Chapter 1:
Theories of decision: given a set of goals, how should/will people pursue those goals
- Descriptive theory: how people in fact make decisions
- Normative: how people should make decisions
Standard economic theories: assume they are both descriptively and normatively correct
Behavioral economics: clear distinction between descriptive vs normative
- People often don’t act in the way that they should
Theory of rational choice: normatively correct theories of decision
- Rational decision: a decision which is in line with the theory
- Irrational: decisions that are not
Neoclassical economics vs behavioral economics
- Neoclassical: people may not act rational all the time, but deviations are small and
unsystematic → do not matter
- Hedonic psychology: individuals maximize pleasure and minimize pain
- Behavioral econ: deviations from rationality are large enough and systematic
- Cognitive science: beh. econ is comfortable talking about things ‘in the head’,
while neoclassicals only want to talk about observable things (preferences).
Methods:
- In the beginning: surveys with hypothetical scenarios
- Now:
- lab experiments, making real decisions about real money
- Field experiments: assign participants to random groups and see how
behavior differs if they are in different situations (have dif. info etc)
process methods: methods that provide hints about cognitive and emotional processes
underlying decision-making.
process-tracing: software to assess what information people use when making decisions in
games.
Chapter 2: Rational Choice under
Certainty
choice under certainty: there is no doubt as to which outcome will result from a given act
- E.g. you get a vanilla ice cream if you order a vanilla ice cream
Axiomatic theory: theory consists of set of axioms
- Axioms: basic propositions that cannot be proven using resources offered by the
theory (just have to take as given)
, - Choice under certainty is an axiomatic theory
preferences: are relations
Relations:
- Binary relations: relations between two entities
- E.g. Bob is older than Alf
- Notation: ‘R’ denotes the relation ‘is older than’
- bRa → Bob is older than Alf
- Rab → Alf is older than Bob
- Order matters!
- Ternary relations: between three entities
- E.g. Mom stands between Bill and Bob
Weak preference relation: ‘at least as good as’
- If coffee is at least as good as tea → c ≥ t
- For different individuals:
- Alf: c ≥Alf t
- Betsy: t ≥Betsy c
Universe (U): set of all things that can be related to one another.
- {Kwik, Kwek, Kwak}
- Order does not matter
- Universe may have infinite members (for example time)
- Set of alternatives: when talking about preferences relations
- Three apples, two bananas → 〈3,2〉
- Three apples, two bananas, six coconuts: 〈3,2,6〉
- Choice of universe might determine whether relation is transative/intransative,
complete/incomplete.
Weak order preference: preference relation that is transitive and complete
- Transitive: if A > B and B>C then A > C (for all A, B, C)
- Intransitive: if A is in love with B, and B in love with C, does NOT mean A is in
love with C → intransitive relation
- Complete: Either A bears relation R to B or B bears relation R to A (e.g. there must
be at least on relation connecting them)
- Either x ≥ y or y ≥ x (or both) (for all x, y)
- Example: Two people: Alf and Bob, either Alf is at least as tall as Bob or the
other way around
- Incomplete relation: if you take two random people out of the universe, one of
them is not necessarily in love with the other → incomplete
IF SOMETHING IS WEAK ORDER, IT IS ALSO REFLEXIVE
- ANY SET THAT IS COMPLETE IS ALSO REFLEXIVE
- → b/c there must be a relation between x and x (otherwise not complete)
,Logical symbols:
- x&y x and y
- xvy x or y
- x→y if x then y; x only if y
- x ←→ x if and only if y; x just in case y
- streepje down p not p
Indifference: x ~ y if and only if x ≥ y and y ≥ x
- Or: x ~ y ←→ x ≥ y & y ≥ x
- Symmetric: if x is as good as y, then y is as good as x.
- Incomplete: there probably is a preference relation in the universe between which
the agent is not indifferent between all options
Strict preference: x > y if and only if x ≥ y and it is not the case that y ≥ x
- Weak preference: “is at least as good as”.
- Properties:
- Transitive
- Anti- symmetric
- Irreflexive
Indirect proofs:
- Proof by contradiction: proving a proposition by first assuming that the opposite
proposition is true and then showing that this leads to a contradiction
How to do proofs:
- Proof: Sequence of propositions, presented on separate lines of the page (each
numbered), last line is the conclusion.
