Micro Summary
• Positive analysis
o Analysis describing relationships of cause and effect
o About what ‘is’
o EX
▪ For non-Giffen goods an increase in price will decrease demand
▪ A firm that sets MR=MC is maximizing its profit
• Normative analysis
o Analysis examining questions of what ought to be
o About ‘ought’, it always contains a ‘should’
o 2 kinds
▪ Normative analysis without value judgements: conditional-normative analysis
• If a firm strives for maximizing profits, then it should set MR equal to MC
o Contains an ‘if …, then one should’ structure
▪ Normative analysis including value judgements
• Firms should not strive for maximizing profits, but for maximizing social welfare
• Method of decreasing abstractions
o We start in a simple, rather abstract way. Then, step by step, we make the analysis less abstract by introducing more
realistic assumptions.
• Relative risk aversion
o Constant
▪ If RRA is not dependent on the level of wealth
o Increasing
▪ If RRA is increasing if wealth is increasing
o Decreasing
▪ If RRA is decreasing if wealth is decreasing
• The measures of risk aversion are related to the curvature of the utility curve
1
,• Time consistent
o An individual is time consistent if she has the same preferences about future plans at different points in time, including the
current.
(1) Time consistent decision-makers, i.e. decision-makers who have the same preferences about future plans at different points in
time.
The behaviour of this type of decision-makers is described by the standard model. This corresponds to 𝛽̂ = β = 1 in the (β, δ) model.
Time consistent decision-makers do not have any self-control problem.
However, from experiments and evidence in the field we know that people do not behave as time consistent decision makers. In
practice the nearer the future is, the steeper the discounting, i.e. in practice β < 1. Phrased differently, people prove to have present-
biased preferences. Therefore, if we intend to explain the behaviour of decision-makers we better take into account that they are
not time consistent.
(2) Sophisticated decision-makers, i.e. decision-makers who (a) know that their intertemporal preferences are not time consistent,
and (b) have exact knowledge of their intertemporal preferences. This corresponds to 𝛽̂ = β < 1 in the (β, δ) model.
So, sophisticated decision-makers are fully aware of their self-control-problems.
(1) Fully naïve decision makers, i.e. decision-makers who have intertemporal preferences that are not time consistent, but who
erroneously think they have time-consistent preferences. This corresponds to 𝛽̂ = 1 > β in the (β, δ) model.
Naïve decision-makers do have self-control problems but they are not aware of them.
(2) Partially naïve decision-makers are in between sophisticated decision-makers and (fully) naïve decision-makers. This corresponds
to 1 > 𝛽̂ > β in the (β, δ) model.
Partially naïve decision-makers do have self-control problems but they are only partially aware of them.
o P. 319, the example in the second through fifth full paragraph:
(1) Ex ante (desired) one period in advance:
U0 = u0 + β δ u1 + β δ2 u2
which with u1 = b1 and u2 = b2 results in:
U0 = u0 + β δ b1 + β δ2 b2
where
U0 = overall utility at t = 0.
NB Implicitly in the example it is assumed that U0 is normalized at u0 = 0 and
that there are no other factors that influence the decision-maker’s utility in periods 1 and 2 than the consumption (or
investment) activity concerned.
If the decision-maker could set consumption (investment) one period in advance, at t = 0, she would consume (invest) at t = 1 if
β δ b1 + β δ2 b2 > 0
i.e. if
b1 + δ b2 > 0
Phrased differently, this is equivalent to the answer to the question whether the decision-maker wants to consume (invest) in
period 1 from an ex ante position (i.e., from the perspective of t=0).
(2) a. Actual consumption
The decision-maker would consume if U1 = u1 + β δ u2 = b1 + β δ b2 > 0
With β < 1, b1 > 0 and b2 < 0 (and δ > 0), the subtraction (β δ b2) is actually smaller than desired, i.e. future costs are
underestimated. Therefore, the actual condition is less restrictive than the ex-ante one. So, actual consumption will be larger
than desired consumption.
b. Actual investment
The decision-maker would invest if U1 = b1 + β δ b2 > 0
With β < 1, b1 < 0 and b2 > 0 (and δ > 0), the addition (β δ b2) is actually smaller than desired, i.e. future benefits are
underestimated. Therefore, the actual condition is more restrictive than the ex-ante one. So, actual investment will be smaller
than desired investment.
