Pure strategies

Pure strategies

IntroductionImage result for Pure Strategies in operation research diagram

Game theory applies to those competitive situations which are technically known as “competitive games” or in general known an games. As the game is a competition involving two or more decisions makers each of whom is keen to win. The basic aim of this chapter is to study about how the optimal strategies are formulated in the conflict. Thus we can say that game theory is not related with finding an optimum or winning strategy for a particular conflict situation. Afterwards we can say that the theory of game is simply the logic of rational decisions. After reading this unit, you should be able to know how to take decision under the cut-throat competition and know that outcome of our business enterprise depends on what the competitor will do.
In today’s business world, decisions about many practical problems are made in a competitive situation, where two or more opponents are involved under the conditions of competition and conflict situations. The outcome does not depend on the decision alone but also the interaction between the decision-maker and the competitor.
The objective, in theory, of games is to determine the rules of rational behaviour in game situations, in which the outcomes are dependent on the actions of the interdependent players. A game refers to a situation in which two or more players are competing. A player may be an individual, a group or an organisation. Game Theory has formulated mathematical models that can be useful in decision-making in competitive situations. To get a better insight of the concept, we consider an example of a simple game.
Let us assume that there are only two car manufacturers, company A and company B. The two companies have market shares for their product. Company A is planning to increase their market share for the next financial year. The vice-president of company A has come up with two strategies. One strategy is to modify the outer shape of the car and to advertise on TV. Company B, knowing that if these strategies are adopted by company A, it may lead to decrease in its market share, develops similar strategies to modify the shape of their car and to advertise on TV. Table 8.1 below, gives the pay off if both the companies adopt these strategies.

Pure Strategies: Game with Saddle Point

The aim of the game is to determine how the players must select their respective strategies such that the pay-off is optimized. This decision-making is referred to as the minimax-maximin principle to obtain the best possible selection of a strategy for the players.
In a pay-off matrix, the minimum value in each row represents the minimum gain for player A. Player A will select the strategy that gives him the maximum gain among the row minimum values. The selection of strategy by player A is based on maximin principle. Similarly, the same pay-off is a loss for player B. The maximum value in each column represents the maximum loss for Player B. Player B will select the strategy that gives him the minimum loss among the column maximum values. The selection of strategy by player B is based on minimax principle. If the maximin value is equal to minimax value, the game has a saddle point (i.e., equilibrium point). Thus the strategy selected by player A and player B are optimal.
The aim of the game is to determine how the players must select their respective strategies such that the pay-off is optimized. This decision-making is referred to as the minimax-maximin principle to obtain the best possible selection of a strategy for the players.
In a pay-off matrix, the minimum value in each row represents the minimum gain for player A. Player A will select the strategy that gives him the maximum gain among the row minimum values. The selection of strategy by player A is based on maximin principle. Similarly, the same pay-off is a loss for player B. The maximum value in each column represents the maximum loss for Player B. Player B will select the strategy that gives him the minimum loss among the column maximum values. The selection of strategy by player B is based on minimax principle. If the maximin value is equal to minimax value, the game has a saddle point (i.e., equilibrium point). Thus the strategy selected by player A and player B are optimal.