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Public goods provision and endogenous coalitions (experimental approach)

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

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Public goods provision and endogenous coalitions (experimental approach)

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  1. Public goods provision and endogenous coalitions(experimental approach)

  2. 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

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

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

  5. The linear public goods game • Two goods : private and public • N players, : endowment w • ci = Contribution of player i to the public good (C = total) • ui(xi ,y) = axi + by • a : marginal payoff of the private good • b : marginal payoff of the public good • y = g( C ) = C • MPCR = b/a • Normalization : a = 1 • If b < 1, ci = 0 is a dominant strategy and ui = w. • Finitely repeated game : unique subgame-perfect equilibrium ci = 0 each period • If 1 > b > 1/N social optimum is ci = w adn ui = bNw > w.

  6. Experiment by Isaac, Walker et Thomas (1984) wi = w = 100

  7. Mean contribution

  8. MPCR

  9. Group Size

  10. Experience

  11. Possible explanations for overcontribution • 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)

  12. 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

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

  14. 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)

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

  16. Binding agreements • 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

  17. 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

  18. Procedures for agreement formation Sequential procedure • Veto • Dictator

  19. 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 decide : accept or reject • If all accept the proposal becomes binding • If one potential members rejectsthe proposal he makes a new proposal • The process ends when all agents belong to an agreement

  20. Procedure with a 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 cannot reject the proposal • The process ends when all agents belong to an agreement

  21. 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 ?

  22. 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)

  23. 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 :

  24. partition of the n regions into m binding agreements : π = (S1.....Sm) • Each coalition (agreement) decides about a level of contribution :

  25. f(B) = benefit generated by the existing coalition structure 2 players remaining : Stand alone : ui (B,1,1) = f(B) + 2 – ½ = f(B) + 1.5 Group of 2 : ui (B,2) = f(B) + 4 – ( ½) 4 = f(B) + 2 3 players remaining : Stand alone : ui (B,1,2) = f(B) + 5 – ½ = f(B) + 4.5 Group of 3 : ui (B,3) = f(B) + 9 – ( ½) 9 = f(B) + 4.5

  26. 4 players remaining : Stand alone : ui (B,1,3) = f(B) + 9.5 Group of 2 : ui (B,2,2) = f(B) + 6 Group of 4 : ui (B,4) = f(B) + 8 5 players remaining : Stand alone : ui (B,1,1,3) = f(B) + 10.5 Group of 2 : ui (B,2,3) = f(B) + 11 Group of 4 : ui (B,4,1) = f(B) + 9 Group of 5 : ui (B,5) = f(B) + 12.5

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

  28. 3 predictions for the 7 players case • The social optimum is the grand coalition • The equilibrium coalitional structure is (2, 5) • The smaller coalition is formed before the larger one. and freerides on the larger coalition

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

  30. 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 s1 = 1 , a singleton is formed • If 7 > s1 > 1 , the s1 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

  31. 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 • 10-14 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

  32. Results for the Veto treatment

  33. Session 5 group 1 (random) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 5 2 2 3 1 7 7 1 7 1 7 7 7 7 3 2 6 2 5 7 2 6 1 1 1 1 1 1 3 1 7 7 1 2 1 5 5 6 6 6 1 4 2 7 3 4 1 5 1 5 1 6 1 1 2 2 2 5 3 5 1 5 1 5 1 2 2 6 5 1 5 1 2 1 1 1 2 1 1 3 1 2 1 1 6 1 3 3 4 1 2 1 1 4 2 2 4 2 1 1 2 2

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

  35. 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.

  36. Result 2 (cntd) • Optimal performance (Grand Coalition): 172.00 • Equilibrium performance (2. 5) : 137.00 (72 of the optimum) • Average performance : 104.59 (46 of the optimum)

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

  38. Low Gini High Frequency High Gini High Frequency Low Gini Low Frequency

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

  40. All pe riods 3 final periods grand coalition 25 42 at least 3 single 54 46 others 21 13 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.

  41. 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

  42. 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

  43. 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.

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

  45. Proposals in subgames

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