4. Oligopoly Topics Review of basic models of oligopolistic competition How can firms change the rules of game to their advantage? How can firms avoid intensive rivalry? Read or review Oligopoly chapter in any modern Micro or IO textbook to make sure you are comfortable with game theoretic reasoning and Nash equilibrium Europe Economics report Note: topics following oligopoly (Collusion and Mergers) will be based on oligopoly theory HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Assumptions Market demand: price function of total quantity produced, p = p(q), eg. p = a - bq Assume 2 firms on relevant market denoted by i and j Firms produce quantities qi and qj Firms have total costs ci(qi,qj) No threat of entry Profits for firm i = Total Revenue - Total Costs = pi(qi,qj) = p(qi+qj)qi - ci(qi,qj) Note: i's profit depends on what rival j does, unlike in monopoly or perfect competition Firm faces a problem of strategic interaction or plays a game HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition How much will i want to produce? Depends on how much i expects j to produce, qje How much will j want to produce? Depends on how much j expects i to produce, qie Note, for each qje, there is an optimal output qi*(qje) = argmax i(qi,qje) qi*(qje) is called i’s reaction function Compare with monopoly profit max Problem i needs to put himself on j’s position and try to predict how j will behave j needs to put himself on i’s position and try to predict how i will behave i needs to to put himself on j’s position and try to predict how j will think how i will behave 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition j needs to ... predict how i will think how j will behave etc. ad inf. Solution Suppose both i and j know p(q), ci(qi,qj), and cj(qj,qi), and also expect that rival will produce profit-maximizing quantity qi*(q-ie) = argmax j(qi,q-ie) Now i chooses qi* = argmax i(qi,qj*) and j chooses qj* = argmax j(qj,qi*) Each firm chooses its strategy taking rivals equilibrium strategy as given Firm i needs to predict j’s equilibrium production To solve, simplify further: ci(qi,qj) = ciqi, ci = constant MC Now i = p(qi+qj)qi - cqi 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Simultaneously but individually max i = p(qi+qj)qi - cqi max j = p(qi+qj)qi - cqj  di/dqi = q(dp/dqi) + p(qi+qj) - ci = 0 dj/dqj = q(dp/dqj) + p(qi+qj) - cj = 0 These are familiar 1st order conditions MR - MC = 0 Compare with monopoly profit max Plug in p(qi+qj) = a - b(qi+qj) and solve for qi*(qje) and qj*(qie), you get reaction fns: (1) qi*(qj) = (a - ci)/2b - qj/2 (2) qj*(qi) = (a - cj)/2b - qi/2 Solve simultaneously [eg, insert qj*(qi) from (2) into (1)] to get Cournot-Nash equilibrium quantities 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition (3) qi* = (a + cj - 2ci)/3b (4) qj* = (a + ci - 2cj)/3b Note: Each firms is on her reaction function In equil, no firm has incentive to alter her strategy choice unilaterally Insert qi* and qj* to demand fn to get equil price p*, and then plug these to profit fn to get equilibrium profits Note: reaction fns (1) and (2) are downward-sloping: dqi*(qi)/dqj = -1/2 < 0 This also applies to more general Cournot games If j increases her production (eg, due to reduction in marginal cost cj), i will want to reduce his output Lower action from one firm induces higher reaction from her rivals 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Strategies qi are here strategic substitutes Downward-sloping rfs  strategic substitutes Properties of Cournot-Nash Equil Go back to reaction functions (1) and (2), and rewrite as (5) p(q) - ci = -qi dp/dqi |:p  (6) Li = si/e, si = qi/q is i’s market share, q = iq, Li = (p - ci)/p is firm i’s mark-up or Lerner Index e = -p(q)/qp’(q) is elasticity of market demand (6) is basic Cournot pricing formula In Cournot-Nash equilibrium, market share determined by firm’s relative cost efficiency and demand elasticity 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Each firm has limited mkt power: i’s marginal revenue MRi = p + qip’, so p - MRi = qip’(q) > 0  MR > M Smaller mkt shares s (or more rivals)  smaller mark-up, ie. competion more vigorous Greater demand elasticity  larger mark-up, less competitive equil Mark-up is proportional to firm mkt share Mkt shares are directly related to firms cost-efficiency ci Less efficient firms are able to survive sj > 0 even if cj >> min c Average industry-wide mark-up i si (p - ci)/p = MU In Cournot-Nash equil, MU = i si2/e = HHI/e, where HHI is the Herfindahl-Hirschman Index Performance negatively related to HHI HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Aside What if there are more than 2 firms? Interpert j as vector of all other firms and proceed as above Each firm takes the actions of other firms as given, and assumes all firms are maximizing profits What if i doesn’t know j’s costs cj(qj,qi) exactly? Just assume i is Bayesian decision-maker, who makes subjective probability assesment for cj(qj,qi), uses expected costs Eicj(qj,qi), and then proceed as above Existence of equil? Uniqueness of equil? Not guaranteed for general p(q) and c(.) Coordination problem if more than one equil strategy combination 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.2 Bertrand or Price Competition In reality, firms choose and compete w/ prices Often prices are easier to adjust than quantities Who chooses prices in Cournot game? Cournot unrealistic model? Naive thought: