Open loop and feedback solutions to an institutional game under non-quadratic preferences

Until now most research in dynamic games focus on models with quadratic objective functions because of practical considerations. But in reality, all problems are not quadratic. In this paper, we solve a differential game where players have non-quadratic preferences. In particular we consider an institutional game governing a permanent interaction between civil society organizations and Government in the economy in the presence of corruption. At the first stage, we compute analytically and solve numerically the open loop and cooperative outcome of the differential game. At the second stage, we approximated analytically and solved numerically the feedback strategies at equilibrium. As results, we found that both open loop and cooperative solution are unique and stable while multiple feedback Nash equilibria should arise. As economic implications, we found that under cooperative play the magnitude of the civil monitoring effort is lower than the one in open loop game. This in turn is smaller than the magnitude of effort associated to the best feedback equilibrium. Total factor productivity effects always dominate the detrimental effect of individual effort devoted to production in almost all situations. Furthermore, institutions improve much faster under cooperative scenario than in open loop game. These results have a similar format with the ones obtained under linear quadratic differential game at least for open loop and cooperative games.