Searching for equilibria can be infohazardous. You might not like the one you find first, but you might end up sticking with it (or worse, deviating from it and being punished). This is because which equilbrium gets played by other people depends (causally or, in some cases, acausally) not just on what equilibrium you play but even on which equilibria you think about. For reasons having to do with schelling points. A strategy that sometimes works to avoid these hazards is to impose constraints on which equilibria you think about, or at any rate to perform a search through equilibria-space that is guided in some manner so as to be unlikely to find equilibria you won't like. For example, here is one such strategy: Start with a proposal that is great for you and would make you very happy. Then, think of the ways in which this proposal is unlikely to be accepted by other people, and modify it slightly to make it more acceptable to them while keeping it pretty good for you. Repeat until you get something they'll probably accept.