Microeconomics Semester 2

Question 1

What is a consumers consumption bundle?

Answer 1

This is the quantity of the two different goods that a consumer will choose.

A consumers affordable consumption bundle describes the bundle of goods that does costs no more than m, the consumers income/budget.

Question 2

What is required to understand a consumer demand for goods?

Answer 2

1) The goods (a description of all feasible choices
2) A description of preferences (how the consumer views two particular goods)
3) A description of economic circumstances (the prices)

Question 3

What would we do if there are more than two goods in the consumption bundle?

Answer 3

Although we will only have to deal with two goods, if we did have more than this then we can let the price of the second good be equal to 1. Therefore, when you get the budget constraint expression, it will be made up of demand for good 1, and then demand for all other goods.

In this case we call good 2 the composite good, which is also known as a numeraire good.

Question 4

How do we graph budget constraints?

Answer 4

This is done by getting the point where the consumption bundle equals the budget (known as the budget line). Then re-arrange to get good 2 on the y-axis, and plot. Using this re-arranged formula, we can analyse the impact of changes in prices, as well as changes in the budget. E.g an increase in income will cause a parallel shift of the budget line.

The slope of the budget line is the rate at which we are willing to substitute good 1 for good 2, or in other words, the opportunity cost of consuming good 1.

Question 5

What is the benefit of having a numeriare price?

Answer 5

When we do this, there will be one less price to worry about, which can make analysis of the budget and bundles easier.

Question 6

What external factors could impact a budget line in real life economics?

Answer 6

-Rationing (if there is a limit to the quantity available of one good, the budget line will become vertical (or horizontal) after a specific amount in the bundle.
-Taxes and subsidies will impact the slope of the budget line.
-Taxes, subsidies and rationing can also be combined, such as having a tax applied after a specific quantity of a good has been purchased.

Question 7

What is significant about optional choice with perfectly balanced inflation?

Answer 7

When all prices and budgets are raised at the same rate, there will be no change in anybodies optimal choice, and the budget set won’t change, everything has been multiplied by the same amount.

Question 8

What is the endowment bundle?

Answer 8

This is the quantity of goods than an individual has before they enter the market.

When there is an endowment bundle, the income (m) that we had previously can be replaced by this bundle, because the consumer can always ‘afford’ their bundle or less, but cannot leave the market with excess of what their endowment was worth.

Question 9

What is important to consider graphically when there is an endowment bundle in the budget line?

Answer 9

Whenever there is a change in the conditions of the budget prices, the budget line must still travel through the point where the endowment lies, this is because the maximum the consumer can obtain from trade must equal their original endowment,

Question 10

What complications come with budget constraints overtime?

Answer 10

-The introduction of time allows for the possible of prices to change due to inflation.
-To make things easier, we will assume borrowers and savers will have equal interest rates.

Question 11

What is the difference between a discount factor and discount rate?

Answer 11

The discount rate is just r (the interest rate), but the discount factor is (1/1+r). With each time period, the discount factor is to the power of as many periods as there have been, so this shows that the further into the future consumption occurs, the less value it holds.

Question 12

What does pi and rho symbolise in the imtertemporal budget constraint?

Answer 12

-Pi symbolises Increase in prices over a period (initially period 1).
-Rho is interpreted as the real interest rate, which is the interest rate taking inflation into account
-So, with inflation the new budget constraint will be: c1 = (1+ rho)(m0 - c0) + m1.
-However, if inflation is zero, then the real interest rate is equal to the nominal interest rate.
Look at lecture 1 slides to see this graphically

Question 13

What is a real life example of budget constraints?

Answer 13

The consumption-leisure budget constraint:
We can make a budget as follows:
pC = S + wL with time constraints L + R = T. p = price of consumption (C), S is savings and w is wage of labour (L). R is then leisure and T is total time.

Before entering the labour market, L will be zero, so T = R, and from this we can derive an endowment bundle.

Through re-arranging, we then end up with C = (pC’ + wR’)/p - w/p

Question 14

What is a consumption bundle?

Answer 14

This is a complete list of the goods and services that are involved in the choice problem we are investigating. The word “complete” deserves emphasis: when you analyze a consumer’s choice problem, make sure that you include all of the appropriate goods in the definition of the consumption bundle

Question 15

What are the 3 types of preferences we need to know between two bundles?

