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In this Element, we present Dutch Book arguments for the principles of Probabilism, Conditionalization, and the Reflection Principle, among others, and we formulate and consider the most serious objections to them. We show that degrees of belief that don't satisfy the principles will always guide action in some way that is bad or undesirable.

The main aim of this Element is to introduce the topic of limited awareness, and changes in awareness, to those interested in the philosophy of decision-making and uncertain reasoning. While it has long been of interest to economists and computer scientists, this topic has only recently been subject to philosophical investigation.

Evidential Decision Theory is a radical theory of rational decision-making. It recommends that instead of thinking about what your decisions *cause*, you should think about what they *reveal*. This Element explains in simple terms why thinking in this way makes a big difference, and argues that doing so makes for *better* decisions.

Drawing and building on the existing literature, this Element explores the interesting and challenging philosophical terrain where issues regarding cooperation, commitment, and control (particularly self-control) intersect.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement.

Evolutionary game theory originated in population biology from the realisation that frequency-dependent fitness introduced a strategic element into evolution. Since its development, evolutionary game theory has been adopted by many social scientists, and philosophers, to analyse interdependent decision problems played by boundedly rational individuals. Its study has led to theoretical innovations of great interest for the biological and social sciences. For example, theorists have developed a number of dynamical models which can be used to study how populations of interacting individuals change their behaviours over time. In this introduction, this Element covers the two main approaches to evolutionary game theory: the static analysis of evolutionary stability concepts, and the study of dynamical models, their convergence behaviour and rest points. This Element also explores the many fascinating, and complex, connections between the two approaches.

The Nash bargaining problem provides a framework for analyzing problems where parties have imperfectly aligned interests. This Element reviews the parts of bargaining theory most important in philosophical applications, and to social contract theory in particular. It discusses rational choice analyses of bargaining problems that focus on axiomatic analysis, according to which a solution of a given bargaining problem satisfies certain formal criteria, and strategic bargaining, according to which a solution results from the moves of ideally rational and knowledgeable claimants. Next, it discusses the conventionalist analyses of bargaining problems that focus on how members of a society can settle into bargaining conventions via learning and focal points. In the concluding section this Element discusses how philosophers use bargaining theory to analyze the social contract.

Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. This title is also available as Open Access on Cambridge Core.

This Element offers an accessible but technically detailed review of expected utility theory (EU), which is a model of individual decision-making under uncertainty that is central for both economics and philosophy. The Element's approach falls between the history of ideas and economic methodology. At the historical level, it reviews EU by following its conceptual evolution from its original formulation in the eighteenth century through its transformations and extensions in the mid-twentieth century to its more recent supersession by post-EU theories such as prospect theory. In reconstructing the history of EU, it focuses on the methodological issues that have accompanied its evolution, such as whether the utility function and the other components of EU correspond to actual mental entities. On many of these issues, no consensus has yet been reached, and in this Element the author offers his view on them.