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. / Doctor of Philosophy / Competition and Time are two essential aspects of life. Many decisions are made in a competitive environment. Some other decisions are made when time serves as a critical factor. We divide this dissertation into two parts. In the first part, we study strategic behavior in competitions. Specifically, we examine how (1) the importance of each round (weight), (2) the number of competitors, and (3) the ambiguity of the rule affect the result of a multi-round competition. In the second part, we study people's subjective understanding of time, generally the personal beliefs and preferences of the present and future. In part one (Chapter 2 and Chapter 3), first, we find people are very responsive about the importance of a round in a multi-round competition. When a round is more important, people make more effort in such round. People are also sensible about the competition's current status (leading, behind, or tied) rather than the history. Second, at the beginning of a competition, we find an increase in the participation rate when fewer competitors exist. Suppose there are more competitors; the leading position players compete more brutally; on the contrary, the non-leading players are discouraged more. Third, people spend more energy when the rule is less ambiguous in a multi-round competition. In part two (Chapter 4), We find a very diversified subjective belief in the word "present." The concept of "now" lasts longer than we conventionally thought. When the subjective "present'' is captured at the individual level, we find the immediate now is not necessarily the best way to represent the "average present'' for the population.