Crawford PhD Conference 2014

1. Comments on “Global Public Goods and
Coalition Formation under Matching
Mechanism” by Larry Liu
Discussant: Tomohito Okabe,
PhD Candidate, Research School of Economics
November 19, 2014

2. Model Two-Stage Game
n Players
Preference: identical U(xi ;G) where xi is a private good and G is a public good (e.g.
reduction of greenhouse gas).
Endowment: heterogeneous income wi 2 W := [w;w]

3. Model Two-Stage Game
n Players
Preference: identical U(xi ;G) where xi is a private good and G is a public good (e.g.
reduction of greenhouse gas).
Endowment: heterogeneous income wi 2 W := [w;w]
Timing
0 Matching rate 2 [0; 1] is exogenously given by supra-government or
pre-agreement.
1 Given income endowment wi 2 W, player i chooses a group to join,
fcoalition, outsidersg ! How? I will summarize this.
2 Given her group choice, player i chooses x
i and her contribution y
i that
maximize utility U() subject to budget constraint, xi + yi = wi and aggregate
resource constraint G +
P
xi =
P
wi . Public good provision is then given by
G = f1 + (m 1)g
Xm
j=1
y
j
| {z }
contribution by coalition
+
Xn
j=m+1
y
j
| {z }
contribution by outsiders

4. Key points for coalition formation
Coalition formation crucially hinges on two exogenous restrictions:
(I) income distribution W, (II) matching rate

5. Key points for coalition formation
Coalition formation crucially hinges on two exogenous restrictions:
(I) income distribution W, (II) matching rate
(I) How does W affect the coalition formation, holding constant?
Ex-ante problem is given by:
max
fcoalition;outsidersg
n
Vcoalition(w); Voutsiders(w)
o
where V(): ex post payoff function
Case A: Coalition is formed.
Vcoalition ()
Voutsiders ()
w
outsiders coalition
w
[w
]
w
Case B: Coalition is NOT formed.
Vcoalition ()
Voutsiders ()
w
outsiders coalition
w
[w
]
w

6. Key points for coalition formation (cont’d)
(II) How does affect the coalition formation, holding W constant?
If holding all else constant, the graphs of V() are altered.
How the graphs change depends on the values of parameters, but, for instance...
Case where Vcoalition # and Voutsiders # with 1 2
Voutsiders
w
; 1
Vcoalition
; 1
w1
[w
]
w
Vcoalition
; 2
Voutsiders
; 2
w2
Since more players choose to be outsiders, coalition turns to shrink.

7. What else affects coalition formation?
I Why not introduce an idiosyncratic preference parameter i 2 [; ] for public
good consumption? e.g. U(xi ;G) = x
i (iG)

8. What else affects coalition formation?
I Why not introduce an idiosyncratic preference parameter i 2 [; ] for public
good consumption? e.g. U(xi ;G) = x
i (iG)
I i would represent how valuable public good is for the player.
In the context of greenhouse gas reduction, potential reasons that justify the
parameterization are:
X frequency of natural disaster
X conflicts in domestic politics
X etc...
I Joint distribution of wi and i may offer more interesting findings???
Countries with w (poor) and (eager to reduce greenhouse gas)
VS
Countries with w (rich) and (reluctant to reduce greenhouse gas)

9. Concluding remarks
I The paper carefully investigates the behavior of interior- and corner
equilibria à la comparative statics, given heterogeneous income
endowments.
I It offers many insightful propositions from Pareto-improving points of
view.
I It also gives interesting policy implications that are relevant to
variations in matching rate.
!! The author might want to explicitly set up the first stage game where
players choose to join coalition or not.
!! Do the reputation assumption and the introduction of a preference
parameter provide more policy implications?