RAND's publications do not necessarily reflect the opinions of its research clients and sponsors. Related Products. Also available in print form. Shapley, Lloyd S. PDF file. Among the matters discussed in game theory are 1 What does it mean to select strategies "rationally" when outcomes or results depend on the strategies selected by others and when information is partial or incomplete?
Games are a suitable way to model the strategic interactions among economic agents. Many economic topics include strategic interaction.
Game theory is not restricted to Economics Properties of a Game There are finite number of competitors known as 'players' All the strategies and their impacts are specified to the players but player does not know which strategy is to be selected. Each player has a limited number of possible courses of action known as 'strategies' A game is played when every player selects one of his strategies.
The strategies are supposed to be prepared simultaneously with an outcome such that no player recognizes his opponent's strategy until he chooses his own strategy. The figures present as the outcomes of strategies in a matrix form are known as 'pay-off matrix'. The game is a blend of the strategies and in certain units which finds out the gain or loss. The player playing the game always attempts to select the best course of action which results in optimal pay off known as 'optimal strategy'.
The expected pay off when all the players of the game go after their optimal strategies is called as 'value of the game'. The main aim of a problem of a game is to determine the value of the game.
The game is said to be 'fair' if the value of the game is zero or else it s known as 'unfair'. Characteristics of Game Theory 1.
Each player has a record of finite number of possible actions. A play is said to takes place when each player selects one of his activities. The choices are supposed to be made simultaneously i.
Every combination of activities finds out an outcome which results in a gain of payments to every player, provided each player is playing openly to get as much as possible. Negative gain means the loss of same amount. Strategy The strategy of a player is the determined rule by which player chooses his strategy from his own list during the game.
The two types of strategy are Pure strategy Mixed strategy Pure Strategy If a player knows precisely what another player is going to do, a deterministic condition is achieved and objective function is to maximize the profit.
Mixed Strategy If a player is guessing as to which action is to be chosen by the other on any particular instance, a probabilistic condition is achieved and objective function is to maximize the expected profit. Repeated Game Strategies In repeated games, the chronological nature of the relationship permits for the acceptance of strategies that are dependent on the actions chosen in previous plays of the game.
Most contingent strategies are of the kind called as "trigger" strategies. For Example trigger strategies - In prisoners' dilemma: At start, play doesn't confess. Number of persons When the number of persons playing is 'n' then the game is known as 'n' person game.
Two-person, zero-sum game A game with just two players player A and player B is known as 'two-person, zero-sum game', if the losses of one player are equal to the gains of the other one so that the sum total of their net gains or profits is zero. Number of activities The activities can be finite or infinite. Payoff Payoff is referred to as the quantitative measure of satisfaction a person obtains at the end of each play.
Payoff matrix Assume the player A has 'm' activities and the player B has 'n' activities. Then a payoff matrix can be made by accepting the following rules Row designations for every matrix are the activities or actions available to player A Column designations for every matrix are the activities or actions available to player B Cell entry V ij is the payment to player A in A's payoff matrix when A selects the activity i and B selects the activity j.
In a zero-sum, two-person game, the cell entry in the player B's payoff matrix will be negative of the related cell entry V ij in the player A's payoff matrix in order that total sum of payoff matrices for player A and player B is finally zero. That is described in the game theory as a pay-off. It is important for the elements of the theory because until we know the pay-off function for every combination of strategies of the player or participant, we cannot apply the theory of games.
The pay-off function suggests to the player to select the strategy which over the long run will net him the most regardless of what his opponent does. In the words of S. A rule of the game, therefore, can be defined as the distribution of resources and strategic possibilities open to each player in the employment of these resources.
It is the objective the players wish to achieve. There can be possibly three outcomes- namely, win, lose or draw. But in other games, there could be many outcomes that could be defined as prospects. It suggests that when the third player in the game is introduced, new coalitions or alliances are to be formed. The distribution of gains among the players of the coalition creates a problem.
Because players will unite in a manner to get more gains and if any member could not get more gains that he could get in another coalition, he will leave the coalition, bringing loss to the other members in the coalition. While applying the theory of games to particular phenomena of coalition formation. Save my name, email, and website in this browser for the next time I comment.
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