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John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations.
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 ...
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.
Admissibility and Perfection: Each equilibrium in a stable set is perfect, and therefore admissible. Backward Induction and Forward Induction: A stable set includes a proper equilibrium of the normal form of the game that induces a quasi-perfect and therefore a sequential equilibrium in every extensive-form game with perfect recall that has the same normal form.
Selected equilibrium refinements in game theory. Arrows point from a refinement to the more general concept (i.e., ESS Proper). 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 ...
In game theory, an information set represents all possible points (or decision nodes) in a game that a given player might be at during their turn, based on their current knowledge and observations. These nodes are indistinguishable to the player due to incomplete information about previous actions or the state of the game .
The limit-of-means criterion ensures that any finite-time punishment has no effect on the final outcome. Hence, limited-time punishment is a subgame-perfect equilibrium. Coalition subgame-perfect equilibria: [8] An equilibrium is called a coalition Nash equilibrium if no coalition can gain from deviating.
In game theory, fictitious play is a learning rule first introduced by George W. Brown. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies.