Public goods provision and endogenous coalitions (experimental approach)

Background Social dilemmas –Underprovision of public goods –Overexploitation of common pool resources Experiments on voluntary contributions –High levels of contribution in early periods –Decline of contributions over time –Terminal contribution above equilibrium

What can improve cooperation ? Punishments Face-to-Face communication Commitments through binding agreements Background

Some facts about public goods experiments Binding agreements Theoretical predictions Experimental design Results Discussion Plan

Two goods : private and public N players, : endowment  c i = Contribution of player i to the public good (C = total) u i (x i,y) =  x i +  y  : marginal payoff of the private good  : marginal payoff of the public good y = g( C ) = C MPCR =  Normalization :  If  < 1, c i = 0 is a dominant strategy and u i =  Finitely repeated game : unique subgame-perfect equilibrium c i = 0 each period If 1 >  1/N social optimum is c i =  adn u i =  The linear public goods game

Experiment by Isaac, Walker et Thomas (1984) w i = w = 100

Mean contribution

MPCR

Group Size

Experience

PUR ALTRUISM IMPURE ALTRUISM ("war glow giving"); (Andreoni, 1990) CORRELATED ERRORS (Anderson, Goeree, Holt, 1998) REPEATED GAME EFFECTS (Kreps, Milgrom, Roberts, Wilson, 1982) LEARNING (Andreoni, 1988) CONDITIONAL COOPERATION (Keser & Van Winden, 2000) STRENGTH OF THE SOCIAL DILEMMA (Willinger & Ziegelmeyer, 2001) FRAMING (Andreoni 1992, Willinger & Ziegelmeyer, 1999) Possible explanations for overcontribution

Punishment opportunity (Fehr & Gächter, AER 2000) Idea : contributions that do not conform to a given « contribution norm » might be punished The punishment threat increases cooperation Punishments induce losses Punishing others is costly for the punisher

Experimental design 2 stages : stage 1 : standard linear public goods game stage 2 : punishment game After stage 1 individual contributions are publicly announced

Stage 1 Stage 2 Punishment points chosen by j for i Each punishment point reduces i’s profit by 10%: Cost of punishment points for the punishers Individual profit (per period)

Design partners/strangers  with/without punishment (= 4 treatments)

Agents have the opportunity to make binding agreements –Commitment to a contribution (public good) –Quota on harversting (common pool) An agreement is defined as a coalition The size of the coalition determines the level of the members' contribution The total amount of public good provided depends on the structure of coalitions Binding agreements

Why can agreements solve the social dilemma ? Positive side : –Agents who belong to the same coalition maximise the utility of the coalition –Taking into account the group interest reduces the free rider problem Negative side –An agreement covers only its members –Coalitions play a noncooperative game  Free riding occurs across coalitions

Procedures for agreement formation Sequential procedure Veto Dictator

One agent is selected to make an agreement proposal (e.g. choosing a group size) Potential members are randomly selected in the population of potential members Selected members decide : accept or reject If all accept the proposal becomes binding If one potential members rejects the proposal he makes a new proposal The process ends when all agents belong to an agreement Procedure with veto

One agent is selected to make an agreement proposal (e.g.. choosing a group size) Potential members are randomly selected in the population of potential members Selected members cannot reject the proposal The process ends when all agents belong to an agreement Procedure with a dictator

Questions Which coalitions are more likely to emerge in the lab ? What is the sequence of coalition formation ? Do the realized coalitions come closer to the socially optimum outcome ? Does it matter whether potential members have veto power ?

A simplification of the coalition game Result 1 (Bloch. 1996) : identical players  coalition game is equivalent to choosing a coalition size Result 2 (Ray & Vohra. 1999) : if only size matters the endogenous sharing rule is the egalitarian rule (in each coalition)

An example of pollution control (Ray & Vohra. 2001) n regions involved in pollution control (pure public good) Stage 1 : binding agreements State 2 : choice of the level of control in each agreement Z = total amount of pollution control (pure public good) c(z) = cost of pollution control Profit for region i :

partition of the n regions into m binding agreements : π = (S S m ) Each coalition (agreement) decides about a level of contribution :

2 players remaining : Stand alone : u i (B,1,1) = f(B) + 2 – ½ = f(B) Group of 2 : u i (B,2) = f(B) + 4 – ( ½)  4 = f(B) players remaining : Stand alone : u i (B,1,2) = f(B) + 5 – ½ = f(B) Group of 3 : u i (B,3) = f(B) + 9 – ( ½)  9 = f(B) f(B) = benefit generated by the existing coalition structure

