PRESENTED BY

DILEEP KUMAR

IMB2010032

Decision making under Risk and Uncertainty-The

Game Theory

Introduction

The Six steps in decision theory

Types of decision making environments

Decision Making under risk

Decision making under uncertainty

The game theory

Contents

To a extent , the success or failure that a person experiences in life depends upon the decision he or she makes. There are several examples we know where good decisions made individual's destiny.

A good decision is one that is based on logic, considers all available data and possible alternatives, and applies quantitative approach. Its rare possibility, that a good decision brings unexpected or unfavorable results/outcomes.

Sometimes it happened when you make a bad decision but are lucky to get favorable outcome, it is said that you still make a bad decision.

So, the decision theory is an analytic and systematic way to tackle problems

Introduction

Introduction

Language of games

The Minimax Criterion

Pure strategy games

Mixed strategy games

Dominance

Game Theory

History-According the modern history, the game theory dates back to 1944 when John von Neuman and Oscar Morgestern published their book ‘Theory of games and economic behaviour’. Since then the game theory has been used by army generals to plan war strategies , union negotiators and managers in collective bargaining and business of all types to determine the best strategies given a competitive business environment.

Game theory is one way to consider the impact of strategiesof others on our strategies and outcomes.A game is a contest involving two or more decision makers,each of whom wants to win .It is the study of how optimal strategies are formulated in conflict .

Introduction

There are two stores in the market having different advertising strategies for the two products , the radio spots and the newspaper ads.

Store X’s Payoff Matrix

Language of the Game(Payoff Matrix)

Game Game Player Y’s

Strategies

Player X’s Y1(use radio)

Y2(Use newspaper)

Strategies X1(Use Radio)

3 5

X2(Use news papers)

1 -2

Store X’s Strategy Store Y’s Strategy Outcome(%Change in Market Share)

X1(Use radio) Y1(Use radio) X wins 3 and Y loses 3

X1(Use radio) Y2(use news paper) X wins 5 and Y loses 5

X2(Use newspaper) Y1(use radio) X wins 1 and Y loses 1

X2(Use newspaper) Y2(use newspaper) X loses 2 and Y wins 2

Game Outcomes

A player using the minimax criterion will select the strategy that minimizes the maximum possible loss.

The upper value of the game is equal to the minimum of the maximum values in the columns.

The lower value of the game is equal to the maximum values in the rows.

An equilibrium or saddle point condition exists if the upper value of the game is equal to the lower value of the game. This is called as value of the game.

The Minimax Criterion

When saddle point is present, the strategy each player should follow will always be the same regardless of other players strategy. This called as the pure strategy . The saddle point is situation in which both players are facing pure strategies.

Pure strategy Games

In a mixed strategy game, each player should optimize the expected gain.

When there is no saddle point, players will play each strategy for certain percentage of time.

The most common way to solve a mixed strategy game is to use the expected gain or loss approach.

Mixed Strategy Games

The principle of dominance can be used to reduce the size of the games by eliminating strategies that would never be played . A strategy for a player is said to be dominated if the player can always do as well or better playing another strategy Any dominated strategy can eliminated from the game depending on the outcomes.

Dominace

Clearly define the problem at hand.

List the possible alternatives.

Identify the possible outcomes or states of nature.

List the payoff or profit of each combination of alternatives and outcomes.

Select one of the mathematical decision theory models.

Apply the model and make your decision.

The Six steps in decision theory

Here we use the Thompson Lumber Company case as an example to illustrate these decision theory steps. John Thompson is the founder and president of Thompson Lumber Company, a profitable firm located in Portland , Oregon.

Case

The problem that John Thompson identifies is whether to expand his product line by manufacturing and marketing a new product, backyard storage sheds.

Step 1

The second step is to list the alternative.

Thompson’s second step is to generate alternatives that are available to him .In decision theory the alternative is a course of action or strategy that the decision maker can choose .According to him his alternatives are to construct –

1-a large new plant to manufacture the storage sheds

2-a small plant, or

3-no plant at all

So, the decision makers should try to make all possible alternatives ,on some occasion even the least important alternative might turn out to be the best choice.

