4 The Cooperative Solution
We will characterize the explicit cooperative solution as a benchmark steady state in the
following. Assume an outside enforcer or centralized agency has the power to enforce every
contender to execute its command. The cooperative strategy is one for which a centralized
agency chooses the infinite-horizon planning profile of strategy a ∈ Rn+ at the outset of the
game so as to maximize f∞ Ze-ρtdt subject to Z = n — Pn=1 αj∙ - δZ where aj∙ ∈ [0,1]
for all j. Clearly, this optimization yields a totally peaceful solution, that is, aj (t)=0
for t ∈ [0, ∞) and all j . The result is understood by noting that expenditure on appropriation
is socially wasteful in the sense that it causes a deadweight loss because of the non-productive
use of resources. This deadweight loss should be zero in the hypothetical case where a central
agency can directly control the allocation between productive and appropriation. As a result,
the superior authority should establish point (n∕δ, 0) in the long run. Agents would benefit
from an enforced peaceful resolution because socially wasteful aggressive activity is completely
eliminated.
Combined with the comparative static results in the previous section, we obtain the fol-
lowing results:
Proposition 3 Assume that a centralized agency chooses an allocation between aggressive and
productive investment so as to maximize aggregate payoff. The resulting allocation dictates
that agents devote all resources to the socially productive activity to obtain the Pareto efficient
point (n∕δ, 0) in the long run. In an anarchic situation where every agent follows the Markov
perfect equilibrium behavior described in Sections 3 and 4, a decrease in either the productivity
of aggressiveness, the depreciation rate, or the subjective rate of time preference moves the
resulting long run equilibrium closer to the first-best one.
The nuclear nonproliferation treaty which deters the development of nuclear weapons
(i.e., aggressive technology) would be socially desirable in a way that makes the long run
outcome resulting from a non-cooperative equilibrium behavior closer to the peaceful and
efficient one. Another example is patent law, which aims at enforcing property rights on in-
vestment return and thus limits socially wasteful activities. Patent law potentially prevents
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