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

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 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

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

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

Financial bubbles 4 / 13

Financial bubbles ⇒ What are fundamental and structural causes of a bubble? 4 / 13

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

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

Greater fools explanation 6 / 13

Greater fools explanation 6 / 13

Greater fools explanation 6 / 13

Greater fools explanation 6 / 13

Greater fools explanation 6 / 13

Epistemic taste Higher-order beliefs Private information Public information 7 / 13

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

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

Alice, Bob and an orange tree Language for knowledge and belief: K a ( � = $5 ) and B b ( > $5 ) 9 / 13

Alice, Bob and an orange tree Language for knowledge and belief: K a ( � = $5 ) and B b ( > $5 ) Epistemic model: M = �W , V , ∼ i , � i � i ∈ A b w ′ w = $ 4 = $ 7 a 10 / 13

Alice, Bob and an orange tree Language for knowledge and belief: K a ( � = $5 ) and B b ( > $5 ) Epistemic model: M = �W , V , ∼ i , � i � i ∈ A Satisfaction in a model: ◮ M , w | = K a ( � = $5 ) iff M , v | = ( � = $5 ) for all v ∼ a w b w ′ w = $ 4 = $ 7 a 10 / 13

Alice, Bob and an orange tree Language for knowledge and belief: K a ( � = $5 ) and B b ( > $5 ) Epistemic model: M = �W , V , ∼ i , � i � i ∈ A Satisfaction in a model: ◮ M , w | = K a ( � = $5 ) iff M , v | = ( � = $5 ) for all v ∼ a w ◮ M , w | = B b ( > $5 ) iff M , v | = ( > $5 ) for all v ∈ max � b { u ∈ W| u ∼ b w } b w ′ w = $ 4 = $ 7 a 10 / 13

Alice, Bob and an orange tree Language for knowledge and belief: K a ( � = $5 ) and B b ( > $5 ) Epistemic model: M = �W , V , ∼ i , � i � i ∈ A Satisfaction in a model: ◮ M , w | = K a ( � = $5 ) iff M , v | = ( � = $5 ) for all v ∼ a w ◮ M , w | = B b ( > $5 ) iff M , v | = ( > $5 ) for all v ∈ max � b { u ∈ W| u ∼ b w } Higher-order knowledge/belief: K b K a B b ( > $5 ) b w ′ w = $ 4 = $ 7 a 10 / 13

Formalisation of greater fools reasoning Wanting to sell the orange for price p 11 / 13

Formalisation of greater fools reasoning Wanting to sell the orange for price p : M , w | = sell a ( p ) iff M , w | = B a ( < p ) 11 / 13

Formalisation of greater fools reasoning Wanting to sell the orange for price p : M , w | = sell a ( p ) iff M , w | = B a ( < p ) Wanting to buy the orange for price p 11 / 13

Formalisation of greater fools reasoning Wanting to sell the orange for price p : M , w | = sell a ( p ) iff M , w | = B a ( < p ) Wanting to buy the orange for price p : M , w | = buy a ( p ) iff M , w | = B a ( > p ) or there is a k ≥ 1 such that M , w | = B a B j 1 ... B j k ( > p + k ) 11 / 13

Formalisation of greater fools reasoning (contd.) b w ′ w = $ 4 = $ 7 a Even though M , w | = B a ( = $4 ) , it holds that M , w | = buy a ( 5 ) because M , w | = B a B b ( > $6 ) 12 / 13

Formalisation of greater fools reasoning (contd.) b w ′ w = $ 4 = $ 7 a Even though M , w | = B a ( = $4 ) , it holds that M , w | = buy a ( 5 ) because M , w | = B a B b ( > $6 ) Add agents and action models for more complex analyses 12 / 13

Conclusion Economics has been criticised for using unrealistic assumptions , but unrealistic models may clarify concepts under study 13 / 13

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

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