Unit-5
Decision theory
Question bank
Part-A
Q1) Give the concept of decision making (7)
A1)
Decision theory deals with how to determine the best course of action when many options are available and the outcome cannot be reliably predicted.
It's hard to imagine a situation without such a decision problem, but we're primarily limited to problems that occur in the business, and the results can be explained in dollars of profit or revenue, cost or loss. It may be reasonable to consider these issues as the best alternative in the long run, with the highest profit or profit on average, or the lowest cost or loss. This criterion of optimality is not without its drawbacks, but it should serve as a useful guide to behavior in repetitive situations where the results are not critical. (Another criterion of optimality, maximizing expected usefulness, provides consistent decision makers with a more personal and subjective guide to behavior.)
The simplest decision problem is to list the probabilities associated with the possible monetary outcome of each alternative, calculate the expected monetary value of all alternatives, and select the alternative with the highest expected monetary value. You can solve it by doing. Determining the best alternative is a bit more complicated when:
The alternative involves a series of decisions.
Another class of problem often gets additional information about uncertain variables at a particular cost. This additional information is rarely completely accurate. Its value, and the maximum amount you are willing to pay to get it, must depend on the difference from the best you can expect to do with the help of this information.
And the best I expect to do without it. These are the types of problems we are about to start.
Q2) Define decision making theory. (8)
A2)
Definition-
A decision may be defined as the selection of the action, by the decision maker, which is considered to be the best according to some predetermined standard from amongst the available options.
Steps in Decision making
I) Identification of all possible outcomes called states of nature or events.
Ii) Identification of all courses of action called acts.
Iii) Determination of payoff function.
Iv) Choosing from among the alternatives, the best possible action on the basis of some criterion.
Characteristics of decision making
- Decision making is a goal-oriented process. Decisions are made to achieve certain goals.
- It involves choice. Or selection of the most appropriate course of action out of various alternatives.
- It is an ongoing process. Decision making is a recurring activity.
- It is a intellectual process. It involves intuitions and experience.
- It is a dynamic process. Technique used for decision making may vary with the type of problem involved and the time available for its solution
- It is situational. There may also be a decision not to act.
- It involves commitment of time, efforts and resources.
- It is pervasive.
Q3) What do you understand by the term certainty and risk? (7)
A3)
Certainty- it is an environment of very low ambiguity. Under these conditions, the manager has complete and measurable info about the objectives, as well as outcomes of the alternative decisions.
Certainty is an ideal situation where the manager has perfect info.
Another way to ensure a secure environment is for the manager to create a closed system. This means he chooses to focus on only a few options. He gets all the information available about such alternatives that he is analyzing. He ignores other factors that make the information unavailable. Such factors have nothing to do with him.
Risk- This is a condition of moderate ambiguity. Decision makers take decision in a risky environment. In this situation, the decision maker has incomplete info.
However, the possible outcomes can be assigned probability estimates.
Probabilities may be derived from mathematical or statistical models.
In order to make good decisions decision makers must do systematic research and collect info. Related to outcomes.
Even in this scenario, the manager has some information available. However, the availability and reliability of the information is not guaranteed. He needs to graph some alternative behavioral policies from the data he has.
Q4) What is Decisions- Making Environment? (5)
A4) It is said that the main responsibility of all managers is decision making. The manager follows a series of steps to make the right decisions that benefit the company. This process is known as the decision-making process. However, the decision-making environment is also an important part of the process. Learn some important aspects of the decision-making environment.
The quality of decisions made by an organization determines the success or failure of the aforementioned business.
Therefore, you should consider all available information and alternatives before making any important decisions. The decision-making process is very helpful.
Another factor that influences these decisions is the environment in which they are made. There are several different types of environments in which these decisions are made.
Also, the type of decision-making environment influences the way decisions are made. There are three main types of decision-making environments. Let's take a brief look at each one.
Q5) Write short note on Expression. (5)
A5) There are several ways to represent a decision tree. This analysis is usually represented by lines, squares, and circles. Squares represent decisions, lines represent results, and circles represent uncertain results. Keeping the lines as far apart gives you plenty of space to add new considerations and ideas.
A decision tree representation can be created in four steps:
- Explain the decisions you need to make in the square.
- Draw different lines from the square and write a possible solution for each line.
- Put the result of the solution at the end of the line. Uncertain or uncertain decisions are in a circle. The latter can be placed in a new square when the solution leads to a new decision.
- Each of the squares and circles is critically reviewed for the final choice
Q6) Give an Example of Decision Tree Analysis. (8)
A6) Suppose a for-profit company wants to increase sales and related profits next year.
