If you don't know much about the other agent - except that it is also trying to win - I figure you should also probably just do the best you can to pick the most mutually-obvious ordering, hoping that they will be doing much the same. Sometimes, it won't work out - but that is doing as well as you can.

That's assuming linear utility. If the most important thing is to consistently get at least a few points, then randomness may be a better strategy.