1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

A Collective-Action Theory of Fiscal-Military State Building 53

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If corporationirejects the ruler’s fragmented policy proposal,xi=0 and corpo-

rationireceives payoffu 0 =v( 0 ,y) ̄ +θαiy(f ( 0 ,g−i),y) ̄, whereg−idenotes the

contributions of all other corporations given that corporationiis not contributing.

There are positive externalities on those that do not contribute to building an army

becausefis increasing ing−ifor alli.Thatis,ifθ>0, all groups withαi> 0

benefit and cannot be excluded from the military protection.^22

When fiscal centralization is implemented, the (expected) payoff of each corpo-

ration is:

uCi(xi,G)=v(xi,y) ̄ +θαiy(G,y) ̄ −t,

wheretis corporationi’s tax payment. (Recall the ruler setsti=tfor alliwhen

centralizing tax collection.) Because the ruler collects and enforces taxes under fis-

cal centralization,ei=0 for alli.

The ruler’s payoff is the revenue obtained from corporations’ payments. Let

c(x, G)be the cost of providing private and public goods in both fiscal regimes.

Assumecis increasing and convex inxandG, andcxixj=0 andcxiG=0for

alli. Then, the ruler’s payoffs under fragmented and centralized fiscal capacities

are, respectively:

uFR(x, G)=

∑n

i= 1

(τi+gi)−c(x, G),

uCR(x, G)=nt−c(x, G)−F.

1.2 Equilibrium

I solve for the pure-strategy subgame-perfect Nash equilibria (SPNE) of the game

preferred by the ruler.^23 By backward induction, I first study the choice of payments

and private and public goods proposed by the ruler under fiscal fragmentation.

If fiscal capacity is fragmented, corporationiaccepts policy profile{xi,τi,G}if

and only if:

v(xi,y) ̄ +θαiy

(

f(gi,g−i),y ̄

)

−gi−τi−ei≥θαiy

(

f( 0 ,g−i),y ̄

)

. (1)

(^22) This non-exclusion assumption distinguishes defensive warfare from predatory warfare. The for-
mer is a pure public good, whereas the latter is a private good. The spoils of a war can be promised
to only some groups, while others are excluded. For more on the distinction between defensive and
predatory warfare see Emerson (1983).
(^23) I assume the corporations accept the ruler’s proposal when indifferent. This allows me to rule out
trivial equilibria. Also, the ruler makes a take-it-or-leave-it offer and so extracts all of the surplus
from the corporations. Giving a higher share of the surplus to the corporations makes a transition to
centralization more likely as long as the corporations receiving a large share of the surplus benefit
from the public good (highαi).