You can then use the decision tree to map different alternatives. There are two options for increasing both sales and profits: 1-increasing advertising costs and 2-expanding sales activities. This will create two branches. Option 1 to 2 new options are born. That is, 1-1 is the new agency and 1-2 is to use the services of the existing agency. Option 2 presents two follow-up options in sequence. 2-1-Collaboration with agents or use of 2-2-Original sales support system.
The branch continues.
The next choice from 1-1 is:
1-1-1 Budget will increase by 10%-> Final result: Sales will increase by 6% and profit will increase by 2%
1-1-2 Budget will increase by 5%-> Final result: Sales will increase by 4% and profit will increase by 1.5%
Alternatives resulting from 1.2:
1-2-1 Budget increased by 10%-> Final result: Sales increased by 5%, profit increased by 2.5%
1-2-2 Budget increased by 5%-> Final result: Sales increased by 4%, profit increased by 12%
From 2.1 onwards it will probably look like this:
2-1-1 Setup with own dealer-> Final result: Sales increased by 20%, profit increased by 5%
2-1-2 Cooperation with existing dealers-> Final result: Sales increased by 12.5%, profit increased by 8%
From 2.2 onwards it will probably look like this:
2-2-1 Recruitment of new sales staff-> Final result: Sales increased by 15%, profit increased by 5%
2-2-2 Motivate existing sales staff-> End result: Sales will increase by 4% and profit will increase by 2%.The above example probably shows that the company chooses 1-2-2. This is because the forecast for this decision will increase profits by 12%.
This analysis provides clear proof and is especially useful in situations where it may be desirable to develop various alternatives to decision making in a structured way. This method is increasingly being used by practitioners and technicians to make diagnoses and identify car problems.
Q7) Write note on Game theory. (5)
A7)
Game theory is a theoretical framework for imagining social situations between competing players. In some respects, game theory is the best decision of an independent competing actor in the science of strategy, or at least in a strategic setting. Let's look at some examples.
The major pioneers of game theory were the 1940s mathematician John von Neumann and the economist Oskar Morgenstern. Mathematician John Nash is considered by many to provide the first significant extension of the work of von Neumann and Morgenstern!
Q8) How will you explain the Basics of game theory? Do mention the Nash equilibrium. (8)
A8)
The focus of theory of games may be a game that acts as a model for an interactive situation between rational players. The key to game theory is that the rewards of one player depend on the strategy implemented by the other player. The game identifies the player's identity, preferences, available strategies, and how these strategies affect results. Depending on the model, various other requirements and assumptions may be required.
According to game theory, the actions and choices of all participants influence their outcomes!
Let's start with Nash equilibrium
Nash equilibrium is the result reached, which means that once achieved, the payoff cannot be increased by unilaterally changing decisions. You can also think of it as "no regrets" in the sense that once you make a decision, you will not regret a decision that takes into account the consequences.
In most cases, the Nash equilibrium is achieved over time. However, once the Nash equilibrium is reached, it does not deviate. After learning how to find the Nash equilibrium, let's see how unilateral movements affect the situation. Does it make sense? The Nash equilibrium is described as "no regrets" because it should not be. It is generally believed that there are multiple equilibrium in a game.
This mainly happens in games that have more complex elements than the two choices of two players. In a simultaneous game that repeats over time, one of this multiple equilibrium is reached after trial and error. This scenario of various overtime choices before reaching equilibrium is most often performed in the business world when two companies are deciding on prices for compatible products such as airfares and soft drinks. The impact of game theory on economics and business
Game theory has revolutionized economics by addressing the critical problems of previous mathematical economic models. Neoclassical economics, for example, struggled to understand the expectations of entrepreneurs and was unable to cope with imperfect competition. Game theory turned its attention to the market process itself from steady-state equilibrium.
In business, game theory is undoubtedly useful for modelling competing behaviour between economic agents. Enterprises often have several strategic options that affect their ability to achieve economic benefits. For example, companies may face dilemmas such as discontinuing existing products, starting new product development, lowering prices compared to competitors, or adopting new marketing strategies. Economists tend to use game theory to understand the behaviour of oligopolistic businesses. This helps predict the possible consequences of a company engaging in certain actions such as price fixing or collusion.
Q9) What do you mean by repeated oligopoly game? (7)
A9)
The prisoner's dilemma was played once by two players. Players were given a payoff matrix. Each can make one choice and the game ended after the first selection round.
In the real world of oligopoly, there are as many players as companies in the core industry. They play round by round: the company raises its price. When another company introduces a new product and the first company cuts prices, the third company introduces a new marketing strategy. Oligopoly games are a bit like baseball games, with no limit on the number of innings. One company will play one round later and another will be on top on another day. Example: In games in the computer industry, the rules have changed with the introduction of personal computers. Very easy to win in mainframe games, IBM is struggling to keep up with a world where rivals continue to lower prices and improve quality.
