Phase transition in the "price war" game?
Couple of months ago I have started a series of posts on price formation in the free market or how and why the free market does (not) work. This text is a slightly detour from the part four of the series. In which I would like to delve into interesting properties of the gameI have introduced in the part four.
In the part four I have asked you to imagine that the market consists of two competing companies, which produce almost identical products. Each of the companies can charge a high price or a low price. If one company wants to charge low price, then all consumers would prefer buying its product and not the competitors. I have assumed that there are 100 consumers and that companies produce products for all consumers (namely they always produce 100 units of the product), high price is 5 monies, low price is 3 monies and production costs are 0.5 monies. In this post I would like to remove some of these simplifying assumptions and discuss how the model works if different numbers are selected.