with the response exceeding the “provocation” that caused it, flattening out at the 450 line, and
declining thereafter with responses falling short of provocations.11
Both response curves — one for H and one for M — are depicted in Figure 3.12 It follows
immediately that the two curves intersect and that the intersection can only be unique.
The hump-shaped profile of the equilibrium response functions is exactly what one would
expect. When a given group is faced with increasing opposition it will initially respond with
increased activism of its own. However, the limitation of one’s own resources (economic and
human) will eventually lead to a decrease in activism as a response to a further increase in the
opposition.
4. Determinants of Equilibrium Conflict
The equilibrium level of conflict is determined by the intersection of the equilibrium response
functions of the two groups. These functions depend on the individual characteristics of the
group members. In what follows, we are interested in two sorts of changes. We distinguish be-
tween changes across groups — captured by uniform changes in the characteristics of all mem-
bers of one group — and changes within groups — captured by changes of the distribution of
group characteristics while preserving the aggregate values for that group.
4.1. Equilibrium Activism. We begin with a general observation about comparative statics.
Suppose that there is a change in parameters that pushes one side into supplying more activists.
[For instance, the distribution of x for each wealth level could move rightwards in the sense of
first-order stochastic dominance, for one of the groups.] In general, this will affect the equilib-
rium supply of activists for both sides. It turns out that the sign of the cross-group effect tells us
something about the relative strength of the group that experienced the original change.
PROPOSITION 2. Suppose that a change occurs in the parameters for a particular group, thereby shifting
their equilibrium response function outwards: they are now more “aggressive” in supplying activists.
Then
(i) If the change in parameters has taken place for the group that had a smaller number of activists to start
with, then the equilibrium Ah and Am both move in the same direction; while
(ii) If the change in parameters has taken place for the side that had the larger number of activists to start
with, then the equilibrium Ah and Am move in opposite directions.
This result follows immediately from the properties of the equilibrium response functions
described earlier.13 Indeed, Figure 4 contains a self-contained diagrammatic exposition of the
proof.
Thus if a group that has been so far moderate (mobilizing fewer people in equilibrium) be-
comes more aggressive, this has the primary effect of precipitating an escalation of conflict with
both groups contributing more activists. However, if the increase of agressiveness leads this
group to become the more radical (in the sense of mobilizing the larger number of activists) any
further increase in aggressiveness will have the opposite effect on the other group. The more
moderate group will respond to the increase of activists by the aggressive group with a cut in
11There must come a point at which Ah equals Am, for our assumptions on cost function assures us that equilibrium
responses must be bounded.
12
12The depiction of these curves neglects — without any substantive loss — the small flats that correspond to jump
points in the s-function for activists.
13
13This neglects the case in which there are small flats in the response function arising from gaps between the wages
of neighboring types. Such flats might create no change in cross-group activism if the parametric changes are very small,
but in any case does not reverse the sign of the correlation. So we do not emphasize this point in the main text.