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: Max. your profit • # of plays: 1 only • Good: Homogeneous • Choice variable: Quantity • Timing of choice: Simultaneous Game Payoffs Firm 2 (competitor) 15 20 Firm 1 15 (you) 20Game Payoffs Firm 2 (competitor) 15 20 22.5 30 15 20 22.5 Firm 1 (you) 30 450, 450 375, 500 338, 506 225, 450 500, 375 400, 400 350, 394 200, 300 506, 338 394, 350 338, 338 125, 150 450, 225 300, 200 150, 125 0, 0The Game (a*) • Objective: Max. your profit • # of plays: 2 • Good: Homogeneous • Choice variable: Quantity • Timing of choice: SimultaneousThe Game (a**) • Objective: Max. your profit • # of plays: 10 • Good: Homogeneous • Choice variable: Quantity • Timing of choice: SimultaneousAnalytics: 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 QMR1 = dR1/dQ1 = 60 - 2Q1 -Q2 Set MR1 = MC = 0, which yields 1 = 30 - ½ Q2 (Firm 1 reaction curve)Cournot Equilibrium QQ• Symmetric reaction curves: 1 = 30 - 1/2 Q2 (Firm 1) 2 = 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 = 400Duopoly: Graphical Version Q2 Firm 2’s Reaction Curve 15 20 30 60 Collusive Outcomes Q1 30 60 15 20 Firm 1’s Reaction Curve Cournot EquilibriumDuopoly Analytics -- Collusion Demand: P = 60 – Q Π = P · Q - Costs = (60 - Q)·Q dΠ = 60 − 2Q = 0dQ ⇒ Q = Q1+ Q2= 30, P = 30 Total joint Π = 30(30) = 900 If split equally, Π1= Π2 = 450The Game (b) • Objective: Max. your profit • # of plays: 1 • Good: Homogeneous • Choice variable: Q • Timing of choice: Someone goes first Game PayoffsFirm 2 (competitor) 15 20 22.5 30 15 20 22.5 Firm 1 (you) 30 450, 450 375, 500 338, 506 225, 450 500, 375 400, 400 350, 394 200, 300 506, 338 394, 350 338, 338 125, 150 450, 225 300, 200 150, 125 0, 0Analytics 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 accountFirst 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 1) Firm 2’s Reaction (30 - ½ Q2= 30Q1 -½ (Q1)• Firm 1 marginal revenue: MR1 = dR1/dQ1 = 30 - Q1 First Mover - The Result • Firm 1 marginal revenue: MR1 = 30 - Q1 QQ•Set MR1 = MC (= 0), and 1 = 30 2 = 30 - ½ Q1 = 15 • Price: P = 60 - (Q1+ Q2) = 15 Π• Profits: Π1= 30 ·15 = 450 2= 15 ·15 = 225The Game (c) • Objective: Max. your profit • # of plays: 1 • Good: Homogeneous • Choice variable: Price • Timing of choice: SimultaneousStrategic 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: Max. your profit • # of plays: 1 • Good: Differentiated • Choice variable: Price • Timing of choice: SimultaneousTake 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. Preparation for Next Time Regarding “Lesser Antilles Lines” Case: • Good case for developing game and payoff analysis (assumptions, payoffs, etc.). • You do NOT need to prepare this for class (part of Problem Set