4 players remaining : Stand alone : u i (B,1,3) = f(B) Group of 2 : u i (B,2,2) = f(B) + 6 Group of 4 : u i (B,4) = f(B) players remaining : Stand alone : u i (B,1,1,3) = f(B) Group of 2 : u i (B,2,3) = f(B) + 11 Group of 4 : u i (B,4,1) = f(B) + 9 Group of 5 : u i (B,5) = f(B)

N = 2 (2) N = 3 (3) N = 4 (4) N = 5 (5) N = 6 (1,5) N = 7 (2,5) Equilibrium prediction according to population size

1.The social optimum is the grand coalition 2.The equilibrium coalitional structure is (2, 5) 3.The smaller coalition is formed before the larger one. and freerides on the larger coalition 3 predictions for the 7 players case

Experimental design N = 7 2 treatments : Veto and Dictator Same prediction for both treatments : (2,5)

Experimental design Step 1 : at the beginning of each round each subject receives an ID (letter A, B, C...) Step 2 : one ID is randomly chosen to make the first proposal (choose a group size) –If s 1 = 1, a singleton is formed –If 7 > s 1 > 1, the s 1 proposed members are randomly selected Step 3 : each proposed member has to decide whether to "accept" or to "reject" –If all proposed members accept the coalition is formed –If at least one proposed member rejects no coalition if formed Step 4 : One of the rejectors is selected to make a new proposal

Experimental design The process ends after all subjects are assigned to a coalition Individual payoffs are announced after each round for each coalition size that has been formed subjects per session (random / fixed), 4 veto sessions, 3 dictator sessions Random ending 92 coalition structures observed in the veto treatment and 60 in the dictator treatment

Results for the Veto treatment

Result 1 : The most frequently realized "agreement" is the singleton.

Result 2 : We observe a large heterogeneity of coalition structures. The equilibrium structure is never observed. The modal structure is the grand coalition (25 overall). More than 50 of the coalition structures contain 3 or more singletons.

Optimal performance (Grand Coalition): Equilibrium performance (2. 5) : (72 of the optimum) Average performance : (46 of the optimum) Result 2 (cntd)

Result 3 : Coalition structures with low payoff disparity among members are more likely to emerge.

Low Gini High Frequency High Gini High Frequency Low Gini Low Frequency

Regression : Dependent variable : Frequency of the coalition structure Independent variable : Gini coefficient Total payoff not significant

Result 4 Over the 3 last periods the frequency of the grand coalition increases. and the frequency of coalitions structures containing three or more singletons decreases. All periods 3 final periods grand coalition at least 3 single others 21 13

Result 5 : For 1/3 of the coalition structures. the groups are formed from the smallest to the largest. For 2/3 of the coalition structures there is no precise ordering

Result 6 : Myopic best reply predicts most of the observed coalition structures Myopic player : Proposer : acts without anticipating the possibility that subsequent players make couter-proposals Responder : does not anticipate any counter-proposal except her own

A myopic player always proposes the largest possible agreement of the remaining players  Myopic player 1 proposes the grand coalition Mixed populations (Myopic + Farsighted) : A farsighted player always proposes the singleton Proposition : If k players are farsighted and n – k are myopic. the equilibrium coalition structure is formed by k singletons which form first followed by a unique coalition of size n – k.

Summary of alternative prediction : Myopic players propose the grand coalition or the largest possible coalition Farsighted players propose the singleton

Proposal Size of subgame Proposals in subgames

Number of players in the subgame Frequency of consistent Proposals Random Frequency of consistent Proposals Data

Comparison Veto versus Dictator

Frequency of coalition sizes

Frequency of coalition structures

Optimal performance (Grand Coalition): Equilibrium performance (2. 5) : Average performance Veto: Average performance Dictator: Performance

Summary Equilibrium prediction –never observed in the Veto treatment –14% in the Dictator treatment Ordering : Smaller groups emerge earlier but only in 1/3 of the cases (veto treatment) Performance : below equilibrium in the veto treatment and above equilibrium in the dictator treatment High frequency of extreme coalitions : grand coalition and singletons Two explanations : –Mixed population equilibrium (myopic + farsighted players) –Inequality aversion

Questions for future research Individual behaviour/player types Negative externality (large groups emerge earlier in the sequence) Coalition formation rule : dictatorial. renegociation