The halacha (Orah Hayyim 677) is that a guest must contribute a perutah towards the fulfillment of the mitzvah of lighting Chanuka candles. I would like to know why we don't find a similar idea by other mitzvot? For example we don't say that a guest at Sukkot needs to contribute a perutah so that he has partial ownership over the sukkah he is eating in.
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You are correct about the halacha about a guest contributing a perutah towards the Chanukah candles. And interesting enough there is a דעה in the גמרא (we don't paskin like this דעה) but there is a דעה in מסכת סוכה who says that a person isn't Yotzeh residing in his succah unless he owns it. So contributing to the succah would be like having a חלק of the succah. However since we don't paskin like this דעה we cannot use him as a proof to your question. However the answer I believe is that the guidelines for the mitzvah of נר חנוכה was set up strictly by the rabbis who said that a person has to sell the clothes off his back to be Yotzeh the mitzvah! Chazal doesn't say that about נר שבת or נר יום טוב. So if you have to go to that extent then surely you must have a חלק in the candles by contributing a perutah