page_title: History of microeconomics
section_title: Imperfect competition and game theory
hierarchical_section_title: History of microeconomics / Imperfect competition and game theory
caption_attribution_description: English: Extensive form game 1A Treborbassett 00:13, 14 Mar 2005 (UTC)
context_page_description: Microeconomics is the study of the behaviour of individuals and small impacting organisations in making decisions on the allocation of limited resources. The modern field of microeconomics arose as an effort of neoclassical economics school of thought to put economic ideas into mathematical mode.
context_section_description: In 1929 Harold Hotelling published "Stability in Competition" addressing the problem of instability in the classic Cournout model: Bertrand criticised it for lacking equilibrium for prices as independent variables and Edgeworth constructed a dual monopoly model with correlated demand with also lacked stability. Hotteling proposed that demand typically varied continuously for relative prices, not discontinuously as suggested by the later authors.
  Following Sraffa he argued for "the existence with reference to each seller of groups who will deal with him instead of his competitors in spite of difference in price", he also noticed that traditional models that presumed the uniqueness of price in the market only made sense if the commodity was standardised and the market was a point: akin to a temperature model in physics, discontinuity in heat transfer (price changes) inside a body (market) would lead to instability. To show the point he built a model of market located over a line with two sellers in each extreme of the line, in this case maximising profit for both sellers leads to a stable equilibrium. From this model also follows that if a seller is to choose the location of his store so as to maximise his profit, he will place his store the closest to his competitor: "the sharper competition with his rival is offset by the greater number of buyers he has an advantage". He also argues that clustering of stores is wasteful from the point of view of transportation costs and that public interest would dictate more spatial dispersion.
  A new impetus was given to the field when around 1933 Joan Robinson and Edward H. Chamberlin, published respectively, The Economics of Imperfect Competition (1933) and The Theory of Monopolistic Competition (1933), introducing models of imperfect competition. Although the monopoly case was already exposed in Marshall's Principles of Economics and Cournot had already constructed models of duopoly and monopoly in 1838, a whole new set of models grew out of this new literature. In particular the monopolistic competition model results in a non efficient equilibrium. Chamberlin defined monopolistic competition as, "...challenge to traditional viewpoint of economics that competition and monopoly are alternatives and that individual prices are to be explained in terms of one or the other." He continues, "By contrast it is held that most economic situations are composite of both competition and monopoly, and that, wherever this is the case, a false view is given by neglecting either one of the two forces and regarding the situation as made up entirely of the other."
  Later, some market models were built using game theory, particularly regarding oligopolies. A good example of how microeconomics started to incorporate game theory, is the Stackelberg competition model published in 1934, which can be characterised as a dynamic game with a leader and a follower, and then be solved to find a Nash Equilibrium.
  William Baumol provided in his 1977 paper the current formal definition of a natural monopoly where “an industry in which multiform production is more costly than production by a monopoly” (p. 810): mathematically this equivalent to subadditivity of the cost function. He then sets out to prove 12 propositions related to strict economies of scale, ray average costs, ray concavity and transray convexity: in particular strictly declining ray average cost implies strict declining ray subadditivity, global economies of scale are sufficient but not necessary for strict ray subadditivity.
  In 1982 paper Baumol defined a contestable market as a market where "entry is absolutely free and exit absolutely costless", freedom of entry in Stigler sense: the incumbent has no cost discrimination against entrants. He states that a contestable market will never have an economic profit greater than zero when in equilibrium and the equilibrium will also be efficient. According to Baumol this equilibrium emerges endogenously due to the nature of contestable markets, that is the only industry structure that survives in the long 
caption: Stackelberg competition represented as an extensive form game with Infinite action space.
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