Page 197 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 9.6 Summary

 Game theory is the study of the ways in which strategic interactions among rational
players produce outcomes with respect to the preferences of those players, none of which
might have been intended by any of them.
 Game theory describes the situations involving conflict in which the payoff is affected by
the actions and counteractions of intelligent opponents.
 Two-person zero-sum games play a central role in the development of the theory of
games.
 There are many ways to solve a game theory problem, for e.g., that of linear programming,
matrix or graphical.

 Every way has its own significance and advantages, thus making game theory a model for
winning business in a competitive environment.

9.7 Keywords

Minimax Criterion: Minimax criterion is selecting the strategies that minimize the loss for each
player. In other words, the player always anticipates worst possible outcome and chooses the
strategy to get maximum for profit and minimum for loss.
Mixed Strategy: Selects at least 2 courses of action, while a probability of selecting an individual
strategy will be less than 1, but the sum of the strategies will be 1.
Pure Strategy: The strategy to select a course of action with the probability of one.
Saddle Point: A situation where both the players are facing pure strategies.

Strategy: All possible actions that can be taken for every pay–off.
Value of the game: The Value of the game is the expected gain of player A if both players use
their best strategies. The best strategy is arrived at using minimax criterion.

9.8 Review Questions

1. What is a game in game theory? What are the properties of a game? Explain the “best
strategy” on the basis of minimax criterion of optimality.
2. What are pure and mixed strategies and how do they differ?

3. When do you say that the game is fair? Give an example for it.
4. Explain the following:
(a) Saddle point

(b) Pay-off matrix
(c) Rectangular games
(d) Optimal strategy
(e) Minimax principle
(f) Value of a two-person-zero-sum game

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