The global dynamics of an equilibrium model of aggregate unemployment that focuses on the job/worker matching process is studied for the case of increasing returns to scale in production and constant returns to scale in the matching process. In anticipation of a particular solution to the wage bargaining problem, unmatched expected present value maximizing workers and employers respectively invest in search and recruiting effort that collectively determines the aggregate matching rate. An equilibrium is a dynamic path for the aggregate number of matches generated by best response investment decisions under rational expectations. There are no periodic solutions if the wage bargain is efficient and the future is discounted. However, when the difference between the elasticity of the matching rate with respect to aggregate search effort and the workers' share of match capital is small and positive, an endogenous cycle exists on an open set of small positive discount rates. The cycle can be either stable or unstable and is unstable if an only if the economy is sufficiently productive. Finally, when a cycle is consistent with initial conditions, an alternative non-periodic equilibrium also exists that yields a higher permanent income now and less unemployment in the future.