(3) a. Expected consumption
This concerns the question whether the decision-maker expects to consume in period 1 from an ex ante position (i.e., from
the perspective of t = 0).
The decision-maker expects to consume in the future if
U1 = b1 + 𝛽̂ δ b2 > 0 with 𝛽̂ > β, b1 > 0 and b2 < 0 (and δ > 0)
where βˆ is the decision-maker’s belief of β.
Compared to actual consumption, the decision-maker underestimates consumption.
b. Expected investment
This concerns the question whether the decision-maker expects to invest in period 1 from an ex ante position (i.e., from the
perspective of t = 0).
The decision-maker expects to invest in the future if
U1 = b1 + 𝛽̂ δ b2 > 0 with 𝛽̂ > β, b1 < 0 and b2 > 0 (and δ > 0).
Compared to actual investment, the decision-maker overestimates investment.
From this it follows:
(i) 1 – β = degree of time inconsistency
(ii) 1 – 𝛽̂ = degree of expected (anticipated) time inconsistency
(iii) 𝛽̂ – β = degree of incorrect belief of time inconsistency.
2
,Chapter 5
• Probability
o The likelihood that a given outcome will occur
• Objective probability
o Relies on the frequency with which certain events tend to occur
• Subjective probability
o The perception that an outcome will occur
• Expected value
o Probability weighted average of the payoffs associated with all possible outcomes
o E(X)=Pr1*X1 +Pr2*X2
• Payoff
o Value associated with a possible outcome
• The expected value measures the central tendency
o The payoff or value that we would expect on average
• Variability
o Extent to which possible outcomes of an uncertain event differ
• Deviation
o Difference between expected payoff and actual payoff
o Do not provide a measure of variability
• Standard deviation
o Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome
from their expected values
• In order to weigh which of the job choices is riskiest, an individual should look at the standard deviation
• The expected value is not a generally accepted measure of the riskiness of an investment
• The variance of an investment cannot be negative
• Expected income can be used as a direct measure of well-being if and only if individuals are risk neutral
• Expected utility
o Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur
• The difference between the utility of expected income and expected utility from income is that the expected utility from
income is calculated by summing the utilities of possible incomes, weighted by their probability of occurring, and the utility of
expected income is calculated by summing the possible incomes, weighted by their probability of occurring, and finding the
utility of that figure
• Risk averse
o Condition of preferring a certain income to a risky income with the same expected value
▪ Diminishing marginal utility of income
• Risk neutral
o Condition of being indifferent between a certain income and an uncertain income with the same expected value
• Risk loving
o Condition of preferring a risky outcome to a certain income with the same expected value
• Risk premium
o Maximum amount of money that a risk averse person will pay to avoid taking a risk
• The greater the variability of income, the more the person would be willing to pay to avoid the risky situation
• All indifference curves are upward sloping, because risk is undesirable, the greater the amount of risk, the greater the expected
income needed to make the individual equally well off.
• Reducing risk
o Diversification
o Insurance
o Obtain more information
• Law of large numbers
o Although single events may be random and largely unpredictable, the average outcome of many similar events can
be predicted
• Actuarial fairness
o When the insurance premium is equal to the expected payout.
