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The GaryVee Content Model. Mammalian Brain Chemistry Explains Everything. Related Books Free with a 30 day trial from Scribd. Dry: A Memoir Augusten Burroughs. Related Audiobooks Free with a 30 day trial from Scribd. Game theory Operation Research 1. Why OR? What is OR? DevelopedinsbymathematiciansJohn von Neumann and economist Oskar Morgenstern Designedtoevaluatesituationswhere individualsandorganizationscanhave conflictingobjectives 3 4.
In game theory, an opponent is referred to as player. The decisions of the players are a Nash Equilibrium if no individual prefers a different choice. In other words, each player is choosing the best strategy, given the strategies chosen by the other players. An alternative that yields a lower payoff than some other strategies a strategy is dominated if it is always better to play some other strategy, regardless of what opponents may do It simplifies the game because they are options available to players which may be safely discarded as a result of being strictly inferiorto other options.
What is the best decision for Bonnie? 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.
Value of the game Value of the game is the maximum guaranteed game to player A maximizing player when both the players utilizes their best strategies. Classification of Games Simultaneous v. Sequential Move Games Games where players select activities simultaneously are simultaneous move games.
Games where players select activities in a particular series or sequence are sequential move games. Many strategic situations include both sequential and simultaneous moves. One-Shot versus Repeated Games One-shot: play of the game takes place once. Advise: If you plan to follow an aggressive strategy, ask yourself whether you are in a one-shot game or in repeated game.
If a repeated game then think again. Usually games are divided into Pure strategy games Mixed strategy games The technique for solving these two types changes. Saddle point method can be used to solve pure strategy games. The diverse methods for solving a mixed strategy game are Dominance rule Analytical method Graphical method Simplex method Limitations of game theory The main limitations are The hypothesis that the players have the information about their own payoffs and others is rather impractical As the number of players adds in the game, the analysis of the gaming strategies turns out to be increasingly intricate and complicated.
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