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Strategy space S n i 1 Si ; where Si is the strategy space for agent i: We say that si 2 Si is a strategy chosen by player i; and s (s1 ; :::; sn ) 2 S is referred to as a strategy pro le. 3. A payo function u : S ! Rn ; where ui (s) is the utility for agent i given strategy pro le s 2 S: In terms of interpretations, the strategy space for an agent should be thought of as anything the player could conceivably do. Hence, the set of all strategy pro les describes everything that can.
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Qi FAQ
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The payoff matrix offers a complete description of the game because it lists the three elements: players, strategies, and payoffs. It is now time to think about individual strategy choices. We will start by examining the difference between dominant and dominated strategies.
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Game theory studies three general phases in the process of interaction: the choice of strategies, the formation of coalitions, and bargaining within coalitions.
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The strategic (or normal) form is a matrix representation of a simultaneous game. For two players, one is the “row” player, and the other, the “column” player. Each rows or column represents a strategy and each box represents the payoffs to each player for every combination of strategies.
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It provides a framework for understanding situations in which people are trying to optimize their outcomes. While the principles and applications of game theory can be complex, at its core the theory rests on three basic elements: players, strategies, and payoffs.
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The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome.
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A game in strategic form consists of a set of players, a strategy set for each player, and an outcome to each vector of strategies, which is usually given by the vector of utilities the players enjoy from the outcome.
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List of games GamePlayersStrategies per playerCoordination gameNvariableCournot game2infiniteDeadlock22Dictator game2infinite34 more rows
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The three basic elements of any game are: A set of participants, or "players." The moves, or "actions," that each player may make. The scores, or "payoffs," that each player earns at the end of the game.
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