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Traditionally, real experiments testing subjective expected utility theory take for granted that subjects view the Ellsberg task as a one-person decision problem. We challenge this view: Instead of seeing the Ellsberg task as a one-person decision problem, it can be perceived as a two-player game. One player chooses among the bets. The second player determines the distribution of balls in the Ellsberg urn. The Nash equilibrium predictions of this game depend on the payoff of the second player, with the game ranging from a zero-sum one to a coordination game. Meanwhile, the predictions by ambiguity aversion models remain unchanged. Both situations are implemented experimentally and yield different results, in line with the game-theoretic prediction. Additionally, the standard scenario (without explicit mention of how the distribution is determined) leads to results similar to the zero-sum game, suggesting that subjects view the standard Ellsberg experiment as a game against the experimenter.

This thesis deals with decision making under ambiguity. Ambiguity refers to situations in which probabilities for uncertain events are partially known. Ambiguitysensitive behavior, as manifested in Ellsberg-type experiments, is today a widely studied phenomenon, then, first of all, there is an ample empirical evidence confirming ambiguity-sensitive behavior, and second, it cannot be explained by the subjective expected utility theory. The goal of this thesis is to explore further the nature of ambiguity-sensitive behavior in the context of static, dynamic and interpersonal decision problems. For this purpose we apply experimental as well as formal methods. Our first investigation focuses on static decision problems. We test the descriptive validity of the widely accepted methodology used to formalize the notion of different ambiguity attitudes, namely, that ambiguity-averse subjects are randomization-loving, while ambiguity-loving subjects are randomization-averse. Our experimental data do not support this view. Ambiguity-averse subjects are more likely to be randomizationneutral rather than randomization-loving. Furthermore, we also observe a considerable number of ambiguity-averse subjects who exhibit a contempt for randomization. These observations suggest that ambiguity models which do not exogenously assume a specific relationship between ambiguity and randomization attitudes would be better suited to describe real behavior in the presence of ambiguity. Next, we focus on dynamic decision problems. In a dynamic version of the classical 3-color experiment of Ellsberg (1961) we test whether subjects behave consistently with either dynamic consistency or consequentialism. We find that more subjects act in line with consequentialism rather than with dynamic consistency and that this result is even stronger among ambiguity-averse subjects. This evidence can be seen as support for theories of updating ambiguity-sensitive preferences which maintain consequentialism and relax dynamic consistency. Furthermore, we find additional violation of the subjective expected utility theory in the dynamic experiment. Several subjects who are classified as ambiguity-neutral in the static choice situation do not exhibit Bayesian behavior in the dynamic extension. They violate either dynamic consistency or conse quentialism. Therefore, the dynamic version of the 3-color experiment can also be seen as a tool to test Bayesianism and to make the observation from static experiment more robust. In the second part we continue to study dynamic choice problems, but constrain the analysis to the class of Choquet expected utility preferences of Schmeidler (1989). We argue that this class of preferences has a very attractive feature. Namely, it is possible to characterize dynamic properties of Choquet preferences from a static point of view by constraining the analysis to a fixed collection of events. Assuming consequentialism, we show that Choquet expected utility preferences respect dynamic consistence on a fixed collection of events if and only if these events are unambiguous in the sense of Nehring (1999). Accordingly, one can apply the same techniques used in expected utility theory to solve optimization problems, e.g. backward induction. In the last part of this thesis we apply the Choquet expected utility theory to interpersonal decision problems. We show that, unlike in the subjective expected utility theory of Savage, asymmetric information matters in presence of ambiguity and can explain differences in commonly known decisions. Under the assumption of common capacity distribution it is shown that whenever agents’ private information partitions are made up of unambiguous events in the sense of Nehring (1999) then it is impossible that the agents disagree on commonly known decisions, whatever these decisions are, whether conditional beliefs or conditional expectations. Consequently, the possibility of speculative trade is precluded only if private information is made up of unambiguous events in this peculiar sense. Even a small departure from that notion of unambiguous events creates profitable trade opportunities due to differences in agents’ private and ambiguous information. We conclude that the presence of ambiguous private information provides an intuitive explanation for the existence of widely observed speculative activities. Ellsberg, D. (1961): “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics, 75, 643–669. Nehring, K. (1999): “Capacities and Probabilistic Beliefs: A Precarious Coexistence,” Mathematical Social Science, 38, 197–213. Schmeidler, D. (1989): “Subjective Probability and Expected Utility without Additivity,” Econometrica, 57, 571–587.

Individuals exhibit a randomization preference if they prefer random mixtures of two bets to each of the involved bets. Such preferences provide the foundation of various models of uncertainty aversion. However, it has to our knowledge not been empirically investigated whether uncertainty-averse decision makers indeed exhibit such preferences. Here, we examine the relationship experimentally. We find that uncertainty aversion is not positively associated with randomization preferences. Moreover, we observe choices that are not consistent with the prevailing theories of uncertainty aversion: a non-negligible number of uncertain-averse subjects seem to dislike randomization.