• Value of information
o Difference between the expected value of a choice when there is complete information and the expected value
when information is incomplete
• The demand curve for a particular stock at any point in time is infinitely elastic
3
,• Behavioural economics
o Reference point
▪ Point from which an individual makes a consumption decision
o Endowment effect
▪ Tendency of individuals to value an item more when they own it than when they do not
o Loss aversion
▪ Tendency for individuals to prefer avoiding losses over acquiring gains
o Framing
▪ Tendency to rely on the context in which a choice is described when making a decision
o Anchoring
▪ Tendency to rely on one prior (suggested) piece of information when making a decision
▪ Refers to the impact that a suggested (perhaps unrelated) piece of information may have on your final
decision
o Law of small numbers
▪ Tendency to overstate the probability that a certain event will occur when faced
with relatively little information (plane crash, winning the lottery)
o Rule of thumb
▪ A common way to economize on the effort involved in making decisions is to
ignore seemingly unimportant pieces of information
• Shipping costs are ignored, when purchase is made online
• Prospect theory
o Assumes that people evaluate outcomes in terms of gains and losses with respect to a
reference point (instead of total states as in the expected utility theory)
Risk attitudes
Risk neutrality: 𝑬( 𝑼) = 𝑼[𝑬( 𝒀) ]
• a loss of $ 10,000 compared to a certain income of $ 20,000
has equal weight in utility terms as
• a gain of $ 10,000 compared to a certain income of $ 20,000
Example:
𝑬( 𝑼) = 0.5 𝑈( $ 30,000) + 0.5 𝑈( $ 10,000)
Risk averse person 𝑼[𝑬( 𝒀) ] = 𝑈( $ 20.000)
U(Y) P
Because 𝐸𝑏 𝑈 𝑗𝑜 𝑏 1 = 𝐸( 𝑈) 𝑗𝑜 2
UP = U[E(Y)]
Decision maker is indifferent between the job with the certain
UM = E(U)
income and the job with the uncertain income, given the same
M expected value. 25
Risk attitudes
Risk averse: 𝑬( 𝑼) < 𝑼[𝑬( 𝒀) ]
0 10,000 20,000 30,000 Y
• a loss of $ 10,000 compared to a certain income of $ 20,000
in utility terms outweighs
So in case of risk aversion: E(U) < U[E(Y)] 28 • a gain of $ 10,000 compared to a certain income of $ 20,000
Example:
Risk averse person 𝑬( 𝑼) = 0.5 𝑈( $ 30,000) + 0.5 𝑈( $ 10,000)
𝑼[𝑬( 𝒀) ] = 𝑈( $ 20.000)
U(Y) P
Because 𝐸𝑏 𝑈 𝑗𝑜 𝑏 1 > 𝐸( 𝑈) 𝑗𝑜 2
UP = U[E(Y)] Decision maker prefers the job with the certain income
over the job with the uncertain income, given the same
UM = E(U)
expected value.
M
Risk attitudes 26
Risk lover (risk seeker): 𝑬( 𝑼) > 𝑼[𝑬( 𝒀) ]
• a loss of $ 10,000 compared to a certain income of $ 20,000
in utility terms has less weight than
• a gain of $ 10,000 compared to a certain income of $ 20,000
Example:
𝑬( 𝑼) = 0.5 𝑈( $ 30,000) + 0.5 𝑈( $ 10,000)
0 10,000 16,000 20,000 30,000 Y 𝑼[𝑬( 𝒀) ] = 𝑈( $ 20.000)
20,000 - 16,000 = risk premium Because 𝐸 𝑈 𝑏 𝑗𝑜 1 𝑏< 𝐸( 𝑈) 𝑗𝑜 2
16,000 = certainty equivalent Decision maker prefers the job with the uncertain income
• Utility of expected value (the utility level of point M can also be achieved in case of a certain income 29 = over the job with the certain income, given the same
of $ 16.000) expected value.
