an average of about 103 possibilities
Shannon_number
Topics referred to by the same term
description. Complexity may also refer to: Complexity Gaming, an American esports organization "Complexity", a song by Front Line Assembly from the 1997
Complexity_(disambiguation)
English saying meaning "equivalent retaliation"
blow", first recorded in 1558. It is also a highly effective strategy in game theory. An agent using this strategy will first cooperate, then subsequently
Tit_for_tat
Paper-and-pencil game for two players
positions (the state space complexity) or the 26,830 possible games up to rotations and reflections (the game tree complexity) on this space. If played
Tic-tac-toe
Military simulation board game
rates the complexity of CNA, on a scale of 1–10, as 10+. The complete campaign game takes 111 turns, each turn representing one week of game time. A number
The_Campaign_for_North_Africa
Conflict between safety and cooperation
In game theory, the stag hunt (also referred to as the assurance game, trust dilemma or common interest game) describes a situation or game where participants
Stag_hunt
Finding an optimal algorithm for playing chess
been solved at least weakly. Calculated estimates of game-tree complexity and state-space complexity of chess exist which provide a bird's eye view of the
Solving_chess
Search algorithm
Wigderson, A. (1986). "Probabilistic Boolean Decision Trees and the Complexity of Evaluating Game Trees". 27th Annual Symposium on Foundations of Computer Science
Alpha–beta_pruning
Game theory scenario
In game theory, a win–win game or win–win scenario is a situation that produces a mutually beneficial outcome for two or more parties. It is also called
Win–win_game
Mental skill based games
or random events. The "input randomness" is close to zero, and the game's complexity arises from the players' moves and position. Minimal theme and narrative:
Abstract_strategy_game
Field of economics and game theory
implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called mechanisms or institutions—that
Mechanism_design
Simultaneous game found in game theory
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they
Coordination_game
Construct, rule, or method designed for interaction with a game's state
of various mechanics determines the game's complexity and how the players interact with the game. All games use game mechanics; however, different theories
Game_mechanics
Game where groups of players may enforce cooperative behaviour
In game theory, a cooperative or coalitional game is a game with groups of players who form binding "coalitions" with external enforcement of cooperative
Cooperative_game_theory
Decision rule used for minimizing the possible loss for a worst-case scenario
decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for minimizing the possible loss for a
Minimax
Concept in game theory
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players
Shapley_value
Israeli-American psychologist and economist (1934–2024)
heuristic Base rate fallacy Cognitive bias Conjunction fallacy Dictator game Framing (social sciences) Loss aversion Optimism bias Peak–end rule Planning
Daniel_Kahneman
Making of satisfactory, not optimal, decisions
than a strict rigid rule of optimization. They do this because of the complexity of the situation. An example of behaviour inhibited by heuristics can
Bounded_rationality
American professional esports player (1989–2020)
3rd–4th Place 2013 Innkeeper's Invitational Miesner, Andrew. "Complexity Gaming". Complexity Gaming. Archived from the original on June 27, 2012. Retrieved
Reckful
Complexity class
science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass
PPAD_(complexity)
Application of game theory to evolving populations in biology
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and
Evolutionary_game_theory
Proof all ranked voting rules have spoilers
does not apply to graded systems, Gibbard's theorem still does: no voting game can be straightforward (i.e. have a single, clear, always-best strategy)
Arrow's_impossibility_theorem
Class of games where players choose their actions sequentially
sequential model due to their turn-based nature. The complexity of these games varies widely: a simple game like tic-tac-toe has a manageable decision tree
Sequential_game
Solution concept of a non-cooperative game
even though the equilibrium must exist, it is unknown due to the complexity of the game, for instance in Chinese chess. Or, if known, it may not be known
Nash_equilibrium
Game in economic experiments
The ultimatum game is a popular experimental economics game in which two players interact to decide how to divide a sum of money, first described by Nobel
Ultimatum_game
Simple mathematical game
The pirate game is a simple mathematical game. It is a multi-player version of the ultimatum game. There are five rational pirates (in strict decreasing
Pirate_game
Experimental tool
psychology and economics, the dictator game is a popular experimental instrument that is a derivative of the ultimatum game. It involves a single decision by
Dictator_game
Israeli psychologist (1937–1996)
Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game tree Impartial
