Social Preferences in Public Goods and Prisoner's Dilemma Games

Question 1

When does an individual exhibit social preferences?

Answer 1

When the individual cares about others’ payoffs

Question 2

monetary payoffs in the payoff matrix given to players do not necessarily represent what?

Answer 2

the players’ utilities

Question 3

What is a social dilemma?

Answer 3

An interactive decision where individual interest is at odds with collective interest, the pursuit of individual self-interest by every decision maker leaving everyone worse off than if each had acted cooperatively
- strategic interaction
- what is individually rational is not socially efficient

Question 4

What is the most efficient outcome in a Prisoner’s Dilemma?

Answer 4

both cooperate. When both are selfish they get the lower total surplus - both defect
Dominant strategy - both defect

Question 5

What is Nash Equilibrium in Prison’s Dilemma game?

Answer 5

Both defect

Question 6

What is a dominant strategy?

Answer 6

A strategy X strictly dominates a strategy Y if choosing X is better than choosing Y no matter what the other player does
- gives you a higher payoff compared to the other option, no matter what the other player does
- In the Prisoner’s Dilemma the strategy Defect strictly dominates the strategy Cooperate no matter what the other player does

Question 7

What is a Nash equilibrium?

Answer 7

NE (in pure strategies): Strategy profile where each player’s strategy is a best response to the other strategies in the profile.
idea: No player can be better off by unilaterally changing their strategy

Question 8

Real world examples of Prisoner’s Dilemma

Answer 8

• Price setting duopoly (D = charge low price, C = charge high price).
• Working on a joint project (D = not to work hard, C= to work hard)

Question 9

What is the takeaway from Prisoner’s Dilemma?

Answer 9

It cannot be expected that an efficient outcome will be achieved based on player’s self interest
- illustrate situations where gains from cooperation cannot be achieved (or are difficult to achieve) as it is individually rational for each player to defect.
Empirical Findings: individuals play (Cooperate, Cooperate) more often than predicted by theory. - consider different utility functions.

Question 10

Prisoner’s Dilemma played by two egoists/ selfish

Answer 10

U(x, y) = square root x
NE: (Defect, Defect)
Pareto-superior outcome: (Cooperate, Cooperate)

Question 11

Prisoner’s Dilemma played by two utilitarians

Answer 11

u(x, y) = square root of x + square root of y
- Two Nash-equilibria: (Cooperate, Cooperate) and (Defect, Defect)
- Pareto-Superior equilibrium (Cooperate, Cooperate)

Question 12

Prison’s Dilemma played by two enviers

Answer 12

u(x, y) = square root of x - square root of y
- Nash Equilibrium: (Defect, Defect)
- Game is transformed so that (Cooperate, Cooperate) is no longer a Pareto-superior outcome

Question 13

Prisoner’s Dilemma played by two Rawlsians

Answer 13

u(x, y) = min (square root x, square root y)
- Two Nah-equilibria: (Cooperate, Cooperate) and (Defect, Defect)
- Pareto-superior equilibrium: (Cooperate, Cooperate)

Question 14

Which two preferences help explain cooperation in the Prisoner’s Dilemma as they transform the (Cooperate, Cooperate) outcome in a Nash equilibrium - making it consistent with individual rationality for players

Answer 14

Utilitarian and Rawlsian preferences

Question 15

What is a Public Goods Dilemma?

Answer 15

• Situation where all individuals can benefit from cooperating (contributing) to a common good
• However, each individual has incentive (dominant strategy) to free ride (not cooperate, not contribute)
• Individually rational outcome =/ (does not equal) socially efficient outcome

Question 16

How does a Public Goods Dilemma differ from a Prisoner’s Dilemma game?

Answer 16

Public Goods Dilemma has:
- more than two players possible
- more than two actions possible
- Usually phrased in terms of endowment that can be used to contribute to a public good or to a private good

Question 17

What are some public goods dilemmas? (Free-rider problem examples:

Answer 17

• Tax compliance
• Adhering to Covid rules
• Cleaning the Neighbourhood
• Donating to the campaign of one’s preferred political party
• Managing natural resources (e.g., reducing carbon emissions)

Question 18

What is Pareto-superior outcome?

Answer 18

a situation where at least one person is made better off without making anyone else worse off, relative to an initial allocation or outcome
- If a change or decision improves someone’s well-being (utility) while leaving everyone else’s well-being the same or better, it is considered Pareto-superior.

Question 19

What is an Extensive margin?

Answer 19

Decision whether to become a contributor

Question 20

What is an Intensive margin?

Answer 20

Decision how much to contribute (conditional on becoming a contributor)

Question 21

What is the theoretical analysis of public goods games?

Answer 21

• Pareto dominant (efficient) solution is that all is invest in the public good
• However, individuals have incentive to free ride - the Nash Equilibrium is that each player contributes zero

Question 22

What are the experimental findings?

Answer 22

• In one-shot games, individuals contribute more than predicted by NE
• In one-shot games: average contribution of a group between 40%-60% of optimal level; individual contributions ranging from 0% to 100%; decreasing over time with random rematching each period

Question 23

Can sanctions help sustain cooperation?
Study of 112 participants at the University of Zurich
Key idea: examine the threat of punishment as a mechanism for inducing cooperation

Answer 23

Main Results Stranger Treatment
- Punishment threat causes rise in average contribution in Stranger treatment
Subjects contribute 2-4 times more than in No Punishment treatment
- In No-Punishment opportunities condition of Stranger Treatment contributions decrease over time. In contrast, they stay constant or even increase in the Punishment opportunities condition

Question 24

Main Results Partner Treatment

Answer 24

• existence of punishment opportunities causes large rises in contribution levels in Partner Treatment
• In no-punishment opportunities conditions of partner-treatment, average contributions converge toward free-riding
• In punishment opportunities conditions of partner-treatment they increase and converge towards full cooperation

Question 25

More on punishment

Answer 25

• punishment of those who contribute less than the average; the greater the difference with the average contribution the greater the punishment
• punishment is inconsistent with the predictions of standard theory (that is, with the assumption that an individual cares about own payoff only)
• punishment is inconsistent with altruism models as an altruistic person would not pay to reduce others’ payoffs
• it is consistent with reciprocity models and models of inequity aversion
• punishment can be an effective mechanism to sustain higher cooperation levels

Question 26

What do free riders contribute?

Answer 26

Nothing

Question 27

What do conditional cooperators contribute?

Answer 27

contributions to public good positively correlated with beliefs about contributions by group members

Question 28

What could conditional cooperation be due to?

Answer 28

• Reciprocity - fairness equilibrium
• Inequity aversion - contribute if I believe that others will contribute