SUMMARY MICROECONOMICS: GAMES AND
BEHAVIOUR ~ YEAR 2 SEMESTER 1
WEEK 1: UNCERTAINTY AND TIME
1. Risk and uncertainty
1. Uncertainty: outcomes are unknown
2. Risk: outcome likelihood is known
a. Describes any economic outcome in which there are certain
outcomes
i. Probabilities are numbers between 0 and 1
1. These indicate the likelihood that particular outcome will
occur
B. Expected value
i. Example: 0.5 y1 = 30.000, 0.5 y2 = 10.000
1. -> 0.5(30.000) + 0.5(10.000) = 20.000
C. Utility of expected value U(E(y))
i. Utility of a person had from receiving a certain amount of money equal to the
expected value of an outcome
1. = 20.000
D. The expected utility E(U(y))
i. Sum of all utilities of all possible outcomes -> weighted with their
probabilities
1. = 0.5 x U (30.000) + 0.5 x U (10.000)
2. RATIONAL DECISION MAKING WITH RISK/UNCERTAINTY
A. Chooses the action that maximizes the expected utility
i. Ex: choose A if: E(u(y|a)) > E(u(y|b)) for all b
B. Example gamble: 60% chance 1000, 40% chance 2500
i. Expected value:
1. 0.6 x 1000 + 0.4 x 2500 = 1600
ii. Expected utility:
1. 0.6 x U(1000) + 0.4 x U(2500) = 1600
a. Can be expressed as: √ Y
i. 0.6 x √ 1000+0.4 x √ 2500=¿ 38.97
iii. Utility of expected value:
1. √ E( y ) -> √ 1600 = 40
, C. Utility of expected value > expected value -> individual does not like risk: risk
averse
i. Risk averse: prefers certain income option over uncertain option
E(U(y) < U(E(y))
ii. Risk loving: prefers uncertain income over certain income
E(U(y)) > U(E(y))
iii. Risk neutral: indifferent between certain or uncertain income
E(U(y)) = U(E(y))
Risk averse: is willing to pay to avoid risk but how much?
iv. Certainty equivalent: CE = U(y*) = E(U(y))
1. Certain payoff that generates as much utility as expected utility of this
gamble
i. Example: 0.6 x √ 1000+0.4 x √ 2500=¿ 38.97
ii. 38.97 = √ y∗¿ -> 38.97^2 = 1518.66 = CE
Risk premium: max willingness to pay to eliminate risk
v. = difference expected value and certain equivalent
1. E(Y) – CE
a. Example: 0.6 x 1000 + 0.4 x 2500 = 1600
38.97 = √ y∗¿ -> 38.97^2 = 1518.66 CE
b. 1600 – 1518.66 = 81.34
Absolute risk aversion and Relative risk aversion
1. Absolute risk aversion: outcome
a. Increasing ARA: fewer euros in risky
assets as wealth decreases
b. Constant: same …
c. Decreasing ARA: more euros in risky assets as wealth increases
2. Relative risk aversion: outcome (RRA = ARA x wealth (y))
a. Increasing: smaller % of wealth in risky assets
b. Constant: same % ….
c. Decreasing: larger % of wealth in risky assets
i. Relative risk aversion is measured by the amount of
money a person is willing to put at risk in percentages
of her income or wealth. Example:
1. if a person’s income is twice as high and she
invests twice as much money in risky shares,
her relative risk aversion is said to be constant
(since the absolute amount of money at risk
2
, increases, absolute risk aversion is decreasing,
by the way).
WEEK 2: GAME THEORY; STRATEGIC INTERACTION I
- Oligopoly, Cournot model, Bertrand model
A. The intertemporal budget constraint
i. Discount factor: = 1/(1+r)
1. Discounts the future value of consumption and income to the present
value
B. Strategic interaction
i. Between people: provision of a public good
1. Provision of a public good:
a. 3 citizens, each can contribute ki(1,…..,10) units to the provision of
a public good
i. They benefit from contributing to this public good
b. Wealth increases in all contributions
i. Contributing to public good = higher social benefit than
keeping contribution on private account
1. Each citizens contributes as long as the cost of contributing is
outweighed by the gains for that citizen
a. Optimal decion of the individual -> best response function
i. = 1st derivative of the function of k1
ii. Between firms: oligopoly theory
1. Only few sellers: duopoly = 2 firms competing
a. Entry barriers; scale economies, patents, access to technology,
reputation
b. Behaviour: behaviour of one firm depends on how the firm thinks
the other firm will react.
