Public goods experiments
Jiří Špalek
Overview
• Public good and free rider problem
• VCM model and equilibrium
• Factors alleviating cooperation
• Selected designs (threshold, lottery, sanctions)
• Applications
– Tax compliance
Public good
• Non-rivalrous
• Non-excludable
=> „Market failure“, i.e. impossibility of
voluntary contribution
PG and games
Cooperate Defect
Cooperate 1,1 -1,2
Defect 2,-1 0,0
Prisoners dilemma
Straight Turn
Straight -10,-10 2,-1
Turn -1,2 0,0
Game of Chicken
To defect is dominant strategy No dominant strategy
Unique Nash equilibrium is
Zero contribution
Usually multiple equilibria
PGG as Coordination problem
Voluntary Contributions to PG: the Model
• the participants decide which part of their
disposable income (y) they would contribute to a
PG (gi) and which part they would keep
• a – Marginal Per Capita Return (MPCR)
• Corner solution - Invest all if a>1, else nothing
Why people cooperate?
• Social preferences
– Altruism, warm glow, efficiency-seeking motives
– Conditional cooperation, reciprocity
• Strategic cooperation
– Strategies such as Tit-for-Tat can support cooperation
among selfish players
• By mistake
– Do not understand that ci= 0 is dominant
– Do understand dominance but make systematic errors
Altruism, warm glow
• Becker (1974) Andreoni (1990)
• Motives to donate
– Pure altruism U=U(G)
– Social contract that prevent free riding
– Warm-glow
=> Theory of impure altruism U=U (X,g,G)
PG Experiments objective
• Why people cooperate
– Testing the theory; explaining why people
contribute as much or as little as they do;
• How we can alleviate cooperation
– Manipulating parametres;
– Designing alternative mechanism so that public
goods will be provided at efficient levels.
Possible designs
• One-shot or (infinitely) repeated
• Partners or strangers ƒ
• Equal or unequal endowments ƒ
• Equal or unequal MPCRs ƒ
• Simultaneous or sequential decisions ƒ
• Feedback (on all or average contribution) ƒ
Stylized facts
Three main categories (Ledyard, 1995):
• Environmental variables (easy to control - MPCR,
number of subjects, repetition, gender)
• Systemic variables (control is more difficult beliefs,
economics training, experience, risk
attitudes)
• Design variables (factors identified by
experimentalists, aspects of institutional design enabling
of communication, unanimity rules, or
moral suasion.
Standard results
• ƒInitial cooperation of 40-60%, cooperation
declines with repetition ƒ
• Some effects:
Positive
(i) Strong
• MPCR
• Partners
• Communication
(ii) Weak
• Gender (Women)
• Group identification (friendship)
• Threshold
Negative
(i) Strong
• Experience
• Heterogeneity
(ii) Weak
• Economic training
• Unanimity
• Group size (large) ?!
Alternative mechanisms
• Threshold
• Decentralized Punishment (Rewards)
– Fehr and Gächter (2000, 2002); Nikiforakis (2008), Dunant-Boèmont et al. (2007)
• Lottery (raffle)
– Morgan (2000), Dale (2004)
• Hundreds of others (voting, Groves-
Ledyard,…)
Threshold (provision point)
• PG provision conditioned by some minimal
amount of contributions
• Theoretical equilibrium change (PD=>chicken)
• Game of coordination
• Reimbursement of funds if threshold not met
Threshold (provision point) - results
Threshold – results (2)
• Convergence to Nash
• Increase in contributions
• Effect of communication (followed by steep
drop)
• Weak effect of experience and economic
training
Charitable lottery
• Joint supply of public and private goods
• Prize mechanism
– Fixed prize
– Prize as ration of contributions
• Increase in contribution for fixed
• Prize as a cost of lottery
Charitable lottery – results (1)
• 108 subjects Masaryk University and
Lobachevsky University (Russia)
• 15 rounds
• Earnings 205 CZK (8 €) and 95 RUR (4€)
• Three designs
– VCM
– Fixed prize with p depend on contribution (FPL)
– Fixed prize with equal p (MFPL)
Charitable lottery – results (2)
Charitable lottery – results (3)
Decentralized Punishments
• Subjects informed about individual
contributions and given an opportunity to
punish their co-players by distributing points
reducing the current incomes.
• Punishment is costly
• Change of game equilibria (if credible threat)
• Fehr, Gachter (Nature, 2002), Hermann, Thoni,
Gachter (Science, 2008)
Decentralized punishment - results
• 188 subject Masaryk University 2009
• Replication of Denan-Boèmont et al., 2007
• No country effect
• possibility of decentralized punishment had a
positive effect on voluntary cooperation
– Less effective in stranger matching
• Ruined by counter-punishment
Decentralized punishment – results (2)
Applications – Tax compliance
• Model
E U = 1 − p U W − θX + pU W − θX − π W − X
• If p and π low => dominant strategy to evade
• Variables of interest
– Probability of audit p
– Penalty rate π
– Tax rate θ
Tax compliance - results