Essays on Contest Theory Experiments and Revealed Time Preference Models

In this series of essays, we study the influence of weight and group size in the sequential multi-battle contest with laboratory experiences (Chapter 2 and Chapter 3). We then develop an empirical method to model perceptual present and time inconsistency (Chapter 4).

Chapter 2 examines how the weight and the ordered weights in battles affect the behavior in sequential multi-battle contests with an experiment. We find robustly that the weight of the current battle consistently influences contestants' efforts. Additionally, we discover the math-point-oriented behavior despite differences in history. In other words, the weight effect is expressed in two ways: influencing the effort of the current battle and transferring a contest to the next battle with a designated intensity.

Chapter 3 explores the group size effect and how the contest success functions influence the group size effect in sequential multi-battle contests with an experiment. We capture the negative group size effect on the leaders' efforts, participation and dropout rates; contrarily, the positive effect on the non-leaders' efforts. Compared to the Tullock lottery, the all-pay auction intensifies the group size effect of the high effort in the initial battle. It also enlarges the observed group size effects of the effort gaps between the leaders and the non-leaders.

Chapter 4 develops the quasi-hyperbolic discounting model into the general beta-delta model to parametrically detect and measure the inconsistency in revealed time preference. This method empirically classifies time preference into four categories, i.e., time consistent, present bias, future bias, and mixed inconsistent. Then we applied this method to the convex time budget data of seven experiments, including 3670 subjects. We discover empirical evidence supporting perceptual differences in the present-future threshold. Traditional present bias models may interpret the time preference imprecisely.