German Title: Strategische Interaktion unter Unsicherheit

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## Abstract

The theory of strategic interaction or, game theory, for short, plays an important role in economics. It can offer insights into situations in which two or more interacting individuals choose actions that jointly affect the payoff of each party. Game-theoretic applications cover a wide range of economic, political and social situations such as auctions, contract formation, bargaining situations, political competition, and public good provision, to only name a few. This broad scope of application makes it a powerful concept. Most games involve some kind of uncertainty. For instance, players may be uncertain about the strategy choice of other players or they may lack information about the strategic environment. Game theory is closely tied to decision theory. In fact, the former can be viewed as the natural extension of the latter. In the words of Myerson (1991, p. 5): "The logical roots of game theory are in Bayesian decision theory. Indeed, game theory can be viewed as an extension of decision theory [...]. Thus, to understand the fundamental ideas of game theory, one should begin by studying decision theory." Bayesian decision theory assumes that decision makers' subjective beliefs can be represented by unique probability measures and that they update their prior beliefs in accordance with Bayes' rule when receiving new information. Furthermore, Bayesian decision-makers usually are subjective expected utility maximizers. Savage (1954) provided an axiomatic foundation for the Bayesian approach. His subjective expected utility theory has become the leading model of choice under uncertainty.

However, Ellsberg (1961) questioned the descriptive adequacy of subjective expected utility theory. He exempliffed that the choice behavior of many subjects is not consistent with Savage's theory when facing "ambiguous uncertainty", or "ambiguity", that is, a situation in which some events have known probabilities, whereas for other ones the probabilities are unknown. Ellsberg's observation has received powerful empirical support in the last decades (see Camerer and Weber, 1992). In this thesis, the term "uncertainty" will be used as a generic term to cover both ambiguity and non-ambiguous uncertainty ("risk"). To represent behavior as observed by Ellsberg, several alternatives to subjective expected utility theory have been suggested in recent years. Two prominent alternatives are Choquet expected utility theory of Schmeidler (1989) and the multiple prior approach of Gilboa and Schmeidler (1989). More recent examples are the smooth ambiguity model of Klibanoff et al. (2005) and the variational model of Maccheroni et al. (2006). The main goal of this thesis is to shed some light on the impact of ambiguity-sensitive behavior on strategic decision-making in interactive situations. As Crawford (1990, p. 152) appropriately expressed it: "In recent years, non-expected utility decision models have given us significantly better explanations of observed behavior in nonstrategic environments. These successes, and the weight of the experimental evidence against the expected utility hypothesis, suggest that much might be learned about strategic behavior by basing applications of game theory on more general models of individual decisions under uncertainty." In this spirit, the present thesis investigates non-cooperative game models that are based on alternative models of individual decision-making under uncertainty. The main body of this dissertation consists of three chapters (Chapters 4, 5 and 6), each of which studies strategic interaction under uncertainty. Chapter 4 and 5 explore formal models in which uncertainty arises from exogenous chance moves and incomplete information, respectively. While the game studied in Chapter 4 does not involve private information, the model in Chapter 5 allows for private information. Chapter 6 experimentally examines the extent to which a lack of information about others' preferences affects subject behavior. It is shown that a strategic ambiguity model as well as a quasi Bayesian model of incomplete information explain the findings better than standard Nash equilibrium.

The results of chapters 4 and 6 are based on collaborative work with Boris Wiesenfarth (Chapter 4), and Christoph Brunner and Hannes Rau (Chapter 6). This thesis is organized as follows. Chapter 2 outlines the decision-theoretic foundations of the interactive models studied in this work. First, the historical development of modern decision theory is briefly reviewed. I recall in some detail the fundamentals of subjective expected utility theory as well as the experiments by Ellsberg (1961). Finally, alternative models of choice under uncertainty are considered, especially, the Choquet expected utility model and the multiple prior model. These models will be used in subsequent chapters. Chapter 3 discusses some conceptual foundations of non-cooperative game theory. It starts with sketching the historical roots of modern game theory. Basic concepts such as the concept of a game and the Nash equilibrium concept are recalled. The last part of this chapter deals with different sources of uncertainty in games. In the context of strategic uncertainty, I describe generalized equilibrium concepts that allow for players whose preferences are not represented by expected utility functionals. Furthermore, I review the class of Bayesian games introduced by Harsanyi (1967-68) to analyze games of incomplete information. In Chapter 4, a Hotelling duopoly game that incorporates ambiguous uncertainty about the market demand is examined. The key assumption of this model is that firms' beliefs are represented by neo-additive capacities introduced by Chateauneuf et al. (2007). The related literature is reviewed and the model is specified. Moreover, this chapter discusses implications for possible applications of the Capacity model and limitations of the existing models. Chapter 5 investigates the extent to which we can distinguish expected and uncertainty-averse non-expected utility players on the basis of their behavior. A model of incomplete information games is used in which players can choose mixed strategies. First, this model is illustrated by two examples and described in detail. The following part of the chapter provides the results. Subsequently, I discuss the underlying model and introduce a generalized equilibrium concept. Chapter 6 reports on the results of the aforementioned experimental study testing whether revealing players' preferences to each other leads to more equilibrium play. Chapter 7 concludes with an overall summary.

Document type: | Dissertation |
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Supervisor: | Eichberger, Prof. Dr. Jürgen |

Date of thesis defense: | 9 November 2016 |

Date Deposited: | 28 Nov 2016 07:45 |

Date: | 2016 |

Faculties / Institutes: | The Faculty of Economics and Social Studies > Alfred-Weber-Institut for Economics |

DDC-classification: | 300 Social sciences 330 Economics |