Game Theory and Competitive Strategy I

Overview: Game Theory and Competitive Strategy I Small Numbers and Strategic Behavior • Fun and games with a duopoly example – – – – Simultaneous vs. sequential choice One-time vs. repeated game Quantity vs. price as the choice variable Homogeneous vs. differentiated good • Review of the analytics Key Ideas • Know strategic situation (What is the game?). • Your competitor is just as smart as you are! • Think about the response of others • Nash equilibrium: all participants do the best they can, given the behavior of competitors. The Game (a) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 1 only Homogeneous Quantity Simultaneous Game Payoffs Firm 2 (competitor) 15 Firm 1 15 (you) 20 20 Game Payoffs Firm 2 (competitor) Firm 1 15 20 22.5 30 15 450, 450 375, 500 338, 506 225, 450 20 500, 375 400, 400 350, 394 200, 300 22.5 506, 338 394, 350 338, 338 125, 150 30 300, 200 150, 125 0, 0 (you) 450, 225 The Game (a*) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 2 Homogeneous Quantity Simultaneous The Game (a**) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 10 Homogeneous Quantity Simultaneous Analytics: Simultaneous Cournot • • • • Homogeneous good, simultaneous choice Choosing quantity, Q Objective: Max. your profit Market demand: P = 60 - Q • Production: Q = Q1 + Q2 MC1 = MC2 = 0 What Is the Firm’s Reaction Curve? (Firm 1 example) • To max profit, set MR = MC R1 = PQ1 = (60 - Q)Q1 = 60Q1 - (Q1 + Q2)Q1 = 60Q1 - (Q1)2 - Q2Q1 MR1 = dR1/dQ1 = 60 - 2Q1 - Q2 Set MR1 = MC = 0, which yields Q1 = 30 - ½ Q2 (Firm 1 reaction curve) Cournot Equilibrium • Symmetric reaction curves: (Firm 1) Q1 = 30 - 1/2 Q2 Q2 = 30 - 1/2 Q1 (Firm 2) • Equilibrium: Q1 = Q2 = 20 • Total quantity: Q = Q1 + Q2 = 40 • Price: P = 60 - Q = 20 • Profits: Π1 = Π2 = 20·20 = 400 Duopoly: Graphical Version Q2 60 Firm 1’s Reaction Curve Cournot Equilibrium 30 20 15 Collusive Outcomes Firm 2’s Reaction Curve 15 20 30 60 Q1 Duopoly Analytics -- Collusion Demand: P = 60 – Q Π = P · Q - Costs = (60 - Q)·Q dΠ = 60 − 2Q = 0 dQ ⇒ Q = Q1 + Q2 = 30, P = 30 Total joint Π = 30(30) = 900 If split equally, Π1 = Π2 = 450 The Game (b) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 1 Homogeneous Q Someone goes first Game Payoffs Firm 2 (competitor) Firm 1 15 20 22.5 30 15 450, 450 375, 500 338, 506 225, 450 20 500, 375 400, 400 350, 394 200, 300 22.5 506, 338 394, 350 338, 338 125, 150 30 300, 200 150, 125 0, 0 (you) 450, 225 Analytics with a First Mover (Decision variable is Q) • Suppose Firm 1 moves first • In setting output, Firm 1 should consider how Firm 2 will respond • We know how Firm 2 will respond! It will follow its Cournot reaction curve: Q2 = 30 - 1/2 Q1 • So Firm 1 will maximize taking this information into account First Mover: Max Π given the Reaction of the Follower • Firm 1 revenue: R1 = Q1P = Q1(60 - [Q1 + Q2]) = 60Q1 - (Q1)2 - Q1Q2 = 60Q1 - (Q1)2 - Q1 (30 - ½ Q1) = 30Q1 - ½ (Q1)2 Firm 2’s Reaction • Firm 1 marginal revenue: MR1 = dR1/dQ1 = 30 - Q1 First Mover - The Result • Firm 1 marginal revenue: MR1 = 30 - Q1 • Set MR1 = MC (= 0), and Q1 = 30 Q2 = 30 - ½ Q1 = 15 • Price: P = 60 - (Q1 + Q2) = 15 • Profits: Π1 = 30 ·15 = 450 Π2 = 15 ·15 = 225 The Game (c) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 1 Homogeneous Price Simultaneous Strategic Substitutes vs Complements • Strategic Complement: reactions match – e.g. lower price is reaction to competitor’s lower price • Strategic Substitute: opposite reactions – e.g. lower quantity is reaction to competitor’s higher quantity • Competition tends to be more aggressive with strategic complements than with substitutes. The Game (c*) • • • • • Objective: # of plays: Good: Choice variable: Timing of choice: Max. your profit 1 Differentiated Price Simultaneous Take Away Points • Game theory allows the analysis of situations with interdependence. • Nash Equilibrium: Each player doing the best he/she can, given what the other is doing. • Competition in strategic complements (price) tends to be tougher than in substitutes (quantity). • Commitment is important since you change the rules of the game. It can lead to a first-mover advantage. • Repetition can lead to cooperation, but only when the end-game is uncertain or far away.