We consider the relationship between inequality and the business cycle. Empirical evidence suggests mutual causality between GDP and inequality over the business cycle and the countercyclical nature of inequality. We construct an evolutionary game-theoretic model with two types of workers to explain these observations. Cognitive workers produce capital of varying quality, which determines the productivity of physical workers who obtain the capital through an exogenous search process. We apply the logit dynamic to the model. The model satisfies positive definiteness due to which, both GDP and inequality converge to limit cycles and, therefore, fluctuate over time. These cyclical fluctuations have a common origin in the underlying evolutionary dynamic process, which explains the empirical observation of mutual causality between these variables. Further, simulations suggest an inverse relationship between GDP and inequality in our model, which accounts for the countercyclical nature of inequality.