Prior to its entry into force, an agreement made pursuant to this act shall be filed with the register of deeds of the county where such political subdivision or agency of the state government is located and with the secretary of state. In the event that an agreement entered into pursuant to this act is between or among one or more public agencies of this state and one or more public agencies of another state or of the United States, said agreement shall have the status of an interstate compact, but in any case or controversy involving performance or interpretation thereof or liability thereunder, the public agencies party thereto shall be real parties in interest and the state may maintain an action to recoup or otherwise make itself whole for any damages or liability which it may incur by reason of being joined as a party therein. Such action shall be maintainable against any public or private agency or agencies whose default, failure of performance, or other conduct caused or contributed to the incurring of damage or liability by the state.