Small example from the literature:
Note: John Nash just won the Abel prize (http://www.nature.com/news/beautiful-mind-john-nash-adds-abel-prize-to-his-nobel-1.17179).
We implement different behaviors with a GAMS model:
|Oligopolistic (MCP) |
|Monopolistic (NLP) |
Think of this as firms are merged.
|Competitive (NLP) |
Optimize Social Welfare Objective.
Check solution by: Price= Marginal Cost.
Here q(i) is quantity supplied by firm i. We see most profit is to be made by merging firms and reducing capacity, just as happened in the US airline industry (Europe is a very different story). See also: https://www.nytimes.com/2015/03/24/business/dealbook/as-oil-prices-fall-air-fares-still-stay-high.html.
Another small example from energy markets: https://yetanothermathprogrammingconsultant.blogspot.com/2013/07/microeconomic-principles.html