U[E(Y)] 27
• Expected utility = E(U(Y))
• Expected utility theory Measures of risk aversion
o Individual preferences over risky outcomes satisfy specific axioms
▪ Completeness 1. Arrow-Pratt measure of absolute risk aversion (ARA)
▪ Transitivity
▪ Continuity 𝜕 2 𝑈( 𝑌)
𝑈 ′′𝑌 2
▪ Independence 𝐴 𝑌 = − ′
= − 𝜕𝑌
𝑈 𝑌 𝜕𝑈( 𝑌)
𝜕𝑌
2. Arrow-Pratt measure of relative risk aversion (RRA)
𝜕 2 𝑈( 𝑌)
𝑈 ′′𝑌 2
𝑅 𝑌 = 𝑌 ∗ 𝐴 𝑌 = −𝑌 = −𝑌 𝜕𝑌
𝑈 ′𝑌 𝜕𝑈( 𝑌)
𝜕𝑌 30
4
, • Inter temporal choice
o Humans suffer from a systematic tendency to underestimate future wants, have a systematic preference for present
income
• Budget constraint
o C1=I1+(1+r)(I0-C0) Inter-temporal choice
Present bias
• • Suppose the utility function of the individual is given
If a player at a later period wants to deviate from
by 𝑢( 𝑐0 , , 𝑐1 ) .
his original plan, his behavior is time-inconsistent.
• The maximization problem of the individual becomes
The inter-temporal budget constraint max( 𝑢( 𝑐0 , 𝑐1 ) )
Hyperbolic discounting (‘beta-delta function’)
𝑠. 𝑡. 𝑐0 + 𝑐1 /( 1 + 𝑟) = 𝐼0 + 𝐼1 /( 1 + 𝑟) A player who follows the
Inter-temporal budget constraint: hyperbolic discounting rule
• This leads to U0 = u 0 + β δ ut+1 + β δ2 ut+2 + β δ3 ut+3 ………
to evaluate his present-
c0 + c1/(1 + r) = I0 + I1/(1 + r)
value utility will always
∞
c1 u (c0 ) U0 = u0 + β ∑ δi u t+i
have an incentive to revise
c0 his plan of action at a later
c1 MRS (1 r ) i=1
u (c1 ) point in time: his behaviour
(1 + r)I0 + I1 slope = MRS is time-inconsistent
c1 0≤δ≤1
0 ≤ β ≤ 1 (discounts all of future compared to present consumption)
period 1 slope = -(1+r) 15:21 48
42
slope = –(1 + r) c0
I1
Self-awareness
I0 I0 + I1/(1 + r)
c0
Discounted-utility (DU) model A person with time-inconsistent preferences may or may
not be aware that her preferences will change over
period 0 Present Value of Utility: time.
Utility aggregated over (finitely) many periods:
Exponential versus hyperbolic 41
discounting: changing preferences 𝑈0 = 𝑢0 + 𝛿𝑢1 + 𝛿 2 𝑢2 + ⋯ + 𝛿 𝑡 𝑢𝑡 + ⋯
completely "naïve" completely
𝑇
over time? 𝑈0 = 𝑢0 + 𝛿 𝑖 𝑢𝑖
= believe that
future preferences
"sophisticated" =
correctly predict
𝑖= 1 will be identical to how preferences
current will change over
preferences. time.
Exponential discounting, with 0 ≤ 𝛿 ≤ 1 O'Donoghue and Rabin (2001) introduce a formal model of partial naiveté, in
which a person is aware that she will have future self-control problems
• Maximization leads to optimal per-period consumption. (𝛽 < 1) (but underestimates their magnitude 𝛽 > 𝛽 .
45
Larger, later reward always Preferences change over
preferred over smaller, sooner time
reward
15:21 52
Time-inconsistency
(DellaVigna: Psychology and Economics)
Self-awareness Self awareness and self-control Type of Self-control Aware?
behavior problem?
Compare: expected behavior versus actual behaviour
assuming inconsistent time preferences (‘beta-delta Time-consistent Time-inconsistent
function’) Time- No -
β=𝜷 β=𝜷 β≠𝜷 consistent
Hyperbolic discounting, actual utility Sophisticated Yes Yes, fully
∞
𝑈0 = 𝑢0 + 𝛽 𝛿𝑖 𝑢𝑡+ 𝑖 Partially naïve Yes Yes, partially
𝑖= 1 β=𝜷=1 β = 𝜷<1 1>𝜷>β>0 1=𝜷>β
Self-
Hyperbolic discounting, expected utility Time-consistent Sophisticated Partially naïve Fully naïve Fully naïve Yes No control a
No self-control Self-control Self-control Self-control common
problems problems problems problems problem?
