Volume : 4 | Issue : 2 | Feb 2015 ISSN - 2250-1991 197 | PARIPEX - INDIAN JOURNAL OF RESEARCH Research Paper A Mathematical Version of Cournot’s Oligopoly for N Firms Mathematics Dr. Amanpreet Singh Department of Mathematics ,Sri Guru Teg Bahadur Khalsa Col- lege Anandpur Sahib, Ropar (Punjab) India Ms. Bhupinder Kaur Associate Professor, Govt. College for girls, sec 11, Chandigarh (Punjab) (India) KEYWORDS Oligopoly, Duopoly, Nesh Equilibrium. ABSTRACT Monopoly and Perfect Competition in general are two types of market exist in several countries of world. But after Economical reform there exist a new kind of market in India know as Oligopoly, which is neither perfect competition nor monopoly. The term Oligopoly comes from two Greek words: Oligoi meaning “few”and poleein meaning “to sell”. Oligopoly market refers to a kind of market mechanism that only a few manufacturers control production and vendition of product in entire market .The perfect example of oligopoly in India is Petroleum companies, they follows Cournot’s model. In this paper the original cournot model explained with the help of Mathematical expression. Second part of the paper is a mathematical model for n firms in oligopoly market. Third part of paper explained the need of new model for Indian market. The conclusions have certain academic guiding sense and practical application value. At last, some suggestions for government to control the price of petroleum products and for companies about their product and profits. 1. Introduction The main market structures include perfect competition (many buyers and sellers), oligopoly (few sellers and many buyers), monopoly (single seller and many buyers) and monopsony (single buyer and many sellers). One of the main distinguish- ing factors that we have identified between the different mar- ket structures is the level of barriers to entry. Market entry barriers are relevant when considering new market entry (Niu, Dong & Chen, 2011). Market barriers can adversely affect the speed and extent of entry into a new market (Gruca & Sud- harshan, 1995; Varadarajan & Peterson, 1992). The main bar- riers to entry include Cost advantages of incumbents, Product differentiation of incumbents, Capital requirements, Customer switching costs, Access to distribution channels, Government policy (Porter, 1980; Johnson, Scholes & Whittington, 2011). It is very important to understand country characteristics and other environmental issues before selecting the right entry mode for a new market. Another problem that might arise from not selecting the appropriate entry mode strategy is a substantial limitation of strategic options open to the firm as well as a blockage of opportunities, (Ekeledo & Sivakumar 2004; Alderson 1957). The works of such scholars raise cer- tain questions such as: What factors affect entry mode deci- sions? What barriers commonly exist in oligopolistic market situations? Which entry modes can a firm use to enter an ol- igopolistic market situation? How sufficient is the information available to companies contemplating entry into a new market for making comparisons between entry modes and how ac- cessible is this information? In a market situation where a few suppliers dominate the market, also known as an oligopolistic market, a firm must respond to their rival’s choices and rivals would also respond to the firm’s choices. In an oligopolistic market situation, there is tension between cooperation and self interest. Thus, entry and survival might be different from a more open mar- ket. Firms in an oligopolistic market situation would obvious- ly want to protect their market share and thus would act in ways so as to make entry into their market difficult (Karakaya & Stahl, 1989. It is therefore interesting to find out the most appropriate entry mode that a firm should use when entering an oligopolistic market situation, factors that may influence the choice for entry mode and the challenges that such a firm would face due to barriers. Basar and Ho [l] consider a duopoly model with quadratic cost functions. They show existence and uniqueness of affine equilibrium strategies and that, in equilibrium, expected prof- its of firm i increase with the precision of its information and decrease with the precision of the rival’s information.Clarke [2] considers an n-firm oligopoly model and shows that there is never a mutual incentive for all firms in the industry to share information unless they may cooperate on strategy once in- formation has been shared. Harris and Lewis [6] consider a duopoly model where firms in period one decide on plant capacity before market conditions are known. In period two they choose a level of production contingent on the state of demand and their plant size. They argue that observed differ- ences in firm size and market share may be explained by pro- ducers having access to different information at the time of their investment decisions. Gal-Or [5] considers an oligopoly model with two stages. At the first firms observe a private signal and decide whether to reveal it to other firms and how partial this revelation will be. At the second, they choose the level of output. They shows that no information sharing is the unique Nash equilibrium of the game both when private signals are completely uncorrelat- ed and when they are perfectly correlated. In our model Cournot competition with a homogenous prod- uct is a particular case. Our findings for this case are consist- ent with those of the authors who use the Normal model. The demand structure (with no uncertainty) we consider is a sym- metric version of a duopoly model proposed by Dixit [4] the duality and welfare properties of which are analyzed in Singh and Vives [ 13 ]. 2. Cournot’s Model The Model may present many ways but in the original version, it makes the assumption that the two firms have identical product and cost. Cournot in his model takes two firms own- ing a spring of mineral water, which is produced at zero cost. Here we will present briefly the same version and then we will genelise it to n firm by using mathematical equations.