1. PRESENTED TO: MS. SEEMA. PRESENTED BY: PANKAJ SABHERWAL(46) ANU HOODA(45) “GAME THEORY”
2. “Game theory attempts to study decision-making in situations where two or more intelligent and rational opponents are involved under conditions of conflict and cooperation. The approach game theory is to seek to determine a rival’s most profitable counter-strategy to one’s own ‘best’ moves and to formulate the appropriate defensive measure.” Game theory came into existence in early 20th century. However, the mathematical treatment of the Game Theory was made available only in 1944, when John Von Neumann and Oscar Morgenstern published a book ‘Theory of Games and Economic Behaviour’. Author’s approach was based on the principle of ‘best out of the worst’,i.e., he utilised the idea of minimization of the maximum losses. Introduction
3. No. of Players. Payoff. Strategy. Value of the Game. Payoff Matrix. Two-Person Zero-sum Game. Maximin & Minimax Principle. Characteristics. BASIC TERMINOLOGY.
4. In case of a pure strategy game, the miximizing player arrives at his optimal strategy on the basis of the maximum criterion,while the minimizing player’s strategy on the minimax criterion. The game is solved when the maximin value equals minimax value. The difference b/w pure and mixed strategy games is that pure strategy games possess a saddle point whereas mixed strategy games do not . A presence of a saddle point is identified by comparing the values of each player’s maximin strategy. Solution Methods of Pure Strategy Games(with saddle point)
5. In general the following rules of dominance are used to reduce the size of payoff matrix: Rule 1:- If all the elements in a row of a payoff matrix are less than or equal to the corresponding elements of the other rowthen the player A will never choose the ith strategy or in other words the ith strategy is dominated by the jth strategy. Rule 2:- If all the elements in a column of a payoff matrix are greater than or equal to the corresponding elements of the other column then the player B will never choose the rth strategy or in other words the rth strategy is dominated by the sth strategy. Principle of Dominance
6. Rule 3:- A pure strategy may be dominated ifnit is inferior to average of 2 or more other pure strategies. Nash Equilibrium:- It is a set of strategies such that each player believes (correctly)that it is doing the best it can, given the strategy of the opponents. For Example:- Cont….
7. All problems of game where saddle point does not exist , are taken as mixed strategy problems. In order to solve such a game ,each player adopts the concept of chance move and starts to play in random manner & in such a way that his avg. payoff over a large no. of plays of the game should be optimal, even though he may lose more in any individual play of the game. In other words, the player adopts a certain strategy having probability P1forsome time and then shifts over to another strategy having probability P2and then after sometime to the third strategy having probability P3 and so on , such that the sum of his all probabilities is equal to one & payoff over a large no. of plays of the game becomes optimal Solution Methods of Mixed Strategy Games (Games without saddle Point)
11. Unlike zero-sum games when one firm’s loss is necessarily the other firm’s gain and vice-versa, the non-zero sum refer to a situation where there exists a jointly preferred outcome. The existence of jointly preferred outcome means that both players may be able to increase their payoffs through some form of co-operation or agreement concerning the actions to be chosen. The 2-Person, Non –Zero Sum Games
13. The assumption that the players have the knowledge about their own payoffs & payoffs of others is rather unrealistic. He can only make a guess of his own & his rival’s strategies. As the no. of players increases in the game, the analysis of the gaming strategies becomes increasingly complex 7 difficult. In Practice , there are many firms in an oligopoly situation and the game theory cannot be very helpful in such situations. Limitations of Game Theory
14. The assumptions of maximin & minimax show that the players are risk-averse & have complete Knowledge of the Strategies. These do not seem practical. Rather than each player in an oligopoly situation working under uncertain conditions, that players will allow each other to share the secrets of business in order to work out a collusion. Thus , the mixed strategy are also not very useful. Cont….