- Hints: if you want to prove…
- x → y, you must first assuming x, then derive y
- x ←→ y, first prove x → y, then y → x
- not p, first assume the opposite and then show it leads to a contradiction
Completeness: relation must hold in at least one
direction for all possible combinations
Reflexivity: relation ‘is not married to’
you cannot marry yourself
Irreflexivity: relation ‘is married to’
As you cannot marry yourself
Symmetry: ‘is married to’
If A married to B → B married to A
- So xRy means yRx
Anti-symmetric: if xRy means that IT IS NOT POSSIBLE that yRx
- E.g.: x > y → y cannot be bigger than x
Preference ordering: order all alternatives in a list, with the best at the top and the worst at
the bottom.
, - Completeness ensures each person will have exactly one list
- Transitivity ensures that the list will be linear (e.g. no cycling)
- Indifference curve: each bundle on one of these curves is as good as every other
bundle on the same curve
Menu / budget set: set of options, but you can choose only one option.
- Budget line: set of combinations of goods that you can afford
- Rational decision:
- You have rational preference ordering
- You choose (one of the) the most preferred item
Utility function: gives a number to each member of the set of alternatives
- Higher utilities correspond to more preferred items
- The actual numbers themselves don’t really matter (it is ordinal, only allows
you to order things)
- Rational: to maximize utility (choose highest IC curve)
Representation theorem: If the set of alternatives is finite, then ≥ is a rational preference
relation just in case there exists a utility function representing ≥.
- Given a rational preference relation, there is always a utility function that represents it
(if choice set is finite).
ordinal utility: We can replace u by v with v(x) = f(u(x)) for all x, as long as f is an increasing
function.
- Examples: f(u) = 4u + 10 f(u) = eu
- We don’t care about the actual numbers, just if one is bigger than the other
cardinal utility: We can replace u by v with v(x) = f(u(x)) for all x, as long as f is a linear
increasing function.
- Examples: f(u) = 4u + 10 But NOT f(u) = eu
- f(u) = 4u + 10 and f(u) = 8u + 20 reflect the same preferences
- f(u) =eu and f(u) = eu + 20 reflect the same preferences
- Preferences: we care not about the absolute number, but about the differences
between two states
- As long as the differences between two states are the same → reflect the
same preferences (--> larger difference means stronger preference)
- → any linear transformation preserves the differences between two
states
Theories of decision: given a set of goals, how should/will people pursue those goals
- Descriptive theory: how people in fact make decisions
- Normative: how people should make decisions
Standard economic theories: assume they are both descriptively and normatively correct
Behavioral economics: clear distinction between descriptive vs normative
- People often don’t act in the way that they should
Theory of rational choice: normatively correct theories of decision
- Rational decision: a decision which is in line with the theory
- Irrational: decisions that are not
Neoclassical economics vs behavioral economics
- Neoclassical: people may not act rational all the time, but deviations are small and
unsystematic → do not matter
- Hedonic psychology: individuals maximize pleasure and minimize pain
- Behavioral econ: deviations from rationality are large enough and systematic
- Cognitive science: beh. econ is comfortable talking about things ‘in the head’,
while neoclassicals only want to talk about observable things (preferences).
Methods:
- In the beginning: surveys with hypothetical scenarios
- Now:
- lab experiments, making real decisions about real money
- Field experiments: assign participants to random groups and see how
behavior differs if they are in different situations (have dif. info etc)
process methods: methods that provide hints about cognitive and emotional processes
underlying decision-making.
process-tracing: software to assess what information people use when making decisions in
games.
Chapter 2: Rational Choice under
Certainty
choice under certainty: there is no doubt as to which outcome will result from a given act
- E.g. you get a vanilla ice cream if you order a vanilla ice cream
Axiomatic theory: theory consists of set of axioms
- Axioms: basic propositions that cannot be proven using resources offered by the
theory (just have to take as given)
, - Choice under certainty is an axiomatic theory
preferences: are relations
Relations:
- Binary relations: relations between two entities
- E.g. Bob is older than Alf
- Notation: ‘R’ denotes the relation ‘is older than’
- bRa → Bob is older than Alf
- Rab → Alf is older than Bob
- Order matters!
- Ternary relations: between three entities
- E.g. Mom stands between Bill and Bob
Weak preference relation: ‘at least as good as’
- If coffee is at least as good as tea → c ≥ t
- For different individuals:
- Alf: c ≥Alf t
- Betsy: t ≥Betsy c
Universe (U): set of all things that can be related to one another.