firms select prices as in (6) above: pi* st. (pi* - ci)/pi* = si/e? Bertrand paradox: No Model: identical product, mkt demand q = q(p), eg q = a-bp Demand for firm i: pi > pj  i cannot sell at all, qi = 0 pi = pj  i and j split demand, qi = q(p)/2 pi = pj  i sells total mkt demand, qi = q(p) HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Note: small change in rival’s price causes huge change in firm’s demand Suppose cj = ci = c If i charges pi > c, j can increase her profits by undercutting i slightly If i charges pi < c, i is making losses but j can guarantee j = 0 by staying out of mkt  Only equil price can be pi = pj = c Duopoly enough for perfect competition! Depends crucially on firms able and willing to serve all customers at announced price identical products customers have complete information eg on prices  Then firms have no bargaining power 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Product Differentation and Price Competition Simple example only Products are imperfect substitutes, demands are symmetric qi = a - fpi + gpj Assume constant marginal costs ci Product differentation is assumed fact, not designed by firms g/f measures degree of product differentation (how?) Profit for i here i = pi qi(pi,pj) - ci(q(pi,pj)) = (pi - ci)(a - fpi + gpj) Bertrand-Nash equil found similarly as above: max profit wrt to strategy variable pi solve for rfs find where rfs intersect solve for prices, quantities, and profits 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Rfs slope up  the higher price i charges, the higher the price rival j wants to charge Prices are strategic complements Higher strategy draws a higher reaction from rivals Upward-sloping rfs  strategic complements Homework Assume qi = a - fpi + gpj and ci = 0 Prove: In price competition with differentiated products, reaction functions slope up Solve for Bertrand-Nash equil prices, quantities and profits for game above Solve for Cournot-Nash equil quantities, prices, and profits for game w/ same demands and c = 0 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

3.1 Cournot or Quantity Competition Capacity Constraints and Price Competition What if firms first choose capacities q and then, knowing all q’s, select prices p? We have a 2-stage game (more on this later) In equil, higher price than w/o capacity constraints Intuition: limited capacity  business stealing not attractive option  want to price less aggressively  rival prices less aggressively  higher profits Cournot outcome possible w/ price competition Interpret: Cournot = capacity competition Cournot mkts where production desicions in advance, flexible price, high storage costs consistent w/ empirical evidence Bertrand more realistic assumptions? 3.1 Cournot or Quantity Competition HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Simplest way to model dynamic rivalry; to model j’s reactions to strategic moves by firm i Simplest way of allowing firms to change game they are playing Idea: Choose a strategy now that affects game you play tomorrow st your expected profits increase Capacity-Price -model above an example: Smaller capacity now  reduce ability to compete aggressively in future  draw less aggressive reactions from rivals  higher profit Stackelberg Oligopoly Stackelberg-Cournot game: Firm i chooses its output first, and j after i’s choice Precommitment by i is relevant, not physical timing of moves HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Solve by backward induction: First look at last possible moves of the game What is optimal last move? Then work backward to beginning of game, as in dynamic programming Given last move will optimal, what is optimal penultimate move? Game tree (compare to decision tree) Simple mode: Demand p = a - b(qi + qj), c = 0 Last move When j chooses her capacity, she knows i’s capacity qiS j's optimal capacity determined by her reaction function (2) qj*(qi) = a/2b - qi/2 HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Penultimate move To design good strategy, i must put himself on j’s shoes and try to think how he would behave were he the last to move i chooses qiS to max profits, taking as given i’s reaction function, not equilibrium output as in Cournot game i chooses best point from rival’s reaction function Plug (2) into i’s profit function (a - b(qi+qj))qi and solve for qiS Plug qiS back to (2) and solve for qj*, and then solve for prices and profits In Stackelberg game, i’s profits higher and j’s lower than in Cournot game First-mover advantage Intuition: Commit to flood the market  induces rival to lower output  increases your profit HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Crucial reasons: 1) commitment, 2) strategies substitutes Equil above “subgame perfect Nash equilibrium” Also other Nash equil possible: i announces to produce qi s.t. p(qi) < cj if j enters This is not be credible: i will not want to undertake threat should j enter (more on this later) Homework Solve Stackelberg equilibrium capacities, prices and profits You can assume symmetric demands qi = a - fpi + gpj, qj = a - fpj + gpi and c = 0 Show: In Stackelberg-Bertrand duopoly, there is second mover advantage. You can assume symmetric demands as above HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Dynamic Competition 2 time periods, denoted by 1 and 2 Firm i can take strategic action k on period 1 Strategic action measured by its cost Strategy k is sunk on 2nd period, i cannot revoke it k is investment, precommitment On period 2, i and j compete Assume k does not affect j’s demand or costs directly i’s 2nd period profits are i(qi,qj,k) i’s 1st period profits are i (qi,qj,k) - k k shifts i’s 2nd period profit fn Strategic move k alters i’s own incentives to choose later 2nd period tactics To find equil, solve for by backward induction starting from 2nd period game HKKK TMP 38E050 © Markku Stenborg 2005

