And there's worse: If your temporal discounting follows any curve other than the exponential, you'll have time-inconsistent goals that force you to wage war against your future selves - preference reversals - cases where your self of 2008 will pay a dollar to ensure that your future self gets option A in 2011 rather than B in 2010; but then your future self in 2009 will pay another dollar to get B in 2010 rather than A in 2011.

Eliezer, you're make non-exponential discounting out to be worse that it actually is. "Time-inconsistent goals" just means different goals, and do not "force you to wage war against your future selves" more than my having different preferences from you forces us to war against each other. One's (non-exponential discounting) agent-moments can avoid war by conventional methods such as bargains or unilateral commitments enforced by third parties, or by more exotic methods such as application of TDT.

For your specific example, conventional game theory says that since agent_2009 moves later, backward induction implies that agent_2008 should not pay $1 since if he did, his choice would just be reversed by agent_2009. TDT-type reasoning makes this game harder to solve and seems to imply that agent_2008 might have some non-zero bargaining power, but in any case I don't think we should expect that agent_2008 and agent_2009 each end up paying $1.