follow a cooperative behavior in producing a commonly-accessible good.
The second message is that the use of nonlinear MP strategies would provide multiplicity of
equilibrium strategies and uncountably many long run equilibria including the better outcome
supported by the linear MP strategy, which is consistent with Dockner and van Long (1993)
and Rowat (2007) in a differential game of international pollution control between two coun-
tries.9 In other words, contenders may be able to reach a self-enforcing agreement or implicit
tacit collusion which makes the long-run outcome closer to the first-best one as compared to
the linear MP strategies. However, the problem of selecting among infinitely many nonlinear
strategies clearly requires some coordination, or more explicitly, some preplay communication.
In non-cooperative environments which do not allow such preplay communication or negoti-
ation it may be one of the primary functions of centralized institutions to play a critical role
to resolve such a coordination problem, as stated in Section 4.
In addition to the above-mentioned role of the government, the results of the present paper,
which would be the third message, suggest that the government (or central agency) should also
play the following roles in order to achieve a socially desirable outcome, and thus move the
long run outcome closer to the more efficient ones. To do this, governments should attempt
to deter the development of the conflict technology, reduce the depreciation rate of common-
pool assets or induce people to have longer sight. Such structural or institutional reforms,
including laws or institutional schemes, could reduce the likelihood of aggression, and thus
lead to peaceful and more efficient outcomes in the long run.
The model presented in this paper should be developed further in several directions. In
particular, introducing asymmetry among agents would enable us to compare the results of the
present model with those static models which do incorporate asymmetric agents. The ‘paradox
of power’ (Hirshleifer, 1991) may be generated in such an asymmetric dynamic conflicting
model.
9 Dockner and Long (1993) find that the first-best pollution stock can be approximated through an appro-
priate choice of non-linear MP strategies, when the rate of time preference should be sufficiently small. Our
result slightly differs from theirs in that the linear MP strategy itself becomes closer to the first-best outcome
as the rate of time preference is smaller.
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