For given k, equil again given by di/dqi = 0 di/dqj = 0 2nd period For given k, equil again given by di/dqi = 0 di/dqj = 0 2nd period reaction functions qi(qj,k) and qj(qi,k), and optimal tactics qi*(k) are now functions of k Equil profits are i(qi*(k),qj*(k),k) 1st period How to choose k? Profits i(qi*(k),qj*(k),k) - k To find max profit, differentiate i wrt k to get MR – MC = 0; this gives 1 = - + dk d dq i j  HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition First term is zero because i will choose tactic qi st di/dqi = 0; we have: LHS 2nd term: direct effect LHS 1st term: strategic effect RHS: Direct cost of commitment How can k alter j’s 2nd period tactics since k does not directly affect j’s profits? Strategic move k alters i’s own incentives to choose  alters j’s incentives to react  changes i’s profits Sign of strategic effect is equal to sign of 1 = + dk d dq ) k , q ( i * j  j i dq d dqj dk  2 HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Three effects How commitment k changes i’s own optimal tactics How j reacts to changes in i’s incentives How i’s profits are affected by changes in j’s tactics Strategic effect > 0  overinvest in k Strategic effect < 0  underinvest in k Example: Cost reduction in Cournot and Bertrand games How reaction functions shift as marginal costs of j are decreased? Example: Increased marketing in Cournot and Bertrand games How reaction functions shift as j increases her marketing expenses? HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Taxonomy for Strategies Strategic substitutes vs complements Cournot game = strategic substitutes Bertrand game = strategic complements Commitment makes firm tough vs soft Investment k makes i tough i will produce more or price below k shifts i’s rf right and up in Cournot game k shifts i’s rf right and down in Bertrand game Investment k makes i soft i will produce less or price above k shifts i’s rf left and down in Cournot k shifts i’s rf left and up in Bertrand HKKK TMP 38E050 © Markku Stenborg 2005

Strategic Complements (eg, prices) Puppy Dog Ploy Commitment makes firm Stage 2 variables are Tough Soft Strategic Complements (eg, prices) Puppy Dog Ploy Strategic effect < 0 Commitment cause rivals behave more aggressively Fat Cat Effect Strategic effect > 0 Commitment cause rivals behave less aggressively Strategic Substitutes (eg, capacities) Top-Dog Strategy Lean and Hungry Look Commitment cause rival behave more aggressively HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Strategic Incentives to Commit in Cournot Commitment makes firm tough Firm will produce more for all given rivals’ output Reaction function shifts outward Example: Marginal cost reducing innovation Beneficial side-effect Strategic effect might outweigh direct effect  Invest even if NPV < 0! Top-Dog: Big or strong to become aggressive Commitment makes firm soft Firm will produce less for all given rivals’ output Reaction function shifts inward Example: Marginal cost increasing entry into other mkt  Even monopoly might not be enough Negative side-effect Lean and Hungry Look: Refrain from expanding to avoid weakness HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Strategic Incentives to Commit in Bertrand Commitment makes firm tough Firm will underprice Reaction function shifts inward Example: MC-reducing innovation Negative side-effect Puppy-Dog Ploy: stay small or weak to avoid agressive competition  Do not lower costs! Commitment makes firm soft Firm will overprice Reaction function shifts outward Beneficial side-effect Example: Target small niche, Product differentation Fat-Cat Effect: Become soft to attract only weak competition  Sumo-strategy HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Need to look more than just direct effects of irreversible decisions Nature of future competition affects incentives to make investments or commitments now Examples of 1st Stage Commitments Build excess capacity  deter entry Enter and underinvest  avoid attracting tough competition R&D: reduce costs  price aggressively / gain mkt share Networks: build large customer base, costly to switch  less competition in future Patent licensing  withhold or exchange key info or patents with rivals Underinvest in marketing  less loyal customers  become aggressive in 2nd stage Overinvest in marketing  loyal customers  become soft in 2nd stage HKKK TMP 38E050 © Markku Stenborg 2005

2.4 Two-Stage Competition Merger: profitable under Bertrand, unprofitable under Cournot competition Make products less similar  soften price competition Financial structure: overleverage to make managers more aggressive Managerial compensation: Tie managers’s compensation on sales  Stackelberg equil Long-term contracts with customers, Most favorite nation clause  reduce incentive to cut prices Customer Swithcing Costs: lock in customers  less incentives to go after new customers  draw less aggressive reactions from rivals Multimarket Contact  strategic effects from mkt 1 to mkt 2 HKKK TMP 38E050 © Markku Stenborg 2005