A game theoretical model of inter-group conflicts is revisited. In this model members of each group contribute to secure a public good which becomes then available to all members regardless if they contributed or not, and the groups compete for an exogenous prize simultaneously. We first show that the best response of each group member is mathematically equivalent to that in oligopolies with isoelastic price and linear cost functions. Then a complete equilibrium analysis is given showing that, except in a very special case, there is a unique equilibrium. And finally, a dynamic extension of the game is introduced and analysed, where the players are able to increase their contributions at any time during a given time period.