Tuesday, June 13, 2006

Free riding
(for Zsóka)

In David Lewis' Convention he introduces coordination problems with several examples. One of these is the well known artificiality, convetionality of the traffic regulations. while everyone is driving on the same side of the road it is irrelevant which side they chose. Moreover if only a few participant chooses not to cooperate with the others and take the opposite direction than the rebels won they may be faster than the others. On the other hand if more people prefers to be rebel and go against convention total chaos is resulted.

Cyclists are constant rebels. If they participate in the traffic they can go in any direction practically and they are faster in shorter but reasonable distances (that are driven by cars for the most part in a city). So according to what is said above one would expect that universal cycling results in total chaos...but that's plainly false, that is free riding.

Wednesday, June 07, 2006

Constructive mathematics and agent-based modeling.

Though I suspect that its not only me who saw similarities between the philosophy of the two, I still find it valuable to write some sentences about this issue here.

For one example Leigh Tesfatsion does explicitly refer to constructivism in the philosophy of Mathematics in his Handbook chapter (CHAPTER 16. AGENT-BASED COMPUTATIONAL ECONOMICS:A CONSTRUCTIVE APPROACH TO ECONOMIC THEORY). He highlights that in constructivist circles one have to have an actual construction of a mathematical object if it is to be said to exist. Furthermore he mentions that proofs can be understood as computer programs in constructivist terms. And this is the line of symmetry between philosophies of mathematics and economics.

The symmetry may seem accidental but it may be not. Computational interpretation of constructive mathematics is most famously developed by Kurt Gödel, that became known as the Dialectica interpretation of constructive mathematics. Before that the notion of mathematical construction was somewhat obscure (that is a philosophical notion). Gödel managed to give a precise mathematical description of constructions with the help of recursive functionals. And recursive functions are computer programs, as defenders of functional programming paradigm like to say.

So I'm about to argue that as in the history of constructive mathematics a human cognitive notion (mathematical construction) was made more and more precise mathematically, the same process can be observed in economics, where human rational behavior is being explained with computer programs (that are precise formal entities with definite properties).

Constructive mathematics is usually disdained by mathematicians working in the classical paradigm (as something unusable) and in the same manner ACE is being overlooked by classical economists. On the other hand development of computer science showed how important and insightful discipline is the constructivist theory of mathematics, and I expect that development of multi-agent systems will display similar success for ACE.