Capital accumulation games with a non-concave production function

We consider an economy with a single capital stock that two agents strategically exploit by choosing a consumption profile over an infinite time horizon. We analyze two different games and their corresponding equilibria. In one game firms are able to pre-commit and choose simple time functions as their strategies. In the other game agents are assumed to employ Markov strategies. It turns out that in the case of pre-commitment there exists a threshold level of the capital stock such that if the initial stock is above this threshold, equilibrium consumption converges to the efficient steady state while if the initial condition is below it, the capital stock converges to zero. In case of the Markov equilibrium there exists a unique interior steady state that is globally stable.