A stochastic differential game of capitalism

Comparative Studies on Cooperative Stochastic Differential Game and Dynamic Sequential Game of Economic Maturity

“…Indeed, we have derived closed-form solution of the minimum-time needed to economic maturity in a simple model of endogenous economic growth (e.g., Barro, 1990;Rebelo, 1991;Turnovsky, 2000;Aghion, 2004;Wälde, 2011;Dai, 2012), where competitive assumption is employed for the firm, endogenous savings rate is determined by the representative household and the goal of the self-interested politician is to choose a tax policy such that the utility from tax revenue, which can be viewed as the rent, is maximized. Leong and Huang (2010) confirm that uncertainty will produce more realistic solution than that of the deterministic case (see, Kaitala and Pohjola, 1990). We also consider a stochastic environment as in Merton (1975), i.e., the source of uncertainty is the population size.…”

“…Lancaster (1973) and Kaitala and Pohjola (1990) argued that cooperation between the government and the firm will be more beneficial compared to the dynamic inefficiency of capitalism. Moreover, Leong and Huang (2010) demonstrates that cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium although the cooperative solution is indeterminate. Apart from these papers, the present model defines the concept of dynamic inefficiency of capitalism in the sense of the minimum-time needed to economic maturity.…”

“…However, we will investigate the differential cooperative game between the representative household and the self-interested politician with the time horizon endogenously determined. As a result, our following theorems are new relative to those of Kaitala and Pohjola (1990), and Leong and Huang (2010). Additionally, the following results will be much more complicated owing to the general preference and technology functions we employed here.…”

“…Kaitala and Pohjola (1990), and Leong and Huang (2010) study the differential cooperative game between the firm and the government in deterministic and stochastic environments, respectively. However, we will investigate the differential cooperative game between the representative household and the self-interested politician with the time horizon endogenously determined.…”

“…In other words, we employ backward induction principle to ensure time consistency in the dynamic sequential game while using sub-game consistency to ensure time consistency in the cooperative stochastic differential game. To sum up, the present model has supplied a useful framework for the comparative study of the dynamic sequential game emphasized by Phelan and Stacchetti (2001), Acemoglu et al (2008Acemoglu et al ( , 2010Acemoglu et al ( , 2011 and the cooperative differential game studied by Kaitala and Pohjola (1990), Yeung and Petrosyan (2006) and Leong and Huang (2010) in a stochastic growth model under politicaleconomy constraint. And hence our study would be regarded as a natural extension of existing literatures.…”