ABSTRACT
Studies in econophysics and neuroeconomics show that humans or non humans prefer sooner but smaller monetary rewards to larger but later rewards [1-6], i.e. the present value of a reward decreases as the delay to that reward increases. For example, one typically would choose to receive $100 now over $100 tomorrow, $100 tomorrow over $100 the day after tomorrow, and so on. The classical economic theory assumes that people make rational decisions, and thus have consistent time preference. According to Strotz [7], such time-consistent behavior can be only modeled by exponential discounting. However, empirical studies have provided us with ample evidence, which shows anomaly in intertemporal choices [10-15, 17-19]. People generally exhibit dynamic inconsistency when making intertemporal choices, namely that people tend to make patient plans in the distant future, but act impatiently in the near future. Thus, discount factor between adjacent periods close by is smaller than between similar periods further away [2, 3]. This preference reversal over time is referred as dynamic inconsistency and can be better described by hyperbolic discount models [9, 13].
