to the agents of conflict.
The allocation rule of our game μt is a function
μt : [0,1]I → [0,1]I
such that Pt∈ι μt (Pt (It ,αI) ) = 1.
We now give some examples of possible allocation rules.
• Share model: Let μlt = ptt (eI, αI). Then each agent receives a share of the resource that is
totally determined by the contest success function. This is the simpler way to allocate the
resource in dispute.
• Probabilistic model: Let μtt = 1 with pr obability ptt (eɪ, αI) a nd μtt = 0 with probability
1 — Pt Iet ,at)∙ This impliθs a random allocation of the resource, but each agent can increase
the probability of receiving the good. This approach is followed by Maxwell and Reuveny
(2005).
• Auction model: We can interpret the contest success function pt (eI, αI) as the normalized
value offered by agent i for the good in dispute. The parameters αI represent the lobbying
power of each agent. In this way, not only explicit effort influences the result of the auction,
but also the relative power of the bidders. In this case, the allocation rule μt is any standard
auction rule. Let M = argmaxt∈1 {pt (eI, αf)}. For a first-price auction we could have
,.t = ) #m
μt =
I о
if i ∈ M
otherwise
These mechanisms are just examples of many ways of allocating the valuable resource to the
conflict agents. Standard conflict theory assumes a conflict technology that according to the effort
levels assigns a share of the good (or gives a probability of victory). Other mechanisms could be
used as well. There is no reason to think, for instance, that an auction mechanism is better∕worse
than any other mechanisms available in the literature.
Note that the relevant concept of equilibrium and the solution method to this game depends on
the allocation rule. For instance, if we follow an auction approach, then auction theory methods
should be applied (see for example Krishna (2002)).
For simplicity, we follow the conflict theory literature and work with the share model from now
on. The solution to this game, assuming differentiability, is almost Straigthforward.