Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.
In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.
A strategy game or strategic game is a game in which the players' uncoerced, and often autonomous, decision-making skills have a high significance in determining the outcome. Almost all strategy games require internal decision tree-style thinking, and typically very high situational awareness.
Mindset is an "established set of attitudes, esp. regarded as typical of a particular group's social or cultural values; the outlook, philosophy, or values of a person; frame of mind, attitude, disposition." A mindset may also arise from a person's world view or philosophy of life.
The angel problem is a question in combinatorial game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard. The angel has a power k, specified before the game starts. The board starts empty with the angel in one square. On each turn, the angel jumps to a different empty square which could be reached by at most k moves of a chess king, i.e. the distance from the starting square is at most k in the infinity norm. The devil, on its turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely.
Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject.
An extensive-form game is a specification of a game in game theory, allowing for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as "moves by nature".
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information.
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games. The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria.
In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game. The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. Single stage game or single shot game are names for non-repeated games.
Blue Ocean Strategy is a book published in 2004 written by W. Chan Kim and Renée Mauborgne, professors at INSEAD, and the name of the marketing theory detailed on the book.
James P. Carse was an American academic who was Professor Emeritus of history and literature of religion at New York University. His book Finite and Infinite Games was widely influential. He was religious "in the sense that I am endlessly fascinated with the unknowability of what it means to be human, to exist at all."
Finite and Infinite Games is a book by religious scholar James P. Carse.
Simon Oliver Sinek is a British-American author and inspirational speaker. He is the author of five books, including Start With Why (2009) and The Infinite Game (2019).
The Game is a mental game where the objective is to avoid thinking about The Game itself. Thinking about The Game constitutes a loss, which must be announced each time it occurs. It is impossible to win most versions of The Game. Depending on the variation of The Game, the whole world, or all those aware of the game, are playing it all the time. Tactics have been developed to increase the number of people aware of The Game and thereby increase the number of losses.
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 chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy. An alternate statement is that for a game meeting all of these conditions except the condition that a draw is not possible, then either the first-player can force a win, or the second-player can force a win, or both players can force a draw. The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.
Solving chess means finding an optimal strategy for the game of chess, that is, one by which one of the players can always force a victory, or either can force a draw. It also means more generally solving chess-like games, such as Capablanca chess and infinite chess. According to Zermelo's theorem, a determinable optimal strategy must exist for chess and chess-like games.
Start with Why: How Great Leaders Inspire Everyone to Take Action is a book by Simon Sinek.
Infinite chess is any variation of the game of chess played on an unbounded chessboard. Versions of infinite chess have been introduced independently by multiple players, chess theorists, and mathematicians, both as a playable game and as a model for theoretical study. It has been found that even though the board is unbounded, there are ways in which a player can win the game in a finite number of moves.