Amos_Tversky
1997 video game
concepts. By acting as an arbiter and automatically enforcing the rules, game complexity is kept to manageable levels. After enough sessions, players should
Culdcept_(video_game)
Academic discipline
Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways: Superposed
Quantum_game_theory
Game generalized so that it can be played on a board or grid of any size
In computational complexity theory, a generalized game is a game or puzzle that has been generalized so that it can be played on a board or grid of any
Generalized_game
Game that repeats a base game
In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage
Repeated_game
Complete plan on how a game player will behave in every possible game situation
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends not only on
Strategy_(game_theory)
Condition in economics and game theory
Perfect information is a concept in game theory and economics that describes a situation where all players in a game or all participants in a market have
Perfect_information
Situation where all parties are worse off
no-win outcomes and find more satisfactory results.[citation needed] In game theory, a "no-win" situation is a circumstance in which no player benefits
No-win_situation
Theorem in game theory
satisfy certain restrictions on their variation. Scott Aaronson studied the complexity and rate of convergence of various types of dialogues with more than two
Aumann's_agreement_theorem
Notion in computational complexity theory
In computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves
Parsimonious_reduction
Pairing where no unchosen pair prefers each other over their choice
ISBN 978-1-4503-5559-9. MR 3826305. Irving, Robert W.; Leather, Paul (1986). "The complexity of counting stable marriages". SIAM Journal on Computing. 15 (3): 655–667
Stable_matching_problem
Tendency to overestimate in auctions
significant finding Auction theory – Branch of economics War of attrition (game) – Game theory model of aggression Buyer's remorse – Sense of regret after having
Winner's_curse
Weakly optimal allocation of resources
resources are allocated in the most efficient way possible. In terms of game theory, a strategy profile s is Pareto efficient when there is no other strategy
Pareto_efficiency
Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list
List_of_games_in_game_theory
Calculations of the game complexity of Go
moves, with an average of about 250 choices per move, suggesting a game-tree complexity of 10360. For the number of theoretically possible games, including
Go_and_mathematics
Human behavior pattern in which the participant takes on increasing risk
of software projects experience escalation of commitment due to their complexity and uncertainty. Intangibility makes determining the current status of
Escalation_of_commitment
Military strategy during the Cold War with regard to the use of nuclear weapons
Lindsay, Jon R. (2019). Cross-Domain Deterrence: Strategy in an Era of Complexity. Oxford University Press. doi:10.1093/oso/9780190908645.001.0001. ISBN 978-0-19-090960-4
Deterrence_theory
Game theory concept
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information
Bayesian_game
Model of humans as rational, self-interested agents
foundational assumption in models of market behavior and rational choice. In game theory, Homo economicus is often (but not necessarily) modelled through the
Homo_economicus
Two-player coordination game in game theory
In game theory, the battle of the sexes is a two-player coordination game that also involves elements of conflict. The game was introduced in 1957 by R
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Resource distribution game
A Colonel Blotto game is a type of two-person constant sum game in which the players (officers) are tasked to simultaneously distribute limited resources
Blotto_game
Political model of international conflict resolution
Politics portal Two-level game theory is a political model, derived from game theory, that illustrates the domestic-international interactions between
Two-level_game_theory
Hand game for two players or more
odds of a tie, while increasing the complexity of the game. The probability of a tie in an odd-number-of-weapons game can be calculated based on the number
Rock_paper_scissors
Game theory case weighing own/others' sacrifice
The volunteer's dilemma is a game that models a situation in which each player can either make a small sacrifice that benefits everybody, or instead wait
Volunteer's_dilemma
Hungarian and American mathematician and physicist (1903–1957)
first to talk about the time complexity of computations, which eventually evolved into the field of computational complexity theory. Von Neumann's mathematical
John_von_Neumann
Facilitating a peaceful outcome to a dispute
"cooperation" vs. "competition," a single dimension which has reduced the complexity of conflict phenomena to an easily manageable level. Ruble, Thomas L.;
Conflict_resolution
Game in algorithmic game theory
more. Below is a table of some known complexity results for finding certain classes of equilibria in several game representations. "NE" stands for "Nash