Answer 15

-You can strictly prefer another bundle (>), this means they would choose one bundle over another, given the opportunity.
-You can weakly prefer another bundle (<~)
-you can be indifferent between two bundles (~), if you would be just as satisfied with either bundle.

-When we make assumptions about preferences, use weakly prefer, so we are as general as possible with our assumptions.

Question 16

What are the assumptions we make about preferences?

Answer 16

-Comleteness
-Reflexivity
-Transivity
-Convexity

Question 17

What does completeness mean in preferences?

Answer 17

We assume that any two bundles can be compared. A preference will always be either indifferent with another bundle, or weakly preferred.

Question 18

What is reflexivity?

Answer 18

This is when we assume that a bundle is at least as good as itself.

Question 19

What is transivity in preferences?

Answer 19

In a set of bundles, there has always got to be one bundle which is the best choice, therefore this means we must always be able to rank bundles based on the satisfaction they provides.
If a consumer prefers bundle X to Y and Y to Z. They can’t then prefer bundle Z to X, as this would mean there’s no best option.

Question 20

What does an indifference curve show?

Answer 20

This shows all the consumption bundles that a consumer is indifferent between. All bundles on and above the curve are weakly preferred.

It is essentially for this reason indifference curves cannot cross each other, or there would be a contradiction of preferences.

Question 21

What will I difference curves look like if two goods are perfect substitutes?

Answer 21

This will mean consumers are willing to substitute one good for another at a constant rate, this may not always be a 1:1 ratio, but that is the simplest model.

The indifference curves will be linear and downwards sloping, with a constant slope as they have a constant MRS.

Question 22

What will I difference curves look like for perfect complements?

Answer 22

These are goods that will always be consumed in fixed proportions. This doesn’t necessarily have to be in a 1:1 ratio, however. MRS will be zero of infinity.

Their indifference curves will be L-shaped, as more of one good is pointless without the necessary ratio also of the other good. The utility will be equal to the minimum of the bundle.

Question 23

What do indifference curves look like for bad goods?

Answer 23

This is a commodity the consumer doesn’t like. In this case, the indifference curve would be upwards sloping when there is one bad good, and one ‘good’ good.

If there is a neutral instead of a bad good, the indifference curve will be vertical or horizontal.

Question 24

What happens when we consider satiation in an indifference curve?

Answer 24

Sometime if there is a overall best bundle for the consumers, and the closer they are to this in terms of their own preference, the better of they assume themselves to be.
This occurs when too much of a good makes it become a “bad’ and there will be circular indifference curve around the bliss/satiation point.

Question 25

What is a discrete good?

Answer 25

This is a good which only comes in discrete (whole) units, they will have kinked indifference curves for each whole unit consumed.

Question 26

What do we assume with “well behaved indifference curves’?

Answer 26

-More is better (talking about goods, not bads). This is called ***monotnicity***, as long as both bundles have at least as much of one good, then the bundle with more of another good will be preferred. -Average are preferred to extremes, the weighted average of two bundles on the same indifference curve will be at least as good or strictly preferred to the two more extremes. This will apply for any weighting between 0 and 1.

Question 27

What does monotonicity imply about the shape of indifference curves?

Answer 27

It implies that they would have a negative slope, as moving up will be to a better position, and down to a worse position, if one good remains equal, so moving to an indifferent position will mean moving up and left or down and right.

Question 28

What does the assumption averages are preferred to extremes mean geometrically? What is strict convexity?

Answer 28

It means the set of bundles weakly preferred to the original bundle will be a convex set. We want to assume well-behaved goods are convex because for the most part, these goods will be consumed together. Strict convexity means the weighted average is strictly preferred to two extremes. A perfect substitute would not be strictly convex.

Question 29

What is the marginal rate of substitution?

Answer 29

This is the rate at which the consumer is just willing to substitute one good for the other. The MRS is equal to the negative of the gradient of the indifference curve. Therefore we consider MRS to be positive. This isn’t the same as what they have to pay, as this related to prices, not preferences.

Question 30

What is the diminishing marginal rate of substitution?

