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The book is based on Carse's distinction between two types of games: finite games and infinite games. As Sinek explains, finite games (e.g. chess and football) are played with the goal of getting to the end of the game and winning, while following static rules. Every game has a beginning, middle, and end, and a final winner is distinctly ...
The infinite game - there is only one - includes any authentic interaction, from touching to culture, that changes rules, plays with boundaries and exists solely for the purpose of continuing the game. A finite player seeks power; the infinite one displays self-sufficient strength.
Game theory is the study of ... It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time ...
A finite game (sometimes called a founded game [1] or a well-founded game [2]) is a two-player game which is assured to end after a finite number of moves. Finite games may have an infinite number of possibilities or even an unbounded number of moves, so long as they are guaranteed to end in a finite number of turns.
Sequential game: A game is sequential if one player performs their actions after another player; otherwise, the game is a simultaneous move game. Perfect information : A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. A Gale–Stewart game is a possibly infinite two-player game, where both players have perfect information and no randomness is ...
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 (i.e. can force a win).
When the game is infinite, a common model for the utility in the infinitely-repeated game is the limit inferior of mean utility: If the game results in a path of outcomes , where denotes the collective choices of the players at iteration t (t=0,1,2,...), player i 's utility is defined as