This paper argues that game-theoretic approach is incomplete for institutional studies, because comparative institutions as well as institutional changes involve a possibility of multiple equilibria. In order to solve the common knowledge problem, this paper proposes to unify game theoretic thought with an analysis of public representations/propositions to summarize salient features of the recursive/emergent states of play. From this perspective the paper tries to reconcile differences in three accounts of institutions, endogenous outcome, exogenous rules and constitutive rules accounts. Then, the unified approach is applied to comparative and historical cases of the Tokugawa Japan and the Qing China. Specifically it sheds new light into the coalitional nature of Tokugawa Baku-Han regime nesting the fundamental Samurai-village pact as well as the tendency toward decentralization of political violence and fiscal competence to the provincial level toward the end of the Qing China. From these new historical interpretations, endogenous strategic forces and associated public propositions leading to institutional changes through the Meiji Restoration and the Xinhai Revolution are identified and compared.