We further assume that _A ≤_ 1 _/_ 2 to ensure that probabilities are bounded at 1.

The groups gain utility from consuming a private good _C_ and a public good _G_ , which is financed by imposing distortionary taxes on period 1’s exogenous incomes (see below). In addition, the access to natural resource revenues also provides utility, but it is realized in period 2. Assuming that natural resource windfalls are fully appropriated by the “winner,”<sup>13</sup> and ignoring time discounting, the expected utility of each group at the time of army mobilization is given by: where _f_ ( _C_<sup>_i_</sup> _, G_ ) denotes the utility derived from consuming the private and public goods, _C_<sup>_i_</sup> and _G_ , respectively, and _h_ ( _W_ ) denotes the utility from receiving oil rents _W_ , which, given our focus on oil rich countries, is large enough. We further assume that (i) preferences for the consumption of the private and public good are homothetic and thus _f_ ( _._ ) is a well behaved concave function, and (ii) _h_ ( _W_ ) is a continuously differentiable function with _h_ (0) = 0, _h_<sup>_′_</sup> ( _W_ ) _>_ 0, _h_<sup>_′′_</sup> ( _W_ ) _≤_ 0. The amount of public good available to each party is given by: where _G_<sup>_I_</sup> and _G_<sup>_O_</sup> denote the contributions of the incumbent and the opposition to the public good, respectively. This means that the public goods provided by each group are perfect substitutes, and that the public good game is “aggregative;” agents’ utility only depends on the total provision of the public good. Lately, such kind of games have received a lot of attention because of a number of appealing properties, which will become apparent in the next section; we refer the interested reader, among others, to Kotchen (2007), Cornes and Hartley (2007), and Acemoglu and Jensen (2013) for a more comprehensive discussion. The consumption of private goods is subject to the following budget constraint: where _w_ denotes the initial endowment, which we assume to be identical for the two groups, and _λ >_ 0 denotes the distortionary cost of taxation. We allow the cost of mobilization _c_<sup>_i_</sup> ( _δ_ ) to be higher for the opposition, and we assume that _c_<sup>_I_</sup> ( _δ_ ) = _δ_ and _c_<sup>_O_</sup> ( _δ_ ) = _δ/ζ_ , where _ζ ∈_ (0 _,_ 1].<sup>14</sup> Taxes are raised to finance mobilization of armies and the provision of the public good. To simplify notation, it is useful to define the income that group _i_ can devote to the

> 13All our results would hold true had we followed BP and assumed that the incumbent group can only grab a fraction _θ_ of the natural resource revenues. The decision to set _θ_ = 1 is only made to simplify notation. In addition, given that in the case of no violence each group has probability one half of appropriating the natural resource windfall, our model is equivalent to one in which, if all parties abide by the democratic rules, natural resource rents are equally split between them.

> 14Note that the allocation of costs across players could be more general and each player could pay for a fraction of the other player’s mobilization costs, i.e., _C_<sup>_I_</sup> _≤ w −_ (1 + _λ_ ) � _αδ_<sup>_I_</sup> + (1 _− β_ )<sup>_<u>δ</u>_</sup> _ζ_<sup>_O_+</sup><sup>_GI_�</sup> _,_ and _C_<sup>_O_</sup> _≤ w −_ (1 + _λ_ ) �(1 _− α_ ) _δ_<sup>_I_</sup> + _β_<sup>_<u>δ</u>_</sup> _ζ_<sup>_O_+</sup><sup>_GO_�</sup> . For instance, BP assume _α_ = 1 _/_ 2, _β_ = 1. However, in our set up, where, as long as both groups contribute to the public good, the equilibrium outcome does not depend

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