Markets are of course, one of the oldest mechanism of exchanging commodities and cultural artifacts. While their history is over 5000 years old, their mathematical theory is rather recent. The first such models were by Fisher and Walras. Later models have been by Arrow, Debreu and others. Markets are now the central philosophical cornerstone of much of the discourse on efficiency and development, and it is imperative that we should investigate their functioning.
We begin by Fisher markets, a simple model of buyers with money and utilities, and sellers with goods. The standard efficient-market hypothesis predicts that unique prices are discovered and the market clears. We study this market under strategic behaviour by buyers who may report fictitious utlities. We show, in fact, that buyers may actually benefit from such behaviour. We then formulate the Fisher market game and examine its Nash equilibria and show some not-so-surprising features.
The key to a market is its implementation, whence we explore some standard laws (e.g., price discovery and the supply/demand curve intersection) and their strategic basis. We close by highlighting two commonly occuring market-games which need further research--the cowherd of gokul game, and the engineering college placement game.