C. Toolbox 1: game theory: static games with
complete information
i. Mixed strategies:
1. When players best response do
not stabilize or multiple
equilibria
3
BEHAVIOUR ~ YEAR 2 SEMESTER 1
WEEK 1: UNCERTAINTY AND TIME
1. Risk and uncertainty
1. Uncertainty: outcomes are unknown
2. Risk: outcome likelihood is known
a. Describes any economic outcome in which there are certain
outcomes
i. Probabilities are numbers between 0 and 1
1. These indicate the likelihood that particular outcome will
occur
B. Expected value
i. Example: 0.5 y1 = 30.000, 0.5 y2 = 10.000
1. -> 0.5(30.000) + 0.5(10.000) = 20.000
C. Utility of expected value U(E(y))
i. Utility of a person had from receiving a certain amount of money equal to the
expected value of an outcome
1. = 20.000
D. The expected utility E(U(y))
i. Sum of all utilities of all possible outcomes -> weighted with their
probabilities
1. = 0.5 x U (30.000) + 0.5 x U (10.000)
2. RATIONAL DECISION MAKING WITH RISK/UNCERTAINTY
A. Chooses the action that maximizes the expected utility
i. Ex: choose A if: E(u(y|a)) > E(u(y|b)) for all b
B. Example gamble: 60% chance 1000, 40% chance 2500
i. Expected value:
1. 0.6 x 1000 + 0.4 x 2500 = 1600
ii. Expected utility:
1. 0.6 x U(1000) + 0.4 x U(2500) = 1600
a. Can be expressed as: √ Y
i. 0.6 x √ 1000+0.4 x √ 2500=¿ 38.97
iii. Utility of expected value:
1. √ E( y ) -> √ 1600 = 40
, C. Utility of expected value > expected value -> individual does not like risk: risk
averse
i. Risk averse: prefers certain income option over uncertain option
E(U(y) < U(E(y))
ii. Risk loving: prefers uncertain income over certain income
E(U(y)) > U(E(y))
iii. Risk neutral: indifferent between certain or uncertain income
E(U(y)) = U(E(y))
Risk averse: is willing to pay to avoid risk but how much?
iv. Certainty equivalent: CE = U(y*) = E(U(y))
1. Certain payoff that generates as much utility as expected utility of this
gamble
i. Example: 0.6 x √ 1000+0.4 x √ 2500=¿ 38.97
ii. 38.97 = √ y∗¿ -> 38.97^2 = 1518.66 = CE
Risk premium: max willingness to pay to eliminate risk
v. = difference expected value and certain equivalent
1. E(Y) – CE
a. Example: 0.6 x 1000 + 0.4 x 2500 = 1600
38.97 = √ y∗¿ -> 38.97^2 = 1518.66 CE
b. 1600 – 1518.66 = 81.34
Absolute risk aversion and Relative risk aversion
1. Absolute risk aversion: outcome
a. Increasing ARA: fewer euros in risky
assets as wealth decreases
b. Constant: same …
c. Decreasing ARA: more euros in risky assets as wealth increases
2. Relative risk aversion: outcome (RRA = ARA x wealth (y))
a. Increasing: smaller % of wealth in risky assets
b. Constant: same % ….
c. Decreasing: larger % of wealth in risky assets
i. Relative risk aversion is measured by the amount of
money a person is willing to put at risk in percentages
of her income or wealth. Example:
1. if a person’s income is twice as high and she
invests twice as much money in risky shares,
her relative risk aversion is said to be constant
(since the absolute amount of money at risk
2
, increases, absolute risk aversion is decreasing,
by the way).
WEEK 2: GAME THEORY; STRATEGIC INTERACTION I
- Oligopoly, Cournot model, Bertrand model
A. The intertemporal budget constraint
i. Discount factor: = 1/(1+r)
1. Discounts the future value of consumption and income to the present
value
B. Strategic interaction
i. Between people: provision of a public good
1. Provision of a public good:
a. 3 citizens, each can contribute ki(1,…..,10) units to the provision of
a public good
i. They benefit from contributing to this public good
b. Wealth increases in all contributions
i. Contributing to public good = higher social benefit than
keeping contribution on private account
1. Each citizens contributes as long as the cost of contributing is
outweighed by the gains for that citizen
a. Optimal decion of the individual -> best response function
i. = 1st derivative of the function of k1
ii. Between firms: oligopoly theory
1. Only few sellers: duopoly = 2 firms competing
a. Entry barriers; scale economies, patents, access to technology,
reputation
b. Behaviour: behaviour of one firm depends on how the firm thinks
the other firm will react.
C. Toolbox 1: game theory: static games with
complete information
i. Mixed strategies:
1. When players best response do
not stabilize or multiple
equilibria
3