This paper explores the relationship between dynamic consistency and the existing notions of unambiguous events for Choquet expected utility preferences. A decision maker is faced with an information structure represented by a filtration. We show that the decision maker's preferences respect dynamic consistency on a fixed filtration if and only if the last stage of the filtration is composed of unambiguous events in the sense of Nehring (1999). Adopting two axioms, conditional certainty equivalence consistency and constrained dynamic consistency to filtration measurable acts, it is shown that the decision maker respects these two axioms on a fixed filtration if and only if the last stage of the filtration is made up of unambiguous events the sense of Zhang (2002).

Two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory: dynamic consistency and consequentialism. Dynamic consistency requires that ex ante contingent choices are respected by updated preferences. Consequentialism states that only those outcomes which are still possible can matter for updated preferences. We test the descriptive validity of these rationality arguments with a dynamic version of Ellsberg's three color experiment and find that subjects act more often in line with consequentialism than with dynamic consistency.

Individuals exhibit preferences for randomization if they prefer random mixtures of two bets to each of the involved bets. Such preferences underpin various models of uncertainty aversion. However, it has to our knowledge not been empirically investigated whether uncertainty-averse decision makers indeed exhibit such preferences. Here, we examine the relationship experimentally. We find that uncertainty aversion is not positively associated with preferences for randomization. Moreover, we observe a puzzling behavior that is not predicted: a non-negligible number of uncertain-averse subjects seem to dislike randomization.

This dissertation focuses on exploring individual and strategic decision problems in Economics. I take a different approach in each chapter to capture various aspects of decision problems. An overview of this dissertation is provided in Chapter 1. Chapter 2 studies an individual's decision making in extensive-form games under ambiguity when the individual is ambiguous about an opponent's moves. In this chapter, a player follows Choquet Expected Utility preferences, since the standard Expected Utility cannot explain the situations of ambiguity. I raise the issue that dynamically inconsistent decision making can be derived in extensive-form games with ambiguity. To cope with this issue, this chapter provides sufficient conditions to recover dynamic consistency. Chapter 3 analyzes the strategic decision making in signaling games when a player makes an inference about hidden information from the behavioral hypothesis. The Hypothesis Testing Equilibrium (HTE) is proposed to provide an explanation for posterior beliefs from the player. The notion of HTE admits belief updates for all events including zero-probability events. In addition, this chapter introduces well-motivated modifications of HTE. Finally, Chapter 4 examines a boundedly rational individual who considers selective attributes when making a decision. It is assumed that the individual focuses on a subset of attributes that stand out from a choice set. The selective attributes model can accommodate violations of choice axioms of Independence from Irrelevant Alternative (IIA) and Regularity. Doctor of Philosophy This dissertation focuses on exploring individual and strategic decision problems in Economics. I take a different approach in each chapter to capture various aspects of decision problem. An overview of this dissertation is provided in Chapter 1. Chapter 2 studies an individual’s decision making in extensive-form games under ambiguity. Ambiguity describes the situation in which the information available to a decision maker is too imprecise to be summarized by a probability measure (Epstein, 1999). It is known that ambiguity causes dynamic inconsistency between ex-ante and interim decision making. This chapter provides sufficient conditions under which dynamic consistency is maintained. Chapter 3 analyzes the strategic decision making in signaling games in which there are two players: informed sender and uninformed receiver. The sender has a private information about his type and the receiver makes an inference about hidden information. This chapter suggests a notion of the Hypothesis Testing Equilibrium (HTE), which provides an alternative explanation for the receiver’s beliefs. The idea of the HTE can be used as a refinement of Perfect Bayesian Equilibrium (PBE) in signaling games to cope with the known limitations of PBE. Finally, Chapter 4 examines a boundedly rational individual who considers only salient attributes when making a decision. The individual considers an attribute only when it stands out enough in a choice set. The selective attribute model can accommodate violations of choice axioms of Independence from Irrelevant Alternative (IIA) and Regularity.

This dissertation studies two-person signaling games where the players are assumed to be Choquet expected utility maximizers a la Schmeidler (1989). The sender sends an ambiguous message to the receiver who updates his non-additive belief according to a f-Bayesian updating rule of Gilboa and Schmeidler (1993). When the types are unambiguous in the sense of Nehring (1999), the receiver's conditional preferences after updating on an ambiguous message are always of the subjective expected utility form. This property may serious limit the descriptive power of solution concepts under non-additive beliefs, and it is scrutinized with two extreme f-Bayesian updating rules, the Dempster-Shafer and the Bayes' rule. In chapter 3, the Dempster-Shafer equilibrium proposed by Eichberger and Kelsey (2004) is reappraised. Under the assumption of unambiguous types, it is shown that the Dempster-Shafer equilibrium may give rise to a separating behavior that is never supported by perfect Bayesian equilibrium. However, it does not support any additional pooling equilibrium outcome. Since the Dempster-Shafer equilibrium may support implausible behaviors as exemplified in Ryan (2002), a refinement based on coherent beliefs is suggested. In chapter 4, a variant of perfect Bayesian equilibrium, the quasi perfect Bayesian equilibrium, is proposed, and its descriptive power is investigated. It is shown that the quasi perfect Bayesian equilibrium does not support any additional separating behavior compared to perfect Bayesian equilibrium. It may support additional pooling behavior only if the receiver perceives a correlation between the types and messages. Ph. D.