Session 14: Explicit and Implicit Cooperation ➥ 1. Nash equilibrium versus collective action. 2. Honeywell-GE merger. 3. P&M meets LPG: Sustaining cooperation through repeated interaction. Session 14 • Explicit and Implicit Cooperation Slide 1 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Individual versus Collective Action Nash equilibrium Collection action Game Externality (compared to Nash) Higher prices Hotels set prices Higher prices help others Low speeds Driving Higher speeds hurt others Lower quantities Cournot Higher quantities hurt others Parties (tables) in a restaurant Talk less loudly Talking louder hurts others decide how loudly to talk Session 14 • Explicit and Implicit Cooperation Slide 2 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Complementors game If firms “collude”, do they raise or lower prices? Session 14 • Explicit and Implicit Cooperation Slide 3 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Complementors game What is the cooperative outcome? Session 14 • Explicit and Implicit Cooperation Slide 4 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Complementors game: Nash equilibrium Session 14 • Explicit and Implicit Cooperation Slide 5 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Ways to improve upon Nash 1. External enforcement: Sign contracts, pass laws, merge two firms. 2. Tacit, self-enforcing cooperation: through repeated interaction. Session 14 • Explicit and Implicit Cooperation Slide 6 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 14: Explicit and Implicit Cooperation ✓ 1. Nash equilibrium versus collective action. ➥ 2. Honeywell-GE merger. 3. P&M meets LPG: Sustaining cooperation through repeated interaction. Session 14 • Explicit and Implicit Cooperation Slide 7 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 14: Explicit and Implicit Cooperation ✓ 1. Nash equilibrium versus collective action. ✓ 2. Honeywell-GE merger. 3. P&M meets LPG: Sustaining cooperation through repeated interaction. ➥ Session 14 • Explicit and Implicit Cooperation Slide 8 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Repeated Prisoner’s Dilemma Suppose the stage game is the following “Prisoner’s Dilemma”. Akbar and Jeff own competing gas stations, and can choose either to price high or to price low. Akbar P-low P-high 300 150 P-low 300 850 Jeff 850 700 P-high 150 700 Strategy: A plan of what to do at each time (e.g., each day) based on the history of play so far. Session 14 • Explicit and Implicit Cooperation Slide 9 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Suppose game is repeated forever Which of these are equilibrium strategies? 1. “Price low no matter what has happened so far”. 2. “Price high until Jeff prices low. Then price low forever, no matter what happens.” Session 14 • Explicit and Implicit Cooperation Slide 10 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
When is Grim Trigger an equilibrium in this example? 1 What are the outcomes if Jeff sticks to the strategy? HH , HH , HH , . . . 700 700 700 2 PDV of flow of payoffs? 700 + 700 r 3 What are the outcomes if Jeff defects in period 1? LH , LL , LL , . . . 850 300 300 4 PDV of flow of payoffs? 850 + 300 r 5 When is it better for Jeff to stick to the strategy? 700 + 700 ≥ 850 + 300 ⇒ 400 / r ≥ 150 ⇐ ⇒ r ≥ 400 / 150 = 267% ⇐ r r Session 14 • Explicit and Implicit Cooperation Slide 11 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Wrap up on repeated games If a static game is repeated: • there is room for players to make credible threats and promises that support cooperation. • cooperation is not assured, but give it a try if the gain from cooperation is high. Session 14 • Explicit and Implicit Cooperation Slide 12 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
Session 14: Explicit and Implicit Cooperation ✓ 1. Nash equilibrium versus collective action. ✓ 2. Honeywell-GE merger. 3. P&M meets LPG: Sustaining cooperation through repeated interaction. ➥ Session 14 • Explicit and Implicit Cooperation Slide 13 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets
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