Game Theory is the concept of Operation Research used in decision making for analyzing competitors’ strategies and planning to gain competitive advantage in the market
Competitors play a vital role in the decision-making of an organization. Each strategy by an organisation is formulated after keeping its competitors’ actions in mind. In the same way, the competitors also formulate their strategies after analysing the actions of their opponents. Many practical problems require decision-making in a competitive situation, where there is conflicting interest of two or more parties involved. For example, candidates for an election, advertising and marketing campaigns by competing business firms, countries involved in military wars, etc. have conflicting interests. The competitive situation involved in these conditions will be called a ‘Game’, if it has the following properties:
- Players are competitors (participants) who are limited in number.
- Each player has a finite number of strategies (alternatives) available for competitors.
- When every participant uses their strategy, the game is played.
- Every game results in a result, e.g., loss or gain or draw, usually called payoff to some player.
Table of Contents
Two-Persons Zero-Sum Games: Game Theory
A game played by two competitors is termed a ‘Two-Person Game’. When the algebraic sum of gain or loss involved in the game is zero, then the game is said to be a ‘Zero-Sum Game’.
Basic Terminology
Player: An individual, a group, or an organisation involved in the competitive game is called a Player.
Strategy: Strategies are the alternative course of action or set of rules available for a player in advance, by which the decision for the course of action to be adopted is taken by the player.
- Pure Strategy: Two-person zero-sum games with saddle points are called pure strategy games. In pure strategy, a player always selects the same strategies. The objective is to maximize gains or minimize losses.
- Mixed Strategy: Two-person zero-sum games without saddle points are called mixed strategy games. In mixed strategy, the player always has several strategies with some specific probabilities to choose. The objective is to maximize expected gains or minimize expected losses for effective game theory.
Optimum Strategy: The strategy that puts a player ahead of its competitors without bothering the strategies of its competitors, is termed as optimum strategy for that player.
Value of the Game: It is the expected payoff of play when all players of the game follow their optimum strategies. If the value of the game is zero, it is said to be fair; if it is not zero, it is said to be unfair.
Pay-Off Matrix: The results of a particular strategy, either gain or loss (Payoff), when represented in the form of a matrix is termed a Pay-off Matrix. A pay-off matrix has n rows and m columns. n are number of strategies of the first player and m are number of strategies of Player B. The pay-offs of each combination are placed as elements of the matrix. A positive element represents gain and a negative entry indicates the loss.
Saddle Point: A saddle point in a pay-off matrix is that element of the matrix that represents the ‘Maximin’ value of a player and the ‘Minimax’ value of his opponent.
The minimax element is found after choosing the maximum element of each column and then finding the minimum value of those entries.
Similarly, Maximin is the minimum element of each row and then finds the Maximum of those entries.
If Minimax = Maximin, then saddle point exists.
If Maximin ≠ Minimax, then saddle point does not exist.
Limitations of Games in Competition
In reality, there is a lack of equal information or intelligence between the two competitors.
There may be such conditions arise in managerial decision-making when both players may lose or gain. Hence, it may not be a zero-sum game.
The competitive situations in most cases are never really two-person games in managerial decision-making as government or other bodies are always present as third or fourth-party roles in the game.
The solution of large pay-off matrices with mixed strategies is very complicated.
The principle of minimax implies the chances of maximum loss to the businessman but a dynamic businessman is always after profit and tries to maximize his gains or profits even by taking greater risks.
Hence, Game theory is the study of how strategic interactions among rational players produce outcomes concerning the preferences of those players, none of which might have been intended by any of them. Game theory describes situations involving conflict in which the payoff is affected by the actions and counteractions of intelligent opponents. The evolution of the theory of games is largely dependent on two-person zero-sum games. A game theory problem can be solved with the help of a linear programming matrix or graphical papers. Every way has its own significance and advantages, thus making game theory a model of winning business in a competitive environment.
Reference Book: Operations Research