∞
fully known partially known not known
15:21 56
𝑈0 = 𝑢0 + 𝛽 𝛿𝑖 𝑢 𝑡 + 𝑖 No overestimation No overestimation Some overestimation More overestimation
𝑖= 1
15:21 54
15:21 55
5
, • Two main differences between EUT and Prospect Theory
o Prospect Theory assumes that:
▪ People evaluate outcomes in terms of gains and losses
with respect to a reference point (instead of total states
as in Expected Utility Theory).
▪ The values of the gains and losses are weighted with
decision weights (instead of probabilities as in Expected
Utility Theory).
• The investment portfolio: RP = bRm + ( 1 – b ) Rf
o To determine how much money the investor should put in each
asset.
o B= fraction of her savings placed in the stock market
o (1-B)= the fraction used to purchase treasury bills.
o Rp= is a weighted average of the expected return on the two assets
o Note: the expected value of the sum of two variables is the sum of
the expected values.
• The expected return on a portfolio increases as the standard deviation of that return increases
• The investor’s choice problem:
o Rp=Rf+b(Rm-Rf)
𝜎
• 𝑏= 𝑝
𝜎𝑚
𝑅𝑚 −𝑅𝑓
• 𝑅𝑝 = 𝑅𝑓 + 𝜎𝑝 this is a budgetline because it describes the trade off between risk and the expected return,
𝜎𝑚
straight line. The slope is the ‘fraction’. Intercept is Rf.
• Kahneman found that
o The impact of incremental gains or losses on value diminishes as the gains or losses become larger
o People are loss averse, valuation of outcome is more sensitive to losses than gains.
o People tend to largely overestimate small probabilities
o People tend to moderately underestimate average and large probabilities.
Week 2+3
Chapter 12
• Until now mainly:
o Many sellers (competitive market) → price takers, setting q by equating P=MR=MC
o Only one seller (monopoly) → price setters, Q is such that MR=MC
▪ In both cases don’t bother what competition is doing
• In oligopolistic markets products may or may not be differentiated
o What matters is that only a few firms account for most or all of total production
o Some or all firms earn substantial profits over the long run because barriers to entry make it difficult or impossible for
new firms to enter
• Barriers to entry
o Natural barriers (they are basic to the structure of the market)
▪ Scale economies
▪ May make it unprofitable for more than a few firms to coexist in the market
▪ Patents or access to technology may exclude potential competitors
▪ The need to spend money on name recognition and market reputation may discourage entry by new firms
o Strategic actions by incumbent firms may deter entry
• Equilibrium in competitive and monopolistic markets
o When a market is in equilibrium, firms are doing the best they can and have no reason to change their price or output
• Nash equilibrium
o Set of strategies or actions in which each firm does the best it can given its competitor’s actions
• Duopoly
o Market in which two firms compete with each other
6
,• Cournot model (inverse demand!!!!!)
