Microeconomics: Strategic Interaction Dr Hamish Low

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MicroeconomicsStrategic InteractionDr Hamish
Low

• Lecture 4

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Main Issues
Why cooperate? How to increase cooperation?
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Outline

• Payoffs and observed time path
• Cooperation or competition
• Communication and reputation
• Public goods characteristics
• Strategic interaction and the Prisoners dilemma

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Why Cooperate?

• Fairness / altruism ?
• Signal (reputation) for private gain?

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Payoffs
Every team contributes 2 red cards Each round
each team receives 38 total earnings of
722 Total for all rounds each team
570 Every team contributes 2 black
cards Each 4 round each team receives
8 total earnings of 152 Total for all
rounds each team receives 120
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Cooperation or Competition
Other 18 Teams
Payoff to team 1
Contribute 2 Red
Contribute 2 Black
Contribute 2 Red
2
38
Team 1
Contribute 2 Black
44
8
Conflict between optimal choice for whole group
and optimal choice for own team
Free-Riding on contributions of others
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Time Path of Cooperation
0.8
Teams on your left
0.7
0.6
0.5
of red cards contributed
0.4
0.3
0.2
Teams on your right
0.1
1
2
3
4
5
6
7
8
9
10
11
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Round Number
8
Average Earnings
0.8
Teams on your left
0.7
0.6
0.5
of max earnings
0.4
0.3
0.2
Teams on your right
0.1
1
2
3
4
5
6
7
8
9
10
11
12
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Playing All Black or All Red
All black
of max earnings
All red
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Comments
(1) Inefficiency (2) Effect of reducing the
value of keeping a red card (3) Cooperation
declines over time
(4) Average number of red cards played per
round up to communication stage (5) Most groups
either 2 red or 2 black
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Two Player Situation
Player 2
Payoff to player 2
Payoff to player 1
Contribute 2 Red
Contribute 2 Black
Contribute 2 Red
2, 10
4, 4
Player 1
Contribute 2 Black
10, 2
8, 8
Nash Equilibrium player 1s strategy is optimal
given player 2s strategy player 2s strategy is
optimal given player 1s strategy
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Alternative Game

• 1 per red card contributed is only paid if both
  players contribute both red cards
• If no one plays a red card, each red card kept
  is only worth 1
• Same relative payoffs as in 10am lecture

Player 2
Contribute 2 Red
Contribute 2 Black
Contribute 2 Red
0, 8
4, 4
Player 1
Contribute 2 Black
8, 0
2, 2
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Nash Equilibrium player 1s strategy is optimal
given player 2s strategy player 2s strategy is
optimal given player 1s strategy

• Nobody wants to change their behaviour given the
  choices made by others.
• Optimising individuals
• Feasible

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Communication

• Each team wants all other teams to contribute 2
  red cards
• Communication seems to enable agreement that
  this is the best strategy
• Problem is that not enforceable - talk is
  worthless?

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Reputation / Repetition

• Each team wants all other teams to contribute 2
  red cards
• A reputation for contributing red cards may lead
  others to contribute red cards
• Need repetition to establish a reputation but
  reputations can be bad as well as good.
• Need a punishment strategy - how to respond if
  the other person cheats (also, for communication
  to work)
• Trigger strategies

Strat Inter
Govt Policy
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Public Goods Characteristics

• Non-rivalrous
• marginal cost of an additional consumer is 0
• if group size increases, no additional cost to
  contributing 2 red cards
• Non-excludable
• cannot stop those who have not contributed from
  benefiting
• (inability to monitor non-cooperation)
• if someone contributes 2 black cards, cannot stop
  them benefiting from total number of red cards

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Public Goods Examples

• Defence spending
• Street lights
• Voluntary provision to charities

Private market leads to under-provision and there
is potential for a Pareto improvement (make
everyone better off)
Possible solutions?
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Government Intervention

• Government uses taxation - forcing everyone to
  contribute 2 red cards.
• Works so long as individuals have identical
  preferences and identical endowments of money
• What if different attitudes towards war? Cannot
  stop others from benefiting
• only make those who want war pay? preference
  revelation problem (free riding again) - pretend
  to dislike war to avoid paying
• make everyone pay. Those who want war do not
  bear the cost that their choice imposes on others

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Strategic Interaction

• Two aspects to economic analysis
• Individuals take advantage of opportunities.
  Optimisation
• The opportunities of one individual depend on the
  actions of others.
• Interaction

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Bargaining Problems

• Goals are non-identical
• Not zero-sum
• competitive markets as extreme where do not need
  to know preferences of neighbour.
• prisoners dilemma

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Prisoners Dilemma
Player 2
Cooperate (deny the charge)
Contribute 2 Red
Contribute 2 Black
Contribute 2 Red
0, 8
4, 4
Player 1
Contribute 2 Black
8, 0
2, 2
Cheat (admit the charge and implicate the other)
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Conclusion

• Incentives to deviate
• experiment showed this in public goods situation
  (Free-riding on the contribution of others)
• more generally, this is an example of a set of
  interactions known as the Prisoners Dilemma.
• interesting when interaction is not zero-sum
  (cooperation would be beneficial)
• Communication does not help
• Repetition allows reputations to develop
• Public goods non-rivalrous and non-excludable.
  Is there a role for government involvement?
• Nash Equilibrium good predictor ?