Contests in two fronts

Abstract

Within the framework of Game Theory, there are games where rewards depend on the relative rank between contenders rather than their absolute performance. We refer to these situations as contests. By relying on the formalism of Tullock success functions, we propose a model where two contenders fight in a contest on two fronts with different technology levels associated: a front with large resource demand and another with lower resource requirements. The parameter of the success function in each front determines the resource demand level. Furthermore, the redistribution or not of resources after a tie defines two different games. We solve the model analytically through the best-response map dynamics, finding a critical threshold for the ratio of the resources between contenders that determines the Nash Equilibrium basin and, consequently, the peace and fighting regimes. We also perform numerical simulations that corroborate and extend these findings. We hope this study will be of interest to areas as diverse as economic conflicts and geopolitics.