o Homogeneous good
o Market demand curve is known
o Each firm must decide how much to produce, and the two firms make their decisions at the same time
o Each firm treats the output of the other firm as fixed
o Market price will depend on the total output of both firms
o Definition
▪ Oligopoly model in which firms produce a homogeneous good, each firm treats the output of the
competitor as fixed, and all firms decide simultaneously how much to produce
o q1=q1(q2)
o q2=q2(q1)
• Reaction curve
o Relationship between a firm’s profit maximizing output and the amount it thinks its competitor will produce
▪ Q1*(Q2)
• Cournot equilibrium
o Equilibrium in the Cournot model in which each firm correctly
assumes how much its competitor will produce and sets its own Nash equilibrium and other outcomes
production level accordingly
o At this equilibrium each firm correctly assumes how much its 𝑞 2
Firm 2 is a Outcome under
monopolist perfect
competitor will produce, and it maximizes its profit accordingly competition
𝑎−𝑐
o Is a Nash Equilibrium, no firm wants to deviate 𝑏 (𝑞 ) 1 2
o The Cournot model doesn’t say anything about the dynamics of the
𝑎−𝑐
adjustment process, so when they are not in equilibrium 2 Cournot
▪ During any adjustment process, the model’s central outcome
∗ ∗
assumption that each firm can assume that its 𝑎−𝑐
(𝑞 , 𝑞 ) 1 2
competitor’s output is fixed, will not hold 3
Cartel with 50-
• If firms collude, use the total form of the P=30-Q, so R=PQ=(30-Q)Q=30Q-Q2 50 profit
𝑏 (𝑞 ) sharing
o So total profit is maximized by choosing total output Q, so that the 2 1
marginal revenue equals marginal cost 0 𝑎−𝑐 𝑎−𝑐 𝑎−𝑐 𝑞 1
o This gives the collusion curve 3 2 60
• Competitive output
o Setting price equal to marginal cost
• First mover advantage with the Stackelberg model
o Oligopoly model in which one firm sets its output before other firms do
o Begin with firm 2, because it makes its output decision after firm 1, it takes firm 1’s output as fixed. Therefore, firm
2’s profit-maximizing output is given by its Cournot reaction curve
o In the revenue equation of firm 1, insert the reaction curve of firm 2
▪ Result is revenue of firm 1
• Calculate marginal revenue
• Set MR=MC
• Announcing the output first creates a fait accompli:
o No matter what your competitor does, your output will be large
▪ To maximize profit, your competitor must take your large output level as given and set a low level of output
for itself.
▪ If the competitor would produce a large amount, the price would be driven down, resulting in a lower
profit for both
• Price competition with homogeneous goods → BERTRAND MODEL (=p1*q1 fill in p2 in p1)
o Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed,
and all firms decide simultaneously what price to charge.
o Critique on Bertrand model
▪ It is more natural to compete by setting An Overview
quantities rather than prices, since the
goods are homogeneous
▪ Even if firms do set prices and choose the
same price, what share will go to each one?
7
, • Price competition with differentiated goods
o It is natural to compete by choosing prices rather than quantities
o Choosing the price
▪ Use the Nash equilibrium concept
▪ Profit of firm 1: P1Q1- costs
• Insert the demand curve in the profit function
o At what price P1 is this profit maximized?
▪ This depends on P2, which firm 1 assumes to be fixed.
o Take the derivative
▪ Gives reaction curve
• P1=3+0,25P2
• With price competition, instead of quantities, a first mover might have a disadvantage, since the second mover can undercut the
first mover, and thereby claim a greater part of the market
• Nash equilibrium in a Bertrand game
o Only (p1,p2)=(c,c) is a NE
o No other pair of (p1,p2) is a NE
• Which of the following markets is most likely to be oligopolistic
o Market for aluminium
• In an oligopoly there is interdependence among firms
§ 12.4/5
• A Nash equilibrium is a noncooperative equilibrium
o The resulting profit earned by each firm is higher than it would be under perfect competition but lower than if the
firms colluded
• The competitor won’t choose to set price at the collusive level, because your competitor would do better by choosing a lower
price, even if it knew that you were going to set price at the collusive level.
• Noncooperative game
o Game in which negotiation and enforcement of binding contracts are not possible
• Payoff matrix
o Table showing profit (or payoff) to each firm given its decision and the decision of
its competitor
• Prisoners’ dilemma
o Game theory example in which two prisoners must decide separately whether to
confess to a crime
▪ If a prisoner confesses, he will receive a lighter sentence and his
accomplice will receive a heavier one, but if neither confesses,
sentences will be lighter than if both confess
▪ Oligopolistic firms face this dilemma
• Because implicit collusion tends to be fragile, oligopolistic firms often have a strong desire for
price stability.
o This is why price rigidity can be a characteristic of oligopolistic industries
▪ By which firms are reluctant to change prices even if costs or demands
change
▪ They fear that lower prices might send the wrong message to their
competitors and set off a price war
▪ And if costs or demand rises, they are reluctant to raise prices because
they are afraid that their competitors may not raise theirs.
