Strategic Thinking Essay Sample
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Nash’s non-cooperative game theory is a contradistinction of Neumann and Morgenstern’s theory of two-person zero-sum games which they developed in their book ‘theory of games and economic behavior’. There are five main concepts derived from the first few pages of Nash’s theory based on his 1950 paper. The first among them is that the game in question should be finite in this case meaning that each participant has a finite number of strategies that they can employ. The second concept is the assumption that participants do not talk to each other and there is no form of collaboration among them whatsoever. Another important concept in the theory is that, unlike Neumann and Morgenstern’s theory, there can be more than two participants in the game making it a generalization of the preceding theory.The essential ingredient of the theory is the notion of the presence of an equilibrium point. Lastly, there is the concept of mixed strategy and it points to the possibility of a participant choosing to employ more that one pure strategy during the course of the game.
Rock-paper-scissors is a game commonly used for choosing and it has three strategies namely: rock, paper and scissors, represented by hand signs. A clenched fist represents rock and an open hand represents paper and two extended separated fingers represent scissors. Rock-paper-scissors has a player set of two and the two participants on the count of three stretch out their hands making one of the three hand signs. On each of the first two counts, one hand is held in a fist and swung down. In the game, the payoff function is, ‘rock’ beats ‘scissors’, ‘scissors’ beats ‘paper’ and ‘paper’ beats ‘rock’. However,if the participants make the same sign, the game is tied thus the participants will have to make another throw and this goes on until a winner emerges.
Rock-paper-scissors is a finite game because the number of strategies that can be employed by any of the participants is three an d thay include rock, paper and scissors.Knowledge of the strategies makes the game finite since the number of strategies is known. Also, there is a clearly defined payoff function.
In the game rock-paper-scissors, there is no pure strategy for winning because the participants in this game randomize between three strategies as they try to outdo each other in order to win
The best strategy for winning rock-paper-scissors is to play rock, paper and scissors with equal probability. That means a third for each strategy and playing equal probability makes one’s opponent indifferent between the strategy choices.
It is possible to represent rock-paper-scissors in matrix form. Let rock be represented by ‘R', paper be represented by ‘P' and scissors be represented by ‘S'. Let a win be ‘1’, a loss ‘-1’ and a draw‘0’. The matrix for rock-paper-scissors is as below.
Nash equilibrium is a theory that proposes a solution to the concept of a non-cooperative game involving two or more players. In the game, each participant is assumed to be aware of the equilibrium strategies of the other participants and no participant has anything to gain by altering only their strategy.
In other words, participants in the game have to make decisions based on both their strategies and those of other players and they are also aware of all the strategies available to the other players.
The Nash equilibrium for the 2X2 game in strategic form is for Mickey to choose South and for Goofy to North. When both Mickey and Goofy choose south, it is disadvantageous to Goofy who gets.When Mickey chooses north and Goofy chooses south, it is disadvantageous to Goofy who gets 1. When both Mickey and Goofy choose North, it is disadvantageous to Mickey who gets 2. Therefore, it is in the interest of Mickey to choose south and Goofy to choose north for both of them to be satisfied.
There are two Nash equilibria in weird game 1. The first one is for player one to go up while player two goes right and the second one is for player one to go down while player two goes left.
There is one Nash equilibrium in ‘weird game two’ and it occurs when both Sue and Ali choose right.
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