The oligopoly game can have more than two players, so the game is much more complicated, but the basic structure remains the same. The fact that the game itself repeats brings new strategic considerations. Players need to consider how their choices will affect their rivals in the future, not how their choices will affect their rivals.
Now keep the game simple and think about duopoly games. The two companies have colluded implicitly or openly to create an exclusive solution. As long as each player just supports the agreement, the two companies will get exactly the maximum financial benefit possible for the company.
Q10) What is Decision process? (7)
A10)
Game theory is about making decisions in an interactive world, so the best decisions of all decision makers depend on what others make. As a result, everyone in this interactive world needs to anticipate the decisions of others in order to promote their own interests.
This was a collaboration between Austrian economist Oskar Morgenstern and Hungarian genius, polymath and multilingually acclaimed John von Neumann.
Von Neumann was an undisputed genius, but he quickly realized that he was a mediocre poker player and couldn't beat poker games in probability theory. His great appreciation for the rough information, secondary guesses, and unpredictability of poker games laid the very foundation for game theory. Poker players can hide information by strategically releasing it through movements and encouraging mistakes from rivals.
In other words, he formalized how poker players "bluff" their rivals by tricking them into hiding information and playing with a set of strategies that are ultimately supposed to win the game.
John Nash's legacy in game theory is a unique and achievable Nash equilibrium, and therefore game theory has become completely clinical and completely excluded from the real world. The only exceptions among skilled economists today are two other Nobel laureates, Thomas C. Schelling and Roger Myerson.
Q11) What is Nash equilibrium? (8)
A11)
Nash equilibrium is the result reached, which means that once achieved, the payoff cannot be increased by unilaterally changing decisions. You can also think of it as "no regrets" in the sense that once you make a decision, you will not regret a decision that takes into account the consequences.
In most cases, the Nash equilibrium is achieved over time. However, once the Nash equilibrium is reached, it does not deviate. After learning how to find the Nash equilibrium, let's see how unilateral movements affect the situation. Does it make sense? The Nash equilibrium is described as "no regrets" because it should not be. It is generally believed that there is multiple equilibrium in a game.
This mainly happens in games that have more complex elements than the two choices of two players. In a simultaneous game that repeats over time, one of these multiple equilibrium is reached after trial and error. This scenario of various overtime choices before reaching equilibrium is most often performed in the business world when two companies are deciding on prices for compatible products such as airfares and soft drinks. The impact of game theory on economics and business
Game theory has revolutionized economics by addressing the critical problems of previous mathematical economic models. Neoclassical economics, for example, struggled to understand the expectations of entrepreneurs and was unable to cope with imperfect competition. Game theory turned its attention to the market process itself from steady-state equilibrium.
In business, game theory is undoubtedly useful for modeling competing behaviour between economic agents. Enterprises often have several strategic options that affect their ability to achieve economic benefits. For example, companies may face dilemmas such as discontinuing existing products, starting new product development, lowering prices compared to competitors, or adopting new marketing strategies. Economists tend to use game theory to understand the behaviour of oligopolistic businesses. This helps predict the possible consequences of a company engaging in certain actions such as price fixing or collusion.
Q12) What is Game theory an its limitations? (7)
A12)
Game theory is a theoretical framework for imagining social situations between competing players. In some respects, game theory is the best decision of an independent competing actor in the science of strategy, or at least in a strategic setting. Let's look at some examples.
The major pioneers of game theory were the 1940s mathematician John von Neumann and the economist Oskar Morgenstern. Mathematician John Nash is considered by many to provide the first significant extension of the work of von Neumann and Morgenstern!
The biggest problem with game theory, like most other economic models, is that it relies on the assumption that people are selfish and rational actors who maximize utility. We are social beings who often cooperate at our own expense and consider the welfare of others! Game theory cannot explain the fact that depending on the social situation and who the player is, the situation may or may not be in Nash equilibrium.
Part-B
Q13) Suppose if our team is making a risk management program, and we identify three risks with probabilities of 20%, 30% and 50%. If the first two risks occur, will cost us 7000 rupees and Rs. 8000, however the third will give us Rs. 9000.
Now determine the EMV. (7)
A13)
We will find EMV one by one-
Here we have,
For first event-
The probability of risk is 20%
And impact of risk is Rs. (-7000)
As we know that-
EMV = probability
EMV = 0.2
The EMV of the risk event is Rs. -1400.
For second event-
The probability of risk is 30%
And impact of risk is Rs. (-8000)
As we know that-
EMV = probability
EMV = 0.3
The EMV of the risk event is Rs. -2400.
For third event-
The probability of risk is 50%
And impact of risk is Rs. (9000)
As we know that-
EMV = probability
EMV = 0.5
The EMV of the risk event is Rs. 4500.