Answer 30

The amount of good 2 a consumer is willing to give up for more of good 1 will reduce as the quantity of good 1 consumed increases, as we now already have more of that good. If not strictly convex, this assumption may not hold.

Question 31

What is utility?

Answer 31

Utility is thought of as the only way by classical economists to describe preferences.

Question 32

What is ordinal utility?

Answer 32

The only property of a utility assignment that is important is how it orders the bundles of goods. The magnitude of the utility function is only important insofar as it ranks the different consumption bundles; the size of the utility difference between any two consumption bundles doesn’t matter, and is arbitrary.

Question 33

What is monotonic transformation?

Answer 33

Since only the ranking of the bundles matters, there can be no unique way to assign utilities to bundles of goods. If we can find one way to assign utility numbers to bundles of goods, we can find an infinite number of ways to do it. If U(x1, x2) represents a way to assign utility numbers to the bundles , then multiplying by 2 (or any other positive number) is just as good a way to assign utilities We typically represent these transformations by a function. Graphically, these transformations is just relabelling indifference curves.

Question 34

What is a budget share?

Answer 34

Expenditure/income. The cobb Douglas utility function will represent a budget share if the two powers of the two goods add up to 1.

Question 35

What is a quasi-linear utility?

Answer 35

This is where the increase in utility will be linear for one good, and non-linear for the other good. When this is the case, each indifference curve will be a vertical translate of the rest of the indifference curves for the quasi linear utility function.

Question 36

What is the optimal choice for a consumer?

Answer 36

The optimal choice for a consumer will occur when the consumer reaches the highest possible indifference curve they can, based on their budget line.

Question 37

Can optimum choice occur where all consumption goes towards one good in the bundle?

Answer 37

Yes, in some cases (such as substitute goods), there will be a boundary optimum, rather than an interior optimum solution. When this is the case, there will not necessarily be the tangent of the two lines being equal.

Question 38

What is needed to ensure that a optimal choice is sufficient?

Answer 38

Having the tangent of the indifference curve equal to the budget constraint will be necessary when there is an interior solution, but that by itself won’t be sufficient. It will also be necessary to obtain the second order condition of the indifference curve, as doing so will allow to ensure the S.O.C is negative, and hence we have definitely found a maximum point where the indifference curve is convex, not concave.

Question 39

What is the demand function?

Answer 39

The demand function is the function that relates the optimal choice (the quantities demanded) to the different values of price and incomes. We write demand functions as depending on both prices and income.

Question 40

How do we find the optimal choice bundle when dealing with perfect substitutes?

Answer 40

1) If p2 > p1, then the indifference curve will be steeper than the budget line, and hence consumers will spend all their money on good 1. 2) If the opposite, then consumers will spend all their money on good 2. 3) If p2 = p1, then there will be a whole range of optimal choices, and we cannot confirm which one will be taken. Look at lecture notes for how to do this mathematically.

Question 41

How do we find the optimal choice of perfect compliments?

Answer 41

Optimal choice must always lie on the diagonal, where the consumer is purchasing an equal amount of both goods, regardless of what the prices are. See lecture slides for how to do this mathematically.

Question 42

What are some other examples of unusual optimal choices?

Answer 42

-With neutrals and bads, consumers will spend all of their money of the good they like, and won’t want to spend any on the neutral or bad good. -With discrete goods (which can only be purchased in integer units), the optimal choice depends on the price of discrete good 1, where good 2 represents everything else. We can use diagram analysis to analyse this. -In the rare case of a concave preference, consumers will spend everything on either one good or another one.

Question 44

How does optimal choice work with the cobb-Douglas example?

Answer 44

Cobb Douglas preferences have a convenient property, which is that their quantities demanded of both goods will me make up of a combination of income/price of that good. -This is done by rewriting the budget constraint with x2 being the subject, and then substituting this into the utility function to derive it in terms of good 1, and hence then solve for the quantity of good 1 demanded, which can be used to then get the quantity of good two. See slides for how to do this, with a method which can be memorised, as you may still be asked to carry it out in the exam.

Question 45

How do we calculate MRS?

Answer 45

MRS is just a ratio of the marginal utility with respect to good 1, over the marginal utility with respect to good 2.

Question 47

What is important to consider when we talk about normal and inferior goods?

