A Dynamic Model of Conflict and Cooperation

monotonically increases toward the steady state S over time. That is, as the common-pool
stock Z gets larger over time, the contenders will become greedier, because the marginal gain
of appropriation will be higher. In the long run the economy will reach a situation where ‘par-
tial cooperation’ prevails in the sense that every agent chooses to contribute to the production
of the common-pool stock Z to some extent. Although such ‘partial cooperation’ is also found
in the static models of Hirshleifer and Skaperdas, differing degrees of ‘partial cooperation’
depending on the coordination of expectations formed by agents in the present model never
emerge in their models.

3 Comparative Static Analysis

In this section we discuss the effects of a change in the model parameters on the transition path
of the linear strategy aL as well as on the associated long-run equilibrium point S , since other
non-linear MP strategies display almost the same comparative statics properties. Consider first
the effects of a change in the productivity (or effectiveness) of conflict technology. The recent
developments in computer networks and their applications mentioned in the introduction
are examples of technological change that potentially puts at risk the intellectual property
rights of the software and music industry. In the model, a change in the productivity of the
conflict technology is captured by a change in r.TheshiftofpointS can be calculated by
differentiating (15) and Z_S in (16) with respect to the parameter r, respectively:

δ (δ + ρ)(n - 1) ∆^-2 > 0,

-n (n - 1) (δ + ρ) ∆^-2 < 0,

where a_S ≡ a_L(Z_S) and ∆ ≡ (n - 1) rρ + δ > 0. Although an increase in r does not affect
the line C1 , this increase strengthens the intensity of appropriation associated with every level
of the common-pool stock Z during the transition path, thus making the linear strategy (15)
steeper. Since the productivity of appropriation becomes more effective with higher r, all
competing agents engage in more aggressive behavior in the hope of capturing more resources.

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