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Game theory, branch of applied mathematics that provides tools for analyzing situations in which parties, called players, make decisions that are interdependent. It is a Mathematical Theory that deals with the general features of competitive situations in a formal and abstract way.Because competitive situations are so ubiquitous,Game theory has applications in variety of areas including in business and Economics.Game theory deals with many complicated types of competitive situations.However the focus of this article is on the simplest and basic case, called two-person, zero-sum games.As the name implies,these games involve only two adversaries or players.They are called zero sum games because one player wins whatever the other one loses,so that the sum of their net winning is zero.

The formulation of Two-Person,Zero-Sum Games

Game theory provides a mathematical framework for analyzing the decision-making processes and strategies of adversaries (or players) in different types of competitive situations. The simplest type of competitive situations are two-person, zero-sum games. These games involve only two players; they are called zero-sum games because one player wins whatever the other player loses.

Example: Odds and Evens

Consider the simple game called odds and evens. Suppose that player 1 takes evens and player 2 takes odds. Then, each player simultaneously shows either one finger or two fingers. If the number of fingers matches, then the result is even, and player 1 wins the bet ($2). If the number of fingers does not match, then the result is odd, and player 2 wins the bet ($2). Each player has two possible strategies: show one finger or show two fingers. The payoff matrix shown below represents the payoff to player 1.

payoff to player 1.

In general ,a two person game is characterized by

1. The strategies of Player 1
2. The strategies of Player 2
3. The Payoff Table

Basic Concepts of Two-Person Zero-Sum Games

This game of odds and evens illustrates important concepts of simple games

• A two-person game is characterized by the strategies of each player and the payoff matrix.
• The payoff matrix shows the gain (positive or negative) for player 1 that would result from each combination of strategies for the two players. Note that the matrix for player 2 is the negative of the matrix for player 1 in a zero-sum game.
• The entries in the payoff matrix can be in any units as long as they represent the utility (or value) to the player.
• There are two key assumptions about the behavior of the players. The first is that both players are rational. The second is that both players are greedy meaning that they choose their strategies in their own interest (to promote their own wealth).

SOME KEY TAKEAWAYS ON ZERO-SUM GAMES

• A zero-sum game is a situation where, if one party loses, the other party wins, and the net change in wealth is zero.
• Zero-sum games can include just two players or millions of participants.
• In financial markets, futures and options are considered zero-sum games because the contracts represent agreements between two parties and, if one investor loses, then the wealth is transferred to another investor.
• Most transactions are non-zero-sum games because the end result can be beneficial to both parties.

Zero-Sum Game vs. Game Theory

Game theory is a complex theoretical study in economics. The 1944 groundbreaking work Theory of Games and Economic Behavior, written by Hungarian-born American mathematician John von Neumann and co-written by Oskar Morgenstern, is the foundational text. Game theory is the study of the decision-making process between two or more intelligent and rational parties.

Poker and gambling are popular examples of zero-sum games since the sum of the amounts won by some players equals the combined losses of the others. Games like chess and tennis, where there is one winner and one loser, are also zero-sum games.

Article courtesy:

Operations Research,an introduction(9th edition) Book by Hamdy A.Thaha

Introduction to operation research ,concepts and cases(9th edition) Book by F.S Hillier and G.J Liberman

Game Theory Game Theory

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