Formalising theories in micro-economics with dynamic epistemic logic - - PowerPoint PPT Presentation

▶

Dec 13, 2023 97 likes •420 views

Formalising theories in micro-economics with dynamic epistemic logic Hanna S. van Lee hannavanlee@hum.ku.dk 1 / 13 Criticism towards economics Few economists saw our current crisis coming, but this predictive failure was the least of the

SLIDE 1

Formalising theories in micro-economics with dynamic epistemic logic

Hanna S. van Lee

hannavanlee@hum.ku.dk

1 / 13

SLIDE 2

Criticism towards economics

“Few economists saw our current crisis coming, but this predictive failure was the least of the field’s problems. More important was the profession’s blindness to the very possibility of catastrophic failures in a market economy.” (Krugman 2009)

2 / 13

SLIDE 3

Criticism towards economics

“Few economists saw our current crisis coming, but this predictive failure was the least of the field’s problems. More important was the profession’s blindness to the very possibility of catastrophic failures in a market economy.” (Krugman 2009) “Of all the economic bubbles that have pricked [since 2008], few have burst more spectacularly than the reputation of economics itself.” (The Economist 2009)

2 / 13

SLIDE 4

Big problem: unrealistic assumptions

For example: common knowledge of rationality Two ways to handle this:

1. Weaken the assumptions
2. Weaken the intended goals into obtaining

◮ (instead of 1:1 description) ◮ structural insights and ◮ formal understanding of basic concepts 3 / 13

SLIDE 5

Financial bubbles

4 / 13

SLIDE 6

Financial bubbles

⇒ What are fundamental and structural causes of a bubble?

4 / 13

SLIDE 7

Greater fools explanation

“Agents are willing to pay more for an asset than they think it is worth, because they anticipate they might be able to sell it to someone else for an even higher price”

5 / 13

SLIDE 8

Greater fools explanation

“Agents are willing to pay more for an asset than they think it is worth, because they anticipate they might be able to sell it to someone else for an even higher price” Consider a great fool (like Donald from USA...)

5 / 13

SLIDE 9

Greater fools explanation

6 / 13

SLIDE 10

Greater fools explanation

6 / 13

SLIDE 11

Greater fools explanation

6 / 13

SLIDE 12

Greater fools explanation

6 / 13

SLIDE 13

Greater fools explanation

6 / 13

SLIDE 14

Epistemic taste

Higher-order beliefs Private information Public information

7 / 13

SLIDE 15

Epistemic taste

Higher-order beliefs Private information Public information Risk Common knowledge (of rationality) (Epistemic) game theory Agreement theory No trade theory etc.

7 / 13

SLIDE 16

Dynamic Epistemic Logic

Static language and models to formalise higher-order knowledge and belief Dynamic operators and models to formalise interaction between agents Helpful to obtain:

◮ structural insights and ◮ formal understanding of basic concepts 8 / 13

SLIDE 17

Alice, Bob and an orange tree

Language for knowledge and belief: Ka( = $5) and Bb( > $5)

9 / 13

SLIDE 18

Alice, Bob and an orange tree

Language for knowledge and belief: Ka( = $5) and Bb( > $5) Epistemic model: M = W,V,∼i,ii∈A = $4 w = $7 w′ b a

10 / 13

SLIDE 19

Alice, Bob and an orange tree

Language for knowledge and belief: Ka( = $5) and Bb( > $5) Epistemic model: M = W,V,∼i,ii∈A Satisfaction in a model:

◮ M,w |

= Ka( = $5) iff M,v | = ( = $5) for all v ∼a w

= $4 w = $7 w′ b a

10 / 13

SLIDE 20

Alice, Bob and an orange tree

Language for knowledge and belief: Ka( = $5) and Bb( > $5) Epistemic model: M = W,V,∼i,ii∈A Satisfaction in a model:

◮ M,w |

= Ka( = $5) iff M,v | = ( = $5) for all v ∼a w

◮ M,w |

= Bb( > $5) iff M,v | = ( > $5) for all v ∈ maxb{u ∈ W|u ∼b w}

= $4 w = $7 w′ b a

10 / 13

SLIDE 21

Alice, Bob and an orange tree

Language for knowledge and belief: Ka( = $5) and Bb( > $5) Epistemic model: M = W,V,∼i,ii∈A Satisfaction in a model:

◮ M,w |

= Ka( = $5) iff M,v | = ( = $5) for all v ∼a w

◮ M,w |

= Bb( > $5) iff M,v | = ( > $5) for all v ∈ maxb{u ∈ W|u ∼b w}

Higher-order knowledge/belief: KbKaBb( > $5) = $4 w = $7 w′ b a

10 / 13

SLIDE 22

Formalisation of greater fools reasoning

Wanting to sell the orange for price p

11 / 13

SLIDE 23

Formalisation of greater fools reasoning

Wanting to sell the orange for price p: M,w | = sella(p) iff M,w | = Ba( < p)

11 / 13

SLIDE 24

Formalisation of greater fools reasoning

Wanting to sell the orange for price p: M,w | = sella(p) iff M,w | = Ba( < p) Wanting to buy the orange for price p

11 / 13

SLIDE 25

Formalisation of greater fools reasoning

Wanting to sell the orange for price p: M,w | = sella(p) iff M,w | = Ba( < p) Wanting to buy the orange for price p: M,w | = buya(p) iff M,w | = Ba( > p) or there is a k ≥ 1 such that M,w | = BaBj1...Bjk( > p+k)

11 / 13

SLIDE 26

Formalisation of greater fools reasoning (contd.)

= $4 w = $7 w′ b a Even though M,w | = Ba( = $4), it holds that M,w | = buya(5) because M,w | = BaBb( > $6)

12 / 13

SLIDE 27

Formalisation of greater fools reasoning (contd.)

= $4 w = $7 w′ b a Even though M,w | = Ba( = $4), it holds that M,w | = buya(5) because M,w | = BaBb( > $6) Add agents and action models for more complex analyses

12 / 13

SLIDE 28

Conclusion

Economics has been criticised for using unrealistic assumptions, but unrealistic models may clarify concepts under study

13 / 13

SLIDE 29

Conclusion

Economics has been criticised for using unrealistic assumptions, but unrealistic models may clarify concepts under study Dynamic Epistemic Logic (DEL) is perfect for formalising higher-order reasoning and interacting agents

13 / 13

SLIDE 30

Conclusion

Economics has been criticised for using unrealistic assumptions, but unrealistic models may clarify concepts under study Dynamic Epistemic Logic (DEL) is perfect for formalising higher-order reasoning and interacting agents DEL may be used to clarify economical concepts such as bubble phenomena

13 / 13