Lecture 5 - CRE & dynamic choice

Dynamic choice under risk

Choice problems where outcome determined by combination of choices and risks (with known probability) with at least one of:

–            More than one moment of choice

–            More than one moment when chance resolved

–            A chance resolved even before agent has any choice to make

How are dynamic decision problems represented

Decision trees

4 principles of rational dynamic decision-making used in orthodox economic modelling

- Frame Independence

- Forward-looking rationality / Separability

- Dynamic consistency

- (Standard) Reduction of compound lotteries

Frame independence definition

Person will make same decisions in any 2 dynamic decision problems that have the same decision tree

• regardless of framing the choices made will be the same if the underlying decision tree is identical

their dynamic choice behaviour can be analysed in decision trees

Compound lottery

A lottery where at least one of the prizes is entry to another lottery

-              Chance node that leads to another chance node

(Standard) Reduction of compound lotteries definition

Decision makers under standard thinking are modelled as reducing compound lotteries to a probabilistically equivalent simple lottery by multiplying out probabilities

(Standard) Reduction of compound lotteries decision tree

Person sees up as a simple lottery and so tree 1 becomes tree 2

Forward-looking rationality / Separability definition

At any choice node, the agent’s choice matches what they would choose at the initial node of the tree obtained by “snipping off” the sub-tree at the choice node from parts of the original tree not reachable from the sub choice node

• The sub tree then becomes ‘identical’ to the agent

Forward-looking rationality / Separability decision tree

Dynamic consistency definition

in a decision problem with a sequence of choices, a rational agent should:

- Plan ahead

- Not change plans unless new information available

Dynamic consistency decision tree

Scaled up vs scaled down CRE preferences overview

Scaled up vs scaled down CRE preferences - CRE choice on decision tree

Scaled up vs scaled down CRE preferences - separability

Scaled up vs scaled down CRE preferences - dynamic consistency

Scaled up vs scaled down CRE preferences - frame independence

Scaled up vs scaled down CRE preferences - standard reduction of compound lotteries

Scaled up vs scaled down CRE preferences - CRE vs SRCL

CRE vs principles of rational dynamic decision-making

Not compatible

• It is impossible to have and always act on CRE preferences while also satisfying ALL of the 4 principles

• BUT it doesn’t tell us which one it violates

CRE preferences require Down in Tree 1 and Up in Tree 4

• BUT rational dynamic choices select either UP or DOWN at every tree