Ronald Reagan and Mikhail Gorbachov having a staring contest.
Who is silly enough to play chicken?
Men, of course. Grown men. Chicken or brinkmanship is also used as a metaphor for contests where there is very little to gain and much to lose. It's basically the proverbial pissing contest or my dad is bigger than your dad, with bigger risks.
Many are of the opinion that an arms race is an example of chicken, though this is often not the case, as there may be more at stake than pure pride. During the Cold War, for example, the arms race was designed to bankrupt the Russian government, in addition to being a preventative measure against Russia's arms.
Game theory often analyses situations in terms of what could have been had different strategies been followed. In the case of an arms race, it is frequently the case that not having a considerable military capability leads to conflict. That is, not having weapons often leads one to be forced into conflict while having military capability often prevents conflict entirely. Like the saying goes, speak softly, but carry a big gun.
What is the optimal strategy for winning chicken?
The optimal strategy for winning chicken is not to play chicken at all. That is, to chicken out at any moment. With the game of chicken, if you chicken out you always win in the sense that you don't lose anything in real terms. If you don't chicken out, you only win if the opponent does chicken out.
Better to play games that are worth winning, like the lottery.