Succinct_game
Set in game theory
In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the
Core_(game_theory)
Two-player extensive form game
In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either
Centipede_game
Paradox of combining strategies
Parrondo's paradox, a paradox in game theory, describes how a combination of losing strategies can become a winning strategy. It is named after its creator
Parrondo's_paradox
2009 book by Robert Hearn and Erik Demaine
Games, Puzzles, and Computation is a book on game complexity, written by Robert Hearn and Erik Demaine, and published in 2009 by A K Peters. It is revised
Games, Puzzles, and Computation
Games,_Puzzles,_and_Computation
Fan-made modification of video games
Woods. After receiving the source code to the game from Crowther, Woods increased the game's complexity and released a modified version in 1977 to instant
Video_game_modding
Economic model
The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially (hence
Stackelberg_competition
Game class in game theory
In game theory, a signaling game is a type of a dynamic Bayesian game. The essence of a signaling game is that one player takes action, the signal, to
Signaling_game
Experimental economics game
The public goods game is a standard of experimental economics. In the basic game, subjects secretly choose how many of their private tokens to put into
Public_goods_game
Representation of a game in game theory
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent
Normal-form_game
Zero-sum game where competitions between strategies contain a cycle
An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy
Intransitive_game
Overuse of a shared resource
commons. In game theory, which constructs mathematical models for individuals' behaviour in strategic situations, the corresponding "game", developed
Tragedy_of_the_commons
In board games that cannot end in a draw, one of the two players has a winning strategy
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
American fantasy drama TV series (2011–2019)
Game of Thrones is an American fantasy drama television series created by David Benioff and D. B. Weiss for HBO. It is the first adaptation of the A Song
Game_of_Thrones
Simple game studied in game theory
Matching pennies is a non-cooperative game studied in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly
Matching_pennies
Abstract strategy board game
pane a player could fill on any given turn, adding to the game's complexity. A third game in the series, Azul: Summer Pavilion, was released in late
Azul_(board_game)
Game theory model of aggression
In game theory, the war of attrition is a dynamic timing game in which players choose a time to stop, and fundamentally trade off the strategic gains from
War_of_attrition_(game)
Chances of card combinations in poker
Combination Combinatorial game theory Effective hand strength algorithm Event (probability theory) Game complexity Gaming mathematics Odds Permutation
Poker_probability
Preference of known risks to unknown risks
experimental test of the influence of ambiguity on behaviour in a Battle of Sexes game which has an added safe strategy, R, available for Player 2 (see Table).
Ambiguity_aversion
Field of artificial intelligence
measures of shogi's game complexity. The complexity of Go can be found at Go and mathematics. More information on the complexity of Chess can be found
Computer_shogi
2026 video game
occurred in the titular manor. The game was well received for its gameplay, narrative, and thematic complexity. The game makes use of a point and click interface
The_Incident_at_Galley_House
Economic model of competition
select its own price p i {\displaystyle p_{i}} .; Timing: Simultaneous move game; Firm Payoffs: Profit; and Information: Complete. Imagine an aggregate demand
Bertrand_competition
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Application of complexity science to economics
Complexity economics, or economic complexity, is the application of complexity science to the problems of economics. It relaxes several common assumptions
Complexity_economics
Set of all possible values of a system
information about state space in probability. Game complexity theory, which relies on the state space of game outcomes Cognitive Model#Dynamical systems
State space (computer science)
State_space_(computer_science)
Problem in game theory
The El Farol bar problem is a problem in game theory. Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too
El_Farol_Bar_problem
Subgenre of role-playing video games
they are in the game. The Interpretation notes that shops like in Angband do break this non-modality. The game has a degree of complexity due to the number
Roguelike
Game theory concept
In game theory, a subgame perfect equilibrium (SPE), or subgame perfect Nash equilibrium (SPNE), is a refinement of the Nash equilibrium concept, specifically
Subgame_perfect_equilibrium
Economic model
the quantity of goods to produce and sell in the market. It is a static game, whereby a Nash equilibrium is found where no firms desire to unilaterally
Cournot_competition
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