of the resource) of exerting a total effort of ezt, θt ∈ Rm is a vector of cost function parameters on
which we will turn briefly5 and xit is the investment level in conflict technology. We denote the
effort !-vector in the period t ∈T a s eI = (eɪ,..., eI ) a nd eI∖{t} = (eɪ,..., et-1, et+1,..., e1t ) the effort
!-vector of everybody but the agent i ∈ I. We assume that every period the valuable resource left
for free use for every agent is nonnegative6
(∀i ∈ I) (∀t ∈ T), (ct ≥ 0)
The share μt is defined by the level of effort exerted in the conflict by all the agents, according to
a typical conflict effort function (or contest success function, Skaperdas (1996))
Pt et ,αt )
where αI = (α⅛1,..., ɑʃ) represents the technological coefficients associated to all the agents. That
is, we assume that the contest success function summarizes all efforts and relative power of the
agents in conflict. The allocation rule μt takes this information and indicates how to split the
resource between agents. We assume that μt is nondecreasing with pt (eI, oI).
t I I∖{t}
We define α∣ ,atf ιn the same way as for the effort levels, and let these symbols represent the
technological coefficients associated to all the agents, and ! — 1 agents, respectively. This technology
satisfies that (∀i ∈ I) (∀t ∈ T) (pt (eI, αI) : R+ × R+ → [0,1]) and Pt∈1 pt (eI, αI) = 1 and will
determine the share of the valuable resource that each agent is able to obtain7.
Then, there is strategic interdependence between agents, because the effort level chosen by all the
opponents affects the share of the good obtained in the conflict. This interdependence is a key factor
of other kind of models, as auction models. These models seek not just to understand the decisions
of each agent, but the implications of complex interactions between them.
We assume that ∀i ∈ I∀t ∈ T, ɪpt (eI, αI,t) ≥ 0, ⅛Pt (et, aI,t) ≥ 0, and for j = i, ∂jPt (eI, ατn,t) ≤
t t et
0: that is, the share of the г esource obtained by agent i is nondecreasing in αlt a nd e^lt, but is nonin-
creasing in the effort level exerted by the opponents.
5We impose that g^l : R "' ' 1 → . ∀i ∈ Ij furthermore gt (∙; θt) is a continuously differentiable convex function. We
also impose that gt (0; θt) = 0. Note that we allow differences among the model’s agents.
6That is imposing a restriction where the cost of exerting a total effort should always be not greater than the
difference between the good obtained and the investment level: μtRt — xt ≥ gt (et; θt)∙
7See Section 3. If μt = pt (ef, αf ), this can be understood naturally like a share model such as in Skaperdas (1996),
Hirshleifer (1989, 1991, 1995) and Maxwell and Reuveny (2001). In a share model every agent wins a fraction of
Rt. A second alternative is the win-approach, in which just one agent wins the whole Rt. To obtain the later
approach it is only necessary to assign an arbitrary rule. The most simple rule could be one in which the winner
has the greatest value of pt (ef, αf). In case of ties whatever random rule could solve the problem.