Alleviating time inconsistent behaviors via a competition scheme

Under quasi-hyperbolic discounting, the valuation of a payoff falls relatively rapidly for earlier delay periods, but then falls more slowly for longer delay periods. When the salespersons with quasi-hyperbolic discounting consider the product sale problem, they would exert less effort than their early plan, thus resulting in losses of future profit. We propose a winner-takes-all competition to alleviate the above time inconsistent behaviors of the salespersons, and allow the company to maximize its revenue by choosing an optimal bonus. To evaluate the effects of the competition scheme, we define the group time inconsistency degree of the salespersons, which measures the consequence of time inconsistent behaviors, and two welfare measures, the group welfare of the salespersons and the company revenue. We show that the competition always improves the group welfare and the company revenue as long as the company chooses to run the competition in the first place. However, the effect on group time inconsistency degree is mixed. When the optimal bonus is moderate (extreme high), the competition motivates (over-motivates) the salesperson to work hard, thus alleviates (worsens) the time inconsistent behaviors.