A recently much debated issue is why observed investment and growth rates inpoor countries are lower than traditional theory predicts. Empirical evidencesuggests that social and political instability is a major reason for thedivergence between poor and rich countries. However, there is still the unsolvedpuzzle that the relationship between development and investment rates is notmonotonic but follows a hump-shaped pattern. The empirical evidence shows thatalthough very poor economies have very low investment rates there are'intermediately' developed economies that exhibit extremely high investmentrates. This paper shows - within the framework of a simple game theoretic model- that if property rights over produced wealth are not perfectly secure verypoor countries are in an instability and inefficiency trap. There exists noredistribution schedule sustaining social stability. However, intermediatelyproductive economies can exhibit investment rates higher than those of highproductive economies. Hence, the results of the model predict the empiricallyobserved hump-shaped relationship. Furthermore, the results also support thehypothesis that inequality and investment rates are negatively correlated.