Answer 47

-Just because for one person on a specific income a good would be considered an inferior good, this doesn’t mean that everyone would consider it to be an inferior good, someone on a lower income would consider it a normal good.

Question 48

What is an income offer curve?

Answer 48

An income offer curve is a line which will connect all the different optimal choices as income, m, varies.

Question 49

What is an Engel curve?

Answer 49

An Engel curve will show how the quantity of a good purchased (x axis) will vary depending on income (y axis). The gradient of the slope will be equal to the price of the good. Usually, the Engel curve will be a linear line.

Question 50

What are homothetic preferences?

Answer 50

A homothetic preference is a preference where if you prefer the original bundle to another bundle, then when both bundles quantities are changed then you will still prefer the original bundle to the new bundle, despite the change in income impacting the quantity of the goods you can consume. If a consumer has homothetic preferences, the the Engel curve will always be a straight line.

Question 51

What will the Engel curve look like for goods with a cobb-Douglas utility function?

Answer 51

The Engel curve will be linear at a slope of p1(a+b)/a (you can work this out using algebra).

Question 52

What will the Engel curve look like for quasi linear preferences?

Answer 52

It will be curving upwards to a point, and then after that it will just be a vertical straight line. This is because the good will be consumers more as income rises, up to a point where it will then no longer be beneficial to consume more of the good, e,g once you have enough income to brush your teeth twice a day, you don’t need to buy more toothpaste after that.

Question 53

What is a price offer curve?

Answer 53

This is a curve which shows how the quantity of two goods will change as prices change rather than income. -For an ordinary good, is x1 (x-axis) falls or rises in price, then the price offer curve will be upwards sloping. -For a griffin good, if the price of the good falls or rises in price, the change in in quantity demanded will reflect the change in price, so the price offer curve will be downwards sloping.

Question 54

What will the quantity demanded of x1 in bundle (x1, x2) look like if the goods are perfect substitutes?

Answer 54

If p1>p2, then zero of x1 will be consumed. If P1 = P2, then any amount of the good p1 could be consumed, and as p1

Question 55

What happens when the price of a good within a bundle changes?

Answer 55

There will be 2 different effects, the rate at which you exchange one good for another, and the total purchasing power of your income will be altered. This is called the substitution and income effect respectively. The combined effect of the two is known as the total effect.

Question 56

How do we find the individual impacts of the substitution and income effect?

Answer 56

First, we have to let the relative prices (good 1 price in relation to good 2 price), and then adjust the income so that purchasing power is held constant. Secondly, we will let the purchasing power adjust and hold the relative prices constant. To see how to do this mathematically, refer to the lecture slides.

Question 57

What is the income effect in more detail?

Answer 57

The income effect is the change in demand for a good as we move from the new purchasing power parity back to the old purchasing power parity, while keeping the relative price at the new relative price. Change in good due to income effect = x1(p1’, m) - x1(p1’, m’). If the good is an inferior good, a decrease in relative income will lead to a increase in demand, but if a normal good, then a decrease in income will lead to a decrease in demand

Question 58

What fact can we always associate with the substitution effect?

Answer 58

Despite the fact that the income effect can either be positive or negative, the substitution effect will always move opposite to price movement. Therefore, we say the substitution effect is negative, because the change in demand for a good will always be the opposite of the price change.

Question 59

When will the income and substitution effect work in the same direction?

Answer 59

This will occur when we have a normal good. If the price of good 1 was to decrease, we would see the demand for good 1 increase due to the substitution effect as good 1 have become relatively cheaper. And the relatives purchasing power has also increased, so the new incomes will also cause an increase in demand for good 1.

Question 60

What is the difference between an inferior and giffen good?

Answer 60

A giffen good must be an inferior good, but an inferior good doesn’t have to be a giffen good. For a giffen good to occur, not only does the income effect have to be the ‘wrong’ sign, but it also has to outweigh the substitution effect acting in the opposite direction. Therefore, to be a giffen good, the good must be very inferior.

Question 61

What is the law of demand?

Answer 61

The law of demand is that if demand for a good increases when income increases, then the demand for that good must also decrease when it’s price increases.

Question 62

What is the substitution and income effect for some different examples?

