Oligopoly in Homogenous Good Markets: Static Analysis. * At the heart of oligopoly theory is the Bertrand model of price competition

Unique Nash Equilibrium: p1 = p2 = c. Proof: If pi = c, then there is no price at which firm j can earn strictly positive profit so that pj = c is a best response. Thus, p1 = p2 = c is a NE. To show uniqueness, note that if c < pi < pj , then firm j earns zero profit and can do strictly better by unilaterally deviating and charging a price ∈ (c, pi). If c = pi < pj , then firm i earns zero profit and can do strictly better by unilaterally deviating and charging a price ∈ (c, pj). If c < pi = pj = p(say), then firm i earns profit equal to 12D(p)(p − c) < D(p − )(p − − c) for > 0 sufficiently small (using continuity of D) and therefore firm i can do strictly better by unilaterally deviating and charging a price equal to p− .This exhausts all possibilities other than the NE described above. * Two firms sufficient to bring market power to zero and attain the socially optimal or competitive outcome. * Most aggressive model of price competition. * The Bertrand outcome is important not because it predicts real market outcomes but rather because it seems to be so different from observed real market outcome. Understanding why the Bertrand outcome does not occur in real markets helps us understand what kind of market institutions and interaction structures are important in creating real outcomes for example, in softening competition and enabling firms to make lot more money and exert lot more power than the bare Bertrand model. * The Bertrand outcome remains unchanged if there are more than 2 firms. * Asymmetric Duopoly. Each firm produces under CRS, unit cost of firm i is ci where