Transcript Oligopoly
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 1 © 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 2 © Markku Stenborg 2005 • How much will i want to produce? 3.1 Cournot or Quantity Competition – 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 HKKK TMP 38E050 © Markku Stenborg 2005 3 • j needs to ... predict how i will think how j will behave 3.1 Cournot or Quantity Competition • 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 HKKK TMP 38E050 4 © Markku Stenborg 2005 • Simultaneously but individually 3.1 Cournot or Quantity Competition max i = p(qi+qj)qi - cqi max j = p(qi+qj)qi - cqj di/dqi = q(dp/dqi) + p(qi+qj) - ci = 0 dj/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) (2) qi*(qj) = (a - ci)/2b - qj/2 qj*(qi) = (a - cj)/2b - qi/2 Solve simultaneously [eg, insert qj*(qi) from (2) into (1)] to get Cournot-Nash equilibrium quantities HKKK TMP 38E050 5 © Markku Stenborg 2005 (3) (4) qi* = (a + cj - 2ci)/3b 3.1 Cournot or Quantity Competition 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 HKKK TMP 38E050 6 © Markku Stenborg 2005 • Strategies qi are here strategic substitutes 3.1 Cournot or Quantity Competition • Downward-sloping rfs strategic substitutes Properties of Cournot-Nash Equil • Go back to reaction functions (1) and (2), and rewrite as (5) (6) p(q) - ci = -qi dp/dqi |:p 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 HKKK TMP 38E050 7 © Markku Stenborg 2005 Competition • Each 3.1 firm Cournot has limited or mktQuantity 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 8 © Markku Stenborg 2005 Aside 3.1 Cournot or Quantity Competition • 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 HKKK TMP 38E050 9 © 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 10 © Markku Stenborg 2005 • Note: small change in rival’s price causes huge change in 3.1 Cournot or Quantity Competition 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 HKKK TMP 38E050 11 © Markku Stenborg 2005 Product Differentation and Price Competition 3.1 Cournot or Quantity 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 HKKK TMP 38E050 12 © Markku Stenborg 2005 • Rfs slope up the higher price i charges, the higher the 3.1 Cournot or Quantity Competition 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 HKKK TMP 38E050 13 © Markku Stenborg 2005 Capacity Constraints and Price Competition 3.1 Cournot or Quantity 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? HKKK TMP 38E050 14 © 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 15 © Markku Stenborg 2005 • Solve by backward induction: Competition 2.4 Two-Stage – 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 16 © Markku Stenborg 2005 Penultimate 2.4 move Two-Stage Competition • 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 17 © Markku Stenborg 2005 • • • • • Crucial reasons: 1) commitment, 2) strategies substitutes 2.4 Two-Stage Competition 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 18 © 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 19 © Markku Stenborg 2005 2nd period • For given k, equil again given by di/dqi = 0 di/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 d dq i i i dk dq + d dq j dq i j dk + d i dk -1 = 0 HKKK TMP 38E050 20 © Markku Stenborg 2005 • First term is zeroTwo-Stage because i will Competition choose tactic qi st 2.4 di/dqi = 0; we have: d i ( qi* ,q*j ,k ) dq*j d i + =1 dq j dk dk • • • • 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 d 2 i d 2 i d i dqi dk dqi dqj dq j HKKK TMP 38E050 21 © Markku Stenborg 2005 Three effects 2.4 Two-Stage Competition • 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 22 © Markku Stenborg 2005 Taxonomy for Strategies 2.4 Two-Stage Competition • 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 23 © Markku Stenborg 2005 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 Strategic effect > 0 Commitment cause rivals behave less aggressively Lean and Hungry Look Strategic effect < 0 Commitment cause rival behave more aggressively HKKK TMP 38E050 24 © Markku Stenborg 2005 Strategic Incentives to CommitCompetition in Cournot 2.4 Two-Stage • 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 25 Strategic Incentives to CommitCompetition in Bertrand 2.4 Two-Stage • 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 26 © Markku Stenborg 2005 • Need to look more than just direct effects of irreversible 2.4 Two-Stage Competition 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 27 © Markku Stenborg 2005 • Merger: profitable under Bertrand, unprofitable under 2.4 Two-Stage Competition 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 28 © Markku Stenborg 2005