Motivated by the discovery of apparent Edgeworth Cycles in many retail gasoline markets, this paper extends the Maskin & Tirole [1988] theory Edgeworth Cycles to a wide range of more complicated and realistic settings. Taking a computational approach to search for Markov Perfect Equilibria, I examine models involving duopoly and triopoly, differentiation, capacity constraints, and different sharing rules, discount factors and initial beliefs about price leading behavior. I find Edgeworth Cycles equilibrium in many scenarios outside the homogenous-good Bertrand mold. Cycle characteristics and average markups depend on the scenario.