Answer 62

-For perfect complements, the substitution effect is zero, and income effect = total effect. -For perfect substitutes, the income effect is zero, and the substitution effect = total effect -For quasi-linear preferences, the substitution effect also equals the total effect, as a shift in income causes no change in the demand for good 1.

Question 63

What is the marshallian demand?

Answer 63

This where we attempt to maximise our utility given a budget constraint.

Question 64

What is hicksian demand? (Also known as compensated demand functions).

Answer 64

When doing hicksian demand, we use the expenditure minimisation problem, rather than the utility maximisation problem. This means that our equation for the optimal x1 and x2 bundle will include utility, where as in the marshallian demand, we would only of had income and prices within the optimal bundle.

Question 65

What is the compensated bundle in economics?

Answer 65

The compensates bundle is just the bundle of two goods which will equal the utility of the bundle of goods before the price change, but accounting for the change in relative prices. This will allow us to calculate the income and substitution effects.

Question 66

What is the inverse demand function?

Answer 66

The inverse demand function is the demand function viewing price as a function of quantity. This means that for each level of demand for good 1, the inverse demand function measures what the price would have to be to enable that level of demand. If the price of good 2 is equal to 1, then the inverse demand function of good 1 is also inadvertently the measuring the absolute value of MRS. It shows how much of good 2 you would give up to gain a certain amount of good 1.

Question 67

What is the slutsky equation?

Answer 67

The slutsky equations allows us to work out the total change in demand (substitution effect + income effect). In order to use the slutsky equation, we need to use both the marshallian and hicksian demand problems: -The total change in demand will come from the partial derivate of the marshallian demand for x1 w.r.t p1. -The substitution effect will come from the partial derivative of the hicksian demand for x1 w.r.t p1. -The income effect will come from the partial derivative of the marshallian demand curve for x1 w.r.t m, multiplied by marshallian demand for x1. This is essentially composed of two pieces, how demand changes and income changes, multiplied by original demand.

Question 68

When is the equivalence between the marshallian and hicksian demand?

Answer 68

The optimal hicksian demand for good 1 = marshallian demand for good 1 as long as minimum expenditure = income from the budget constraint, and maximum utility = target utility in expenditure minimisation problems.

Question 69

What is the difference between hicksian and slutsky compensation?

Answer 69

Hicksian compensation is compensation to achieve the original indifference curve at new prices while keeping utility constant, but slutsky aims to achieve an original bundle at new prices, keeping purchasing power constant.

Question 70

How does the slutsky equation tell us if a good is a normal, inferior or giffen good?

Answer 70

If a giffen good, equation > 0, if an inferior good equation could be positive or negative (depending on the relative size of the income effect) and if a normal good the slutsky equation will be negative.

Question 72

What are the 3 money measures of utility change that we can use for analysis?

Answer 72

1) Consumer surplus 2) Compensation Variation 3) Equivalent variation We use these because it can be very difficult to aggregate utilities of all the individuals in an economy, but this will be far easier to do in monetary terms.

Question 73

What is consumer surplus?

Answer 73

Consumer surplus is the amount of money that a consumer would be willing to pay over and above what he/she will actually have to pay. When there is a price increase, the consumer surplus will fall because people are now willing to pay a smaller margin above the actual price, and there will also be completely lost consumers who are no longer willing to pay, as the new price exceeds the price they were willing to pay for the good.

Question 74

What is gross consumer surplus?

Answer 74

This is the consumer surplus as well as the amount paid.

Question 75

What is compensation variation?

Answer 75

This is how much money needs to be given to an individual to make them as well off as they were (in terms of utility and indifference curves) before the tax was introduced. To do this, we need to make good 2 the numeraire good (set its price equal to 1, and then the compensation variation is the difference between the new and hypothetical (compensating) budget lines on the y-axis. Algebraically, this is u1 + CV = u0.

Question 76

What is equivalent variation?

Answer 76

Equivalent variation is the amount of money that needs to be taken away in order to make the individual ‘as well off’ -in terms of utility- as when the tax was imposed. This will mean that we give the individual less income so that they obtain the same utility of the post-tax position. As with compensation variation, ensure that good 2 is the numeraire good. Algebraically, this is u0 - EV = u1.

Question 77

How do we graphically depict money measures of utility change using demand curve analysis?

