A Dynamic Model of Conflict and Cooperation

but it has no effect on line C1 . Hence we obtain the following long run effects:

= r (n - 1) [1 - r (n - 1)] δ∆^-2 > 0,

= -n (n - 1) [1 - r (n - 1)] r∆^-2 < 0.

The economic explanation is that as contenders become more patient (i.e., smaller ρ), they
put more weight on future stocks of durable goods rather than the current one, and thus tend
to spend more resources on production activity rather than on aggressive investment. This
result has apparently not been addressed by Hirshleifer (1991, 1995) and Skaperdas (1992),
who use the static conflict models. It stands in contrast to Skaperdas and Syropoulos’s (1996)
result in which the higher is the valuation of the future (i.e., smaller ρ), the stronger is the
intensity of fighting. The reason for this difference is that in their two-period’s model agent’s
first-period expenditure on appropriation increases agent’s second-period payoff. Rather, our
result is similar to Garfinkel’s (1990) Folk Theorem type result in repeated games where a
higher discount factor (i.e., a smaller ρ) makes it easier to sustain cooperative outcomes. An
interpretation of our result is that long-sighted agents become less aggressive because they are
more concerned about the future.

We may then summarize the discussion in the following proposition:

Proposition 2

(i) An increase in the effectiveness of aggression leads to a higher level of aggression and to a
lower level of the common-pool stock;

(ii) an increase in the number of agents leads to a higher level of aggression, but the effect on
the common-pool stock is ambiguous;

(iii) an increase in the depreciation rate leads to lower levels of aggression and of the common-
pool stock; and

(iv)a decrease in the subjective rate of time preference (i.e., agents become more patient) leads
to a lower level of aggression and to a higher level of the common-pool stock.

18

<<   18   19   20   21   22   23   24   >>

More intriguing information