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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.
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.
Unlimited offers—the game keeps going until one player accepts an offer; Alternating offers—the first player makes an offer in the first period, if the second player rejects, the game moves to the second period in which the second player makes an offer, if the first rejects, the game moves to the third period, and so forth; Delays are costly
Cooperative game theory is a branch of game theory that deals with the study of games where players can form coalitions, cooperate with one another, and make binding agreements. The theory offers mathematical methods for analysing scenarios in which two or more players are required to make choices that will affect other players wellbeing. [5]
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games.A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). [1]
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves.
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.
Consider a transferable utility cooperative game (,) where denotes the set of players and is the characteristic function.An imputation is dominated by another imputation if there exists a coalition , such that each player in weakly-prefers (for all ) and there exists that strictly-prefers (<), and can enforce by threatening to leave the grand coalition to form (()).