Crawford PhD Conference 2014

1. Global Public Goods and Coalition Formation under Matching Mechanisms
Larry Liu
5th Annual Crawford PhD Conference
19 November 2014

2. Overview
•Motivation
•Model
•Coalition profitability
•Coalition stability
•Free-riding and reputation
•Coalition depth and breadth
•Conclusions

3. Motivation
•Globalization & Transboundary externalities
–Transnational pollution, international trade, financial crises, development aid, contagious diseases, etc.
•Public goods are underprovided in voluntary contribution.
•International cooperation is required to reach optimal outcomes but proves difficult in practice due to the absence of a supranational government.

4. Motivation
•Cooperative games in coalitional form
•A typical coalitional game:
1)Players decide whether to sign an agreement;
2)Signatories decide on the public good provision cooperatively to maximize aggregate welfare of the coalition;
3)Every outsider chooses the public good provision to maximize the own welfare;
4)Signatories decide how the welfare gain is distributed.
•Major issues in practice:
–Free rides
–Side payments

5. Motivation
•Matching mechanisms
–Two-stage game
•S1: Announce a matching rate
•S2: Decide how much to provide
–Non-cooperative mode of public good provision.
–Subsidize individual public good contributions.
•Matching coalition
–S1: Given a common matching rate, players decide whether to join the coalition.
–S2: All players decide the public good provision independently to maximize their own welfare.

6. Under what conditions
does a matching coalition exist?

7. Coalitions
•Profitability
–Each coalition member must be better off than without coalition.
•Stability
–Internal stability: No insider is better off by leaving the coalition.
–External stability: No outsider is better off by joining the coalition.

8. The model
•One private good, one pure public good and multiple players.
•Players have the same well-behaved preference depending on the private good and the total public good provision.
•Each player has a different initial income.
•One coalition with a common exogenous matching rate.
•Each player’s public good contribution: Flat contribution and Matching contribution.
•Players have the same linear production technology of the public good.
•Prices of the two goods are both normalized to one.

9. Coalition profitability
•Coalition profitability is favoured by
–A large coalition
–A small group of outsiders
–A strong preference for the public good
•Generally speaking, if all players agree to join the coalition, there exist small matching rates making all coalition members better off even if income distribution is large.

10. Coalition stability
•A stable coalition
–Internal stability
–External stability
•Players would stay in the coalition only when
–Players value the public good much higher than the private good.
–There are only a few players in the economy.
•More likely, given other players staying in the coalition, each player has incentives to take free rides and the coalition collapses.

11. Free-riding and reputation
•Assume that players value their reputation
–Players gain reputation if they join the coalition.
–The reputation value is heterogeneous and exogenous.
•U(Out|a set of players) > U(In|a set of players)
•U(Out|a set of players) < U(In|a set of players) + Reputation
•Players would stay in the coalition when the gain of free riding is lower than the reputation loss.

12. Coalition depth and breadth
•International cooperation faces trade-off between depth and breadth.
–A coalition is either “narrow but deep” or “broad but shallow”.
–Bottom-up approaches or decentralized cooperation is likely to reach “narrow but deep” agreements while top-down approaches or centralized cooperation tends to generate “broad but shallow” treaties.
•Trade-off in the matching coalition
–When the matching rate in the coalition gradually increases from zero, the coalition shrinks.
–The matching rate can be flexibly set to compromise between cooperation depth and breadth.

13. Conclusions
•Coalition Profitability
–Generally speaking, there exist small matching rates making all coalition members better off even if income distribution is large.
•Coalition Stability
–More likely, given other players staying in the coalition, players have incentives to take free rides and the coalition collapses.
–If players value their reputation, they would stay in the coalition when the gain of free riding is lower than the reputation loss.
•Trade-off between matching depth and breadth
•Policy implications
–It may achieve Pareto-improving outcomes while avoiding international side payments.
–The matching rate can be flexibly set to compromise between cooperation depth and breadth.