Abstract
The mathematical description of individual utility under incomplete rationality is discussed. Since the assumption of rational economic man was proposed, it has received numerous criticisms. As humanity is complex and variable, the assumption of incomplete rationality is introduced, which is an extension to the traditional complete rationality. An individual utility function under incomplete rationality is proposed to replace the individual benefit under complete rationality. The individual utility function has well analytical and symmetrical characteristics and is in good agreement with the trends of altruistic behaviors. It is helpful to describe the irrational behavior. The individual utility function is applied to find the harmonic solution of the Prisonerpsilas Dilemma.
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