 A more serious threat to the usefulness of game theory is evidence of systematic reversal of preferences, in both humans and other animals. This is more serious both because it extends beyond the human case, and because it challenges Revealed Preference Theory (RPT) rather than just unnecessarily rigid commitment to EUT. As explained in  Section 2.1,  RPT, unlike EUT, is among the axiomatic foundations of game theory interpreted non-psychologically. (Not all writers agree that apparent preference reversal phenomena threaten RPT rather than EUT; but see the discussions in  Camerer (1995),  pp. 660–665, and  Ross (2005a),  pp. 177–181.) A basis for preference reversals that seems to be common in animals with brains is hyperbolic discounting of the future  (Strotz 1956,  Ainslie 1992). This is the phenomenon whereby agents discount future rewards more steeply in close temporal distances from the current reference point than at more remote temporal distances. This is best understood by contrast with the idea found in most traditional economic models of exponential discounting, in which there is a linear relationship between the rate of change in the distance to a payoff and the rate at which the value of the payoff from the reference point declines. The figure below shows exponential and hyperbolic curves for the same interval from a reference point to a future payoff. The bottom one graphs the hyperbolic function; the bowed shape results from the change in the rate of discounting.