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All of the game examples so far are relatively simple in that time plays no part in them, however complex they may be in other ways. The passage of time can make at least three kinds of differences. First, people may learn -- new information may become available, that affects the payoffs their strategies can give. Second, even when people do not or cannot commit themselves at first, they may commit themselves later -- and they may have to decide when and if to commit. Of course, this blurs the distinction we have so carefully set up between cooperative and noncooperative games, but life is like that. Third, there is the possibility of retaliation against other players who fail to cooperate with us. That, too, blurs the cooperative-noncooperative distinction. That means, in particular, that repeated games -- and particularly repeated prisoners' dilemmas -- may have quite different outcomes than they do when they are played one-off. But we shall leave the repeated games out as an advanced topic and move on to study sequential games and the problems that arise when people can make commitments only in stages, at different points in the game. I personally find these examples interesting and to the point and they are somewhat original.
There are some surprising results. One surprising result is that, in some games, people are better off if they can give up some of their freedom of choice, binding themselves to do things at a later stage in the came that may not look right when they get to this stage. An example of this (I suggest) is to be found in Marriage Vows. This provides a good example of what some folks call "economic imperialism" -- the use of economics (and game theory) to explain human behavior we do not usually think of as economic, rational, or calculating -- although you do not really need to know any economics to follow the example in Marriage Vows. Another example along the same line (although the main application is economics in a more conventional sense) is The Paradox of Benevolent Authority, which tries to capture, in game-theoretic terms, a reason why liberal societies often try to constrain their authorities rather than relying on their benevolence.
Also, the following example will have to do with relations between an employer and an employee: A Theory of Burnout. For an example in which flexibility is important, so that giving up freedom of choice is a bad idea, and another non-imperialistic economic application of game theory, see The Essence of Bankruptcy. Of course, that note is meant to discuss bankruptcy, not to exemplify it!
Roger A. McCain 