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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.
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. [124] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics , evolutionary biology , political science , social psychology and military strategy .
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.
In applied game theory, the definition of the strategy sets is an important part of the art of making a game simultaneously solvable and meaningful. The game theorist can use knowledge of the overall problem, that is the friction between two or more players, to limit the strategy spaces, and ease the solution.
In contrast, in classic game theory, even complex games are treated as single, monolithic objects. This makes the analysis of games hard to scale. Compositional game theory (CGT) aims to apply the modularity principle to game theory. The main motivation is to make it easier to analyze large games using software tools.
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In a game process, regardless of the opponent's strategy choice, one of the parties will choose a certain strategy, which is called dominant strategy. If any participant chooses the optimal strategy when the strategies of all other participants are determined, then this combination is defined as a Nash equilibrium .