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Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively. A game modeled after the iterated prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time ...
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
An important notion in combinatorial game theory is that of the solved game. For example, tic-tac-toe is considered a solved game, as it can be proven that any game will result in a draw if both players play optimally. Deriving similar results for games with rich combinatorial structures is difficult.
Several variants are considered in Game Theory Evolving by Herbert Gintis. [2] In some variants of the problem, the players are allowed to communicate before deciding to go to the bar. However, they are not required to tell the truth. Named after a bar in Santa Fe, New Mexico, the problem was created in 1994 by W. Brian Arthur.
A classic example of a dynamic game with types is a war game where the player is unsure whether their opponent is a risk-taking "hawk" type or a pacifistic "dove" type. Perfect Bayesian Equilibria are a refinement of Bayesian Nash equilibrium (BNE), which is a solution concept with Bayesian probability for non-turn-based games.