• Price rigidity is the basis of the kinked demand curve model of oligopoly
o Oligopoly model in which each firm faces a demand curve kinked at the currently
prevailing price
▪ At higher prices demand is very elastic, whereas at lower prices it is
inelastic
• According to this model, each firm faces a demand curve kinked at the currently prevailing price
P*
o At prices above P*, the demand curve is very elastic.
▪ The reason is that the firm believes that if it raises its price above P*, other
firms will not follow suit, and it will therefore lose sales and much of its
market share.
o On the other hand, the firm believes that if it lowers its price below P*, other firms
will follow suit because they will not want to lose their shares of the market
▪ In that case, sales will expand only to the extent that a lower market price
increases total market demand.
• Marginal cost could increase but still equal marginal revenue at the same output level, so that
price stays the same
• The kinked demand curve model, however, doesn’t say anything about how the firms arrived at
the price P* in the first place, and why they didn’t arrive at some different price.
o It is useful mainly as a description of price rigidity, rather than an explanation
▪ The explanation come from the prisoners’ dilemma
8
, • Price signalling
o Form of implicit collusion in which a firm announces a price increase in the hope
that other firms will follow suit
• Price leadership
o Pattern of pricing in which one firm regularly announces price changes that other
firms then match
• Dominant firm
o Firm with a large share of total sales that sets price to maximize profits, taking into
account the supply response of smaller firms
o Graph on the right
▪ The dominant firm sets price, and the other firms sell all they want at
that price. The dominant firm’s demand curve, Dd, is the difference between market demand D and the
supply of fringe firms Sf. The dominant firm produces a quantity Qd at the point where its MRd is equal to
its MCd. The corresponding price is P*. At this price, fringe firms sell Qf, so that total sales equal Qt
• Because the firm’s demand curve is kinked, the marginal revenue curve is discontinuous
• To make a threat credible, reputation
Chapter 13
• Decision theory versus game theory
o 1 decision maker in decision theory & environment is exogenous
o In game theory the environment is endogenous, what others do, depends on what I do
• Game
o Any situation in which players make strategic decisions
▪ Decisions that take into account each other’s actions and responses
• Elements of the game
o The players
o The rules of the game
▪ A complete description of what the players can do, the set of all possible actions and the timing
▪ The information that players have available when choosing their actions
o A description of the payoff consequences of each player for every possible combination of actions chosen by all players
playing the game
o A description of all players’ preferences over payoffs
• Payoff
o Outcomes that generate rewards or benefits
• Strategy
o Rule or plan of action for playing the game
• Optimal strategy
o Strategy that maximizes a player’s expected payoff
• Cooperative game
o Game in which participants can negotiate binding contracts that allow them to plan joint strategies
• Fundamental difference between cooperative and noncooperative games lies in the contracting possibilities
• Dominant strategy
o Strategy that is always optimal no matter what an opponent does
• Equilibrium in dominant strategies
o Outcome of a game in which each firm is doing the best it can regardless of what its
competitors are doing
• Dominant strategies are stable/self-enforcing
• Nash Equilibrium
o A set of strategies (or actions) such that each player is doing the best it can given the action of its opponents, no player
has an incentive to deviate, therefore the equilibrium is stable
• Dominant strategies equilibrium is a special case of a Nash Eq.
• Equilibrium is stable, once the strategies are chosen, no player will unilaterally deviate from them
• The concept of a Nash Equilibrium relies heavily on individual rationality
• Maximin strategy
o Strategy that maximizes the minimum gain that can be earned
o A conservative strategy, but it is not profit maximizing
o Dominant strategies are also maximin strategies
• Prisoners’ dilemma
o The ideal outcome is one in which neither prisoner confesses. Confessing however is a dominant
strategy for each prisoner, it yields a higher payoff regardless of the strategy of the other
prisoner
o The outcome in which both prisoners confess is both a Nash Equilibrium and a maximin solution.