Answer 77

-The change in consumer surplus will be represented by the areas to the left of the marshallian demand curve between the two relevant prices. -The compensation variation (CV) is equal to the area on the left of the Hicksian demand curve x(P0, P1, U0) between P0 and P1. -The equivalent variation (EV) is equal to the area to the left of the Hicksian demand curve x(P0, P1, U1) between P0 and P1.

Question 78

What is special about the relationship between consumer surplus, EV and CV?

Answer 78

The consumer surplus change will always lie in between the measures of the EV and the CV. You will get different values for the change in utility depending on which measure you use. Usually in analysis, the CS money measure will be used, because this doesn’t rely on the use of any hypothetical budget constraints.

Question 79

When is the one time EV = CV?

Answer 79

The one time that the equivalent value will equal the compensating value is in the case of quasi linear preferences. This is because X is only a function of its own price in quasi linear preferences, so the income effect will be zero. Here change in consumer surplus = v(X0) - X0(P0) - (V(X1) - X1(P1))

Question 80

What are the elements of the decision-making problem under uncertainty?

Answer 80

Each individual has a set of actions available (e.g taking an umbrella to work) and there is a range of states of nature (e.g rain or no rain). -Pi is the probability of the likelihood of each state of nature (will be between 0 and 1). -When combined, these will produce a set of outcomes which are determined by a consequence function c(x, s), which show all the consequences as a result of all possible combinations of actions and states. -The utility function c(v) captures the individuals preferences for each different possible consequence.

Question 81

What is expected utility?

Answer 81

Expected utility is the summation of of the utilities of consumption of all the different consequences, weighted by the probability of each state of nature.

Question 82

What is the independence assumption in uncertainty?

Answer 82

Events are mutually exclusive, this means the utility obtained from each consequence is independent of the utility obtained from all the other consequences. This can also be expressed by saying the MRS between any two pairs of outcomes is independent of the quantity of a third outcome.

Question 83

What is specific about expected utility functions?

Answer 83

They rely on being able to assign cardinal utilities to consequences. V(c) is a cardinal measure, meaning the number matters and the difference between the levels of utility have meaning. This is different from choice under certainty as that was ordinal, but in this case the only positive monotonic transformation will be a linear transformation, known as a Positive Affine Transformation.

Question 84

How do we interpret attitudes towards risk?

Answer 84

They are captured by the assumptions we make about how marginal utility changes with consumption. As assume monotonicity, so more consumption will always be better and give more consumption (f.o.c will be positive).

Question 85

What is a fair bet?

Answer 85

A fair bet is where the mathematical expectation of the consequences/outcomes is equal to the certain outcome (what you would have if you didn’t enter the bet).

Question 86

What is a risk averse person?

Answer 86

Their utility function would be concave, and the certain utility will be greater than the expected utility as a result of the gamble. A risk averse person will always reject a fair bet, but this doesn’t mean they would always reject an unfair bet. The opposite of this would be risk loving, and they will have a convex utility function. If you have risk neutrality, then you will be indifferent between taking or not taking a fair bet, and the utility function will be linear.

Question 88

What is fair insurance?

Answer 88

This is when the insurance company breaks even (so their profits are 0).

Question 89

What two indications will show us an individual wants to fully insure?

Answer 89

If the optimal contingent consumption bundle is equal for both options, or if we see that the insurance pay-out in the event of the accident is equal to the cost/loss which would be faced by the individual in the event of the accident.

Question 90

What is the certainty equivalent?

Answer 90

The certainty equivalent is the value which an individual would have as their certain outcome, for which they would be indifferent in the decision of taking, or not taking on the bet/gamble.

Question 92

What is game theory?

Answer 92

Game theory is a theory about how the well-being of different agents is interdependent. Other people’s actions will affects their own, and their actions will affect other peoples, known as strategic interaction.

Question 93

Who are the players in game theory?

Answer 93

In the game, a group of individuals must strategically interact. In any game, there will be N number of players. We will, for simplicity, in most situations analyse a game with just two players, so n = 2.

Question 94

What are the strategies in game theory? (NOTE: A strategy and action are the same thing)

Answer 94

These are the choices available to the players. Some games will have purely simultaneous moves made only once, where each player’s strategy is the action taken on that single occasion. Some games will have sequential moves, where a player who moves later in the game can respond to what the other players have done (or themselves at earlier points). For this reason, each player in the game must have a compete plan of action. -Each players set of strategies can be finite (e,g two strategies) or an interval (of the real line).

