Heat oil in a large skillet over medium-high heat. Cook eggplant, onion, garlic, oregano, cinnamon, allspice, salt, and pepper, stirring frequently, until onion is slightly browned, 7 to 8 minutes.
Reduce heat to medium and add tomatoes, water, wine, and bay leaf. Simmer, stirring frequently, until eggplant is tender and mixture is thickened, 13 to 15 minutes. Remove from heat and stir in sugar, capers, and vinegar. Let cool 30 minutes, then discard bay leaf. Serve at room temperature or chilled.