Step2

Third step is to identify possible outcomes.

The criteria for action are established at this time .According to Thompson there are two possible outcomes :the market for the storage sheds could be favourable means there is a high demand of the product or it could be unfavourable means that there is low demand of the product.

Optimistic decision makers tend to ignore bad outcomes, where as pessimistic managers may discount a favourable outcome. If you don’t consider all possibilities, it will be difficult to make a logical decision, and the result may be undesirable.

There may be some outcomes over which the decision maker has little or no control are known as states of nature.

Step 3

Fourth step is to list payoffs.

This step is to list payoff resulting from each possible combination of alternatives and outcomes. Because in this case he wants to maximize his profits, he use profits to evaluate each consequences .Not every decision,of course, can be based on money alone –any appropriate means of measuring benefit is acceptable.In decision theory we call such payoff or profits conditional values.

Step4

The last two steps are to select and apply the decision theory model.

Apply it to the data to help make the decision. Selecting the model depends on the environment in which you are operating and the amount of risk and uncertainty invovled.

Decision Table with condition values for Thompson-

Step6 &7

STATE OF

NATURE

ALTERNATIVE FAVOURABLE MARKET($)

UNFAVOURABLE MARKET($)

Construct a large Plant

200,000 -180,000

Construct a small Plant

100,000 -20,000

No Plants 0 0

The types of decisions people make depends on how much knowledge or information they have about the situation. There are three kind of decision making environments:

Decision making under certainty.

Decision making under risk.

Decision making under uncertainty.

TYPES OF DECISION MAKING ENVIRONMENTS

Here the decision makers know about the certainty of consequences every alternative or decision choice has.

Naturally they will choose the alternative that will result in the best outcome.

Example: Lets say that you have $10000 to invest for a period of one year. And you have two alternatives either to open a savings account paying 6% interest and another is invest in Govt. Treasury Bond paying 10% interest. If both the investments are secure and guaranteed, the best alternative is to choose the second investment option to gain maximum profit.

Decision Making under Certainty

Here the decision Maker knows about the several possible outcomes for each alternative and the probability of occurance of each outcome.

Example : The probability of being dealt a club is .25.The probability of rolling a 5 on die is 1/6.

In the decision making under risk, the decision maker usually attempts to maximize his or her expected well being . Decision theory models for business problems in this in this environment typically employ two equivalent criteria: maximization of expected monetary value and minimization of expected loss.

Expected monetary value is the weighted value of possible payoffs for each alternative

Decision Making Under Risk

Here there are several outcomes for each alternative, and the decision maker does not know the probabilities occurrences of various outcomes.

Example The probability that a Democrat/Republican will be the President of a country 25 Years from now is not known.

The criteria that is covered in this section as follows:

1- Maximax-This criterion find the alternative that maximizes the maximum payoffs or consequence for every alternative.here we first locate the maximum payoff with every alternative and then pick that alternative with the maximum number.This is also known as optimistic decision criterion.

Maximin- This criterion finds the alternative that maximizes the minimum payoff or consequence for every alternative. Here we first locate the minimum outcome within every alternative and then pick that alternative with maximum number. This is called as pessimistic decision criterion.

Decision Making under Uncertainty

Criterion of Realism:Also called as weighted average, is a compromise between an optimistic and a pessimistic decision.Let the coefficient of realism is ‘a’ selected.The coefficient is between 0 and 1. when ‘a’ is close to 1, the decision maker is optimistic about the future.When ‘a’ is close ‘0’ the decision maker is pessimistic.It helps the decision maker to build feelings about relative optimism and pessimism.

Weighted average =a(maximum in row)+(1-a)(minimum in row).

Equally likely(Laplace)-one criterion that uses all the payoffs for each alternative is the equally likely also called Laplace decision criterion.This is to find alternative with highest payoff.

Minimax Regret-The final decision criterion that we discuss is based on opportunity loss or regret.

Cont’d

THANK YOU