Final answer:
The term to describe secret influence or puppeteer-like control is 'Manipulation', often seen in political negotiations and international power dynamics.
Step-by-step explanation:
The term used to describe when someone exerts secret influence to gain an end or how a puppeteer controls a marionette is Manipulation. This is seen in various contexts, such as political negotiations, where parties may engage in both persuasive tactics and more underhanded means to sway the outcome in their favor. Similarly, the exertion of power by states in the international arena to influence political institutions of other countries for their own strategic ends, as well as the strategic use of influence to safeguard and expand their power, is a form of manipulation.