Optimal Duck Behavior: A Theoretical Analysis Submitted to the Faculty of Economics and Business Administration in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Animal Behavior by Conrad Lorenz Lilienweg 12 12203 Berlin Matr.: 12345467 written under the supervision of Ursula Bauer und Wendelin Schnedler Paderborn, February 1, 2018
Informal teaser Here you write a non-technical teaser in English, which captures the main idea and results of your research for a non-scientific audience. 1
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Contents 1 Introduction 5 2 Simple Example 7 3 Model (replace by content-related title) 8 4 Analysis (replace by content-related title) 9 5 Robustness (replace by content-related title) 10 6 Conclusion 11 4
Chapter 1 Introduction The introduction should include the following elements Motivation (1-3 paragraphs): here you explain why the reader should be interested in your work; at the end, the reader should be able to formulate your research question Claim/Main statement/central Results (1 paragraph): here you describe the main message of your paper as shown by your results; after this paragraph the reader should be able to answer your research question Method (1-3 paragraphs): here you explain the intuition that underpins your results; after this paragraph, the reader should be able to explain why your results are true Contribution to literature (1-3 paragraphs): here you describe how you relate to the existing scientific literature; after this part, the reader should be able to explain what you have done that others have not done before Brief overview on the structure (1 short paragraph): here you describe the outline, the structure of the thesis. When young, ducks have the tendency to follow others. This behavior has been documented in countless observational studies Holmström (see e.g. 1982). It has been pointed out that this behavior is crucial for their survival as a species Gjesdal (1976); Baker (2000); Kim (1995). The observed behavior is not only important for ducks but is also highly relevant for human decision making. Gibbons (1998) argues that humans essentially behave like ducks when it comes to finding a decision in what he calls a stressful situation. Moreover, Kohn (2005) claims that human behavior [in such situations] is best understood by studying ducks. There are, however, two possible reasons why ducks may follow each other. First, it may be a genetically coded program. Second, it may be their conscious decision (deliberation). The difference is crucial also when it comes to human beings. Do they follow because it is in their instinct? Or, is that optimal group behavior? The present paper provides a theoretical model to answer this question. The key message of the paper is that following is automatized in stressful situations but deliberate in calm situations. The analysis rests on three assumptions. First, ducks like mud. Second, they fear the fox. Third,... 5
The intuition for the result is the following. Consider the assumption that,... Duck behavior has been the focus of many economic analysis. There have been various empirical and experimental studies (see the survey article by Feltham and Xie, 1994) and many theoretical contributions. 1 Closest to this paper is the study be Prendergast (1999). The crucial difference is that Prendergast does not consider the possibility that the reasons for duck behavior may depend on the conditions in which they act. Here, we explicitly distinguish between stressful and calm situations... The thesis will be structured as follows. The next chapter introduces a simple example, which illustrates the main mechanisms at work. Chapter 3 presents a general model, which is then analyzed in Chapter 4. In Chapter 5, I show that the assumption that ducks like mud is crucial; it will also turn out that even allowing for rivalry between duck siblings does not affect the results. Chapter 6 concludes. 1 These include amongst others... 6
Chapter 2 Simple Example Here you explain the main insights from your model in the simplest possible form. If you only have one simple example, this chapter is skipped and your example becomes your model. For simplicity, consider only two ducks: Dagobert and Donald. Assume that they both enjoy playing in the mud m, while they fear the fox f. Their utility hence amounts to u i (m, f) = m f 2, where i {Dagobert, Donald}. Let Dagobert be more experienced... The duck stays in the mud until the marginal benefits from the mud equal the marginal losses from encountering the fox: du i dm = du i df (2.1) 7
Chapter 3 Model (replace by content-related title) Here you explain the formal assumptions of the model and relate them to your application; after this part, the reader should be able to judge whether he or she thinks that your assumptions are reasonable. Definition 1 (deliberate and instinctive following). If following maximizes the duck s expected utility in a given situation, we speak of deliberate following. If following is adapted as a response to a specific pattern, it is instinctive. 8
Chapter 4 Analysis (replace by content-related title) Here you explain the logic of your argument, which auxiliary result (lemma) leads to which main result (proposition) and how these results follow from your assumptions; after this part, the reader should be able to describe how you formally get your results. This chapter explains which motive applies to duck s behavior and when. I first show that,... Later, I use this to demonstrate the main result. All proofs can be found in the appendix. Proposition 1. Ducks follow instinctively if and only if they are under stress. The intuition for this results is... 9
Chapter 5 Robustness (replace by content-related title) Here you explain how deviating from assumptions would affect results; after this part, the reader should be able to describe which of the assumptions are crucial and why. One assumption that we made earlier is that ducks like mud. This section examines how results depend on this assumption. It will turn out that it is crucial. We will also look at the assumption that there is no rivalry between ducks. As will become clear, our results hold (under specific circumstances) even if their is rivalry between ducks. 10
Chapter 6 Conclusion Here you have a second chance to motivate your paper; in addition you can state problems that still need to be tackled and you can speculate. Many decisions by humans are made collectively. The very idea of democracy... In order to better understand human behavior in such situations, this paper has focused on our close relative: the duck. Using the natural assumptions that ducks like mud and do not like the fox and... it was possible to show that... This has important implications for policy makers. In particular,... 11
Bibliography Baker, George, Survival of Ducks - An Economic Analysis, American Economic Review, May 2000, 90 (2), 415 420. Feltham, Gerald A. and Jim Xie, Accounting for Duck Behavior, The Accounting Review, July 1994, 69 (3), 429 453. Gibbons, Robert, Ducks and Humans: Some Striking Similarities, Journal of Economic Perspectives, Fall 1998, 12 (4), 115 132. Gjesdal, Froystein, Survival of Ducks in Agency Problems, 1976. Graduate School of Businness, Stanford University. Holmström, Bengt, Follow the Duck, Bell Journal of Economics, 1982, 13 (2), 324 340. Kim, Son Ku, Efficient Behavior in Ducks, Econometrica, January 1995, 63 (1), 89 102. Kohn, Alfie, Ducks and Stress, Atria Books, 2005. Prendergast, Canice, A Theoretical Analysis of Duck Behavior, Journal of Economic Literature, March 1999, XXXII, 7 63. All the reverences are in the file literature.bib. Here, you have to put in all the information. 12
Proofs Here are the formal/mathematical proofs for your results Proposition 1. Take duck δ with an ambition. Due to concavity of the duck s utility... 13
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