This paper introduces a core concept in an economy with an excludable public good. In the economy, we assume that each coalition is allowed to achieve an allocation via a menu, a kind of a nonlinear price. Our core concept is called the menu-induced core that is defined as the set of allocations achievable by menus that are robust against all coalitional improvements achieved via menus. We show that the menu-induced core is nonempty. We also investigate certain properties of the menu-induced core that show the difference between the menu-induced core and the core defined in a standard way.