In this study, we prove that the strategic interaction among agents differing in initial wealth levels leads the poor to be able to catch up with the rich, which is not the case for the standard Ramsey model where the initial wealth differences perpetuate. Extending the analysis to account for relative wealth concern and the adjustment cost of consumption, the strategic interaction among agents is shown to affect not only the distribution of wealth in the long run but also the transitional dynamics substantially. In particular, we show that structurally very simple frameworks may lead to limit cycles thanks to the strategic interaction among agents in the economy.