Thus, it is rational for each prisoner to confess.
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, • Pure strategy
o Strategy in which a player makes a specific choice or takes a specific action
• Mixed strategy
o Strategy in which a player makes a random choice among two or more possible actions, based on a set of chosen
probabilities
▪ EX
• Matching pennies
o No Nash Equilibrium in pure strategies
▪ One player or the other will always want to change
strategies
o Nash Equilibrium in mixed strategies
o One reason to consider mixed strategies is that some games do not have any Nash equilibria in pure
strategies. Once we allow for mixed strategies, every game has at least one Nash Equilibrium
• Some games have Nash Equilibria both in pure strategies and mixed strategies
o Battle of the sexes
▪ Pure Nash Equilibria
• Both Ballet & Both Soccer
▪ Mixed
• Alice chooses ballet with 2/3 and soccer with 1/3
• Bon chooses ballet with 1/3 and soccer with 2/3
o The outcome is random, and they both will each have an expected payoff of 2/3
• Repeated games
o Game in which actions are taken and payoffs received over and over again
• Tit-for-that strategy
o Repeated-game strategy in which a player responds in kind to an opponent’s previous play, cooperating with
cooperative opponents and retaliating against uncooperative ones.
• Infinitely repeated games
o Cooperative behaviour is then the rational response to a tit-for-that strategy
o It is not rational to undercut, since the cumulative loss of profits (every time the price drops) will outweigh the short-
term gain that accrued during the first month of undercutting
• Finite number of repetitions
o Charge a high price until the last month, since the competitor cannot undercut my price after the last month. A
guaranteed higher profit during the last month. But the competitor also plays like this, so the undercutting starts one
month earlier each time
▪ The only rational outcome is for both of us to charge a low price every month
• Tit-for-that can sometimes work and cooperation can prevail
o Most managers don’t know how long they will be competing with their rivals, this also serves to make cooperative
behaviour a good strategy
o My competitor might have some doubt about the extent of my rationality. Suppose my competitor thinks that I am
playing tit-for-that. He also thinks that I am playing tit-for-that blindly, or with limited rationality.
• In a repeated game the prisoners’ dilemma can have a cooperative outcome
• Rabin: Psychology and economics
o Agents are not always
▪ 100% self centred (no pure self-interest)
▪ 100% rational (not perfect calculators)
▪ 100% self controlled (time-inconsistency)
o Mainstream model needs adjustment in some ways
▪ What is the message?
• Games of complete information
o Requires that the following four components be common knowledge among all players of the game
▪ All the possible actions of all the players
▪ All the possible outcomes Mutual-best-response property
▪ How each combination of actions of all players affects which outcome will of the Nash Equilibrium
materialize For simple 2x2 games, just check whether anyone has an incentive to
deviate from a particular outcome:
▪ The preferences of each and every player over outcomes 2
• When both players have a dominant strategy → Nash Equilibrium
C D
3 5
Prisoner’s Dilemma C
o Assumption needed: both players are rational 1
3 0
•
0 1
The existence of dominated strategies may help to find the NE D
5 1
• Is CC a NE?
o We can eliminate strictly dominated strategies, since a rational player has no incentive to No. Given that 1 plays C, 2 would prefer D; same for 1.
play them
• Is DD a NE?
• Iterated Elimination of Strictly Dominated Strategies (IESDS) Yes. For both players, 1 > 0.
o We can use IESDS any number of rounds to come up with a reasonable prediction
o If there is a unique solution after successive elimination this solution is a Nash Equilibrium
• A Nash Equilibrium is not necessarily the ‘best’ or most preferred outcome for each player
• What happens when two players iterate best responses?
o Eventually the game will stabilize
o Equilibrium: no one has an incentive to deviate
• Dominated strategies are never part of any equilibrium, also not in mixed strategies
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