- {Kwik, Kwek, Kwak}
- Order does not matter
- Universe may have infinite members (for example time)
- Set of alternatives: when talking about preferences relations
- Three apples, two bananas → 〈3,2〉
- Three apples, two bananas, six coconuts: 〈3,2,6〉
- Choice of universe might determine whether relation is transative/intransative,
complete/incomplete.
Weak order preference: preference relation that is transitive and complete
- Transitive: if A > B and B>C then A > C (for all A, B, C)
- Intransitive: if A is in love with B, and B in love with C, does NOT mean A is in
love with C → intransitive relation
- Complete: Either A bears relation R to B or B bears relation R to A (e.g. there must
be at least on relation connecting them)
- Either x ≥ y or y ≥ x (or both) (for all x, y)
- Example: Two people: Alf and Bob, either Alf is at least as tall as Bob or the
other way around
- Incomplete relation: if you take two random people out of the universe, one of
them is not necessarily in love with the other → incomplete
IF SOMETHING IS WEAK ORDER, IT IS ALSO REFLEXIVE
- ANY SET THAT IS COMPLETE IS ALSO REFLEXIVE
- → b/c there must be a relation between x and x (otherwise not complete)
,Logical symbols:
- x&y x and y
- xvy x or y
- x→y if x then y; x only if y
- x ←→ x if and only if y; x just in case y
- streepje down p not p
Indifference: x ~ y if and only if x ≥ y and y ≥ x
- Or: x ~ y ←→ x ≥ y & y ≥ x
- Symmetric: if x is as good as y, then y is as good as x.
- Incomplete: there probably is a preference relation in the universe between which
the agent is not indifferent between all options
Strict preference: x > y if and only if x ≥ y and it is not the case that y ≥ x
- Weak preference: “is at least as good as”.
- Properties:
- Transitive
- Anti- symmetric
- Irreflexive
Indirect proofs:
- Proof by contradiction: proving a proposition by first assuming that the opposite
proposition is true and then showing that this leads to a contradiction
How to do proofs:
- Proof: Sequence of propositions, presented on separate lines of the page (each
numbered), last line is the conclusion.
- Hints: if you want to prove…
- x → y, you must first assuming x, then derive y
- x ←→ y, first prove x → y, then y → x
- not p, first assume the opposite and then show it leads to a contradiction
Completeness: relation must hold in at least one
direction for all possible combinations
Reflexivity: relation ‘is not married to’
you cannot marry yourself
Irreflexivity: relation ‘is married to’
As you cannot marry yourself
Symmetry: ‘is married to’
If A married to B → B married to A
- So xRy means yRx
Anti-symmetric: if xRy means that IT IS NOT POSSIBLE that yRx
- E.g.: x > y → y cannot be bigger than x
Preference ordering: order all alternatives in a list, with the best at the top and the worst at
the bottom.
, - Completeness ensures each person will have exactly one list
- Transitivity ensures that the list will be linear (e.g. no cycling)
- Indifference curve: each bundle on one of these curves is as good as every other
bundle on the same curve
Menu / budget set: set of options, but you can choose only one option.
- Budget line: set of combinations of goods that you can afford
- Rational decision:
- You have rational preference ordering
- You choose (one of the) the most preferred item
Utility function: gives a number to each member of the set of alternatives
- Higher utilities correspond to more preferred items
- The actual numbers themselves don’t really matter (it is ordinal, only allows
you to order things)
- Rational: to maximize utility (choose highest IC curve)
Representation theorem: If the set of alternatives is finite, then ≥ is a rational preference
relation just in case there exists a utility function representing ≥.
- Given a rational preference relation, there is always a utility function that represents it
(if choice set is finite).
ordinal utility: We can replace u by v with v(x) = f(u(x)) for all x, as long as f is an increasing
function.
- Examples: f(u) = 4u + 10 f(u) = eu
- We don’t care about the actual numbers, just if one is bigger than the other
cardinal utility: We can replace u by v with v(x) = f(u(x)) for all x, as long as f is a linear
increasing function.
- Examples: f(u) = 4u + 10 But NOT f(u) = eu
- f(u) = 4u + 10 and f(u) = 8u + 20 reflect the same preferences
- f(u) =eu and f(u) = eu + 20 reflect the same preferences
- Preferences: we care not about the absolute number, but about the differences
between two states
- As long as the differences between two states are the same → reflect the
same preferences (--> larger difference means stronger preference)
- → any linear transformation preserves the differences between two
states