Question 95

What are the outcomes/payoffs of the game?

Answer 95

Each player will have a preference over all the different outcomes. We assume each player is able to assign a number to each logically conceivable outcome of the game, corresponding to each logically possible combination of choices made made by all the players. This assigned number to each outcome will be the players payoff.

Question 96

LOOK AT GAME THEORY SLIDES FOR SPECIFIC NOTATION ON OUTCOMES ETC

Answer 96

.

Question 97

What is the expected payoff?

Answer 97

This is the average of the payoffs associated with each potential outcome, weighted by its probability. If an outcome involves money, a player should be indifferent between random prospects (like one selected by a random variable), and non-random outcomes. This then otherwise creates potential difficulty as one would assume an individual would be averse to risk, preferring a sure $100 over a gamble which only gives $100 on average.

Question 98

Why do we need to assume rationality in game theory?

Answer 98

Each players aim is to achieve as high a payoff for themselves as possible. While in reality this depends on how good players are at calculating the strategy in their own best interest, traditional game theory assumes players are perfect calculators, and will be able to follow their own best strategy.

Question 99

What is the difference between decision theory and game theory?

Answer 99

Decision theory analyses a rational individual decision maker who tries to make the best decision based on their understanding of the world, you choose your actions in a calculated way to do the best according to your own criteria. In game theory, there is another dimension, of the fact that you also interactive with equally rational decision makers.

Question 100

What is the common knowledge in game theory?

Answer 100

-Every player knows the rules of a game, but this doesn’t mean they are equally well informed or influential -Everyone knows that everyone knows that the rules are available to all, on a infinite level.

Question 101

What is the equilibrium in game theory?

Answer 101

Each player is using the strategy that is, the best response to the strategies of the other players. -Some games will have a unique equilibrium, some will have many, and some will have none.

Question 102

What occurs in a strategic/normal form game theory?

Answer 102

All players move simultaneously, and only once 1) There is a list of players in the game 2) The set of strategies or actions available to each player 3) The payoffs associated with any strategy combination Formally, a normal form game consists of the set of players, sets of strategies or actions, one for each player and payoff functions.

Question 103

What is a strictly dominated strategy?

Answer 103

A strictly dominated strategy occurs when no matter what the other player selects, the strategy will never be utilised. A rational player will never pick a strictly dominated strategy.

Question 104

What happens if we have a full iterated elimination of dominated strategies?

Answer 104

We will have a unique prediction, if we are able to reach a unique strategy equilibrium following iterated elimination, is it known as a dominance solvable game.

Question 105

What is the difference between weakly and strongly dominant?

Answer 105

Weakly dominant means despite always choosing one strategy, for certain strategies of the other players, you may at times have a strategy which you rate just as much as the one you have selected. If this is never an option, you will have a strongly dominant option.

Question 106

What is a Nash Equilibrium?

Answer 106

A Nash Equilibrium is when each player chooses their best reply against the best reply of their opponent. Finding a Nash equilibrium doesn’t have to involve an iterative elimination process if a 3x3 payoff matrix. One example of a Nash equilibrium would be the prisoners dilemma.

Question 107

What is a node in game theory?

Answer 107

This is a decision which is made along the tree of the extensive form game in game theory. The final node is called the terminal node, which has no more branches emerging from it.

Question 108

What must be satisfied for a tree to represent a game theory game?

Answer 108

1) There must be a single start point 2) There must be no cycles, it should not be possible for for branches of a tree to double back and create a cycle. 3) There must be one way to proceed, there must not be two or more nodes which could lead to a singular branch.

Question 109

What are the predecessors of a node?

Answer 109

This are the nodes for which you can go through to reach another node.

Question 110

What is a game of perfect information?

Answer 110

This is an extensive form game with the property that there is exactly one node in every information set.

Question 111

Will all Nash equilibrium be reasonable in a sequential move game?

Answer 111

No, although a sequential move game may have many Nash Equilibrium, they will only actually be reasonable outcomes if this is an outcome which would occur if we can see a rational player would actually select this (when using backwards induction).