Patron-client relationship' characterized Roman political tradition and operated in both private and public spheres as personal overtures of philanthropy and/or conditional benevolence for public good, respectively. Incorporate your understanding of this concept and practice in your formal and contextual analyses of Emperor Vespasian's Colosseum (Flavian Amphitheater) (ca. 70-80 CE) and Emperor Caracalla's Baths (Baths of Caracalla) (212-216 CE). Besides using specific art historical terms where necessary, ensure that you discuss the political motivation of each Roman emperor, the practice and/or meaning behind the gladiatorial entertainment and/or civic infrastructure for the Roman people, and the consequences of this power in the vast Roman empire.