Higher prices Hotels set prices Higher prices help others Low - - PDF document

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 1

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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.

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Individual versus Collective Action

Nash equilibrium

Game Externality Collection action (compared to Nash) Hotels set prices Higher prices help others

Higher prices

Driving Higher speeds hurt others

Low speeds

Cournot Higher quantities hurt others

Lower quantities

Parties (tables) in a restaurant decide how loudly to talk

Talking louder hurts others

Talk less loudly

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 2

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Complementors game

If firms “collude”, do they raise or lower prices?

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Complementors game

What is the cooperative outcome?

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 3

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Complementors game: Nash equilibrium

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Ways to improve upon Nash

• 1. External enforcement: Sign contracts, pass laws, merge two firms.
• 2. Tacit, self-enforcing cooperation: through repeated interaction.

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 4

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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.

8

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.

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 5

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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 P-low 300 300 150 850 Jeff P-high 850 150 700 700

Strategy: A plan of what to do at each time (e.g., each day) based on the history of play so far.

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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.”

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 6

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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 r

≥ 850 + 300

r

⇐ ⇒ 400/r ≥ 150 ⇐ ⇒ r ≥ 400/150 = 267%

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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.

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 14 • Explicit and Implicit Cooperation Page 7

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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.