Now we will calculate EMV for all three events-
EMV for all three events = EMV of the first event + EMV of the second event + EMV of the third event
Hence the EMV is 700 for three events.
Q14) Determine which of the following two-person zero-sum games are strictly determinable and fair. Give optimum strategies for each player in the case of strictly determinable games (8)
A14)
(a)
(b)
The payoff matrix for player A is
Player A | Player B | Row minima | |
B1 | B2 | ||
A1 | 5+ | 0* | 0 |
A2 | 0* | 2+ | 0 |
Column maxima | 5 | 2 |
|
The payoffs marked with [*] in each row reflect the minimum payoff and the payoffs marked with [+] in each column of the payoff matrix represent the full payoff. (maximinim) is the largest portion of the minimum lines.
Value) and the smallest Column Maximum part represents (minimax value).
Thus obviously, we have =0 and 2.
Since , the game is not strictly determinable.
Issue of the Game
A12. The game is worked out using the minimax method. In each row, find the smallest value and select the largest value from these values. Next, in each column, find the largest value and pick the smallest of these numbers. The following table shows the procedure.
Minimax Procedure
If Maximum value in row is equal to the minimum value in column, then saddle point exists.
Max Min = Min Max
1 = 1
Therefore, there is a saddle point.
The strategies are,
Player A plays Strategy A1, (A A1).
Player B plays Strategy B1, (B B1).
Value of game = 1.
Q15) Explain Two -person zero sum game payoff matrix.(7)
A15)
Determine which of the following two-person zero-sum games are strictly determinable and fair. Give optimum strategies for each player in the case of strictly determinable games:
(a)
(b)
The payoff matrix for player A is
Player A | Player B | Row minima | |
B1 | B2 | ||
A1 | 5+ | 0* | 0 |
A2 | 0* | 2+ | 0 |
Column maxima | 5 | 2 |
|
The payoffs marked with [*] in each row reflect the minimum payoff and the payoffs marked with [+] in each column of the payoff matrix represent the full payoff. (maximinim) is the largest portion of the minimum lines.
Value) and the smallest Column Maximum part represents (minimax value).
Thus obviously, we have =0 and 2.
Since , the game is not strictly determinable.
Q16) Explain the Mixed strategies of Games without saddle point. (8)
A16)
For any given pay off matrix without saddle point the optimum mixed strategies are shown in Table
Mixed Strategies
Let p1 and p2 be the probability for Player A.
Let q1 and q2 be the probability for Player B.
Let the optimal strategy be SA for player A and SB for player B.
Then the optimal strategies are given in the following tables.
Optimum Strategies
p1and p2 are determined by using the formulae,
p1 =
a22-a21
(a11+a22)-(a12+a21
And p2= 1-p1
q1=
a22-a21
(a11+a22)-(a12+a21
and q2= 1-q1
the value of the game w.r.t. Player A is given by,
Value of the game, v =
a11 a22– a12a21
(a11+a22)-(a12+a21
Example: Solve the pay-off given table matrix and determine the optimal strategies and the value of game.
Game Problem
Solution: Let the optimal strategies of SA and SB is as shown in tables.
Optimal Strategies
The given pay-off matrix is shown below in Table.
Pay-off Matrix or Maximin Procedure
Therefore, there is no saddle point and hence it has a mixed strategy. Applying the probability formula,
p1 =
a22-a21
(a11+a22)-(a12+a21
=
4-3
(5+4)-(2+3)
=
1
9-5
=
1
4
And p2= 1-p1
= 1-1/4= 3/4
q1=
a22-a21
(a11+a22)-(a12+a21
4-2
(5+4)-(2+3)
=
2
9-5
=
1
2
And q2= 1-q1
Value of the game, v =
a11 a22– a12a21
(a11+a22)-(a12+a21
=14/4
The optimum mixed strategies are shown in table below.
Optimum Mixed Strategies
Q17) Write note on Two -person zero sum game payoff matrix. (5)
A17)
Determine which of the following two-person zero-sum games are strictly determinable and fair. Give optimum strategies for each player in the case of strictly determinable games:
(a)
(b)
The payoff matrix for player A is
Player A | Player B | Row minima | |
B1 | B2 | ||
A1 | 5+ | 0* | 0 |
A2 | 0* | 2+ | 0 |
Column maxima | 5 | 2 |
|
The payoffs marked with [*] in each row reflect the minimum payoff and the payoffs marked with [+] in each column of the payoff matrix represent the full payoff. (maximinim) is the largest portion of the minimum lines.
Value) and the smallest Column Maximum part represents (minimax value).
Thus obviously, we have =0 and 2.
Since , the game is not strictly determinable.