From Decision Theory to Game Theory shows how the reasoning patterns of common belief in rationality, correct beliefs, and symmetric beliefs can be defined in a unified way. It explores the link between decision theory and game theory, particularly how various important classes of games (e.g., games with incomplete information, games with unawareness, and psychological games) can be analyzed from both a unified decision-theoretic and unified interactive-reasoning perspective. Providing a smooth transition between one-person decision theory and game theory, it views each game as a collection of one-person decision problems – one for every player. Written in a nontechnical style, this book includes practical problems and examples from everyday life to make the material more accessible.The book is targeted at a wide audience, including students and scholars from economics, mathematics, business, philosophy, logic, computer science, artificial intelligence, sociology, and political science.

This chapter starts by showing that a simple belief hierarchy in combination with common belief in rationality leads to psychological Nash equilibrium. It then turns to the weaker notion of symmetric belief hierarchies and shows, in a similar fashion, that a symmetric belief hierarchy in combination with common belief in rationality leads to psychological correlated equilibrium. It subsequently investigates the one theory per choice condition and demonstrates how it leads to canonical psychological correlated equilibrium when combined with common belief in rationality and a symmetric belief hierarchy.

After mastering the fundamentals of theory-driven empirical networks research, there are many options for what to do next. If you do not yet have a particular project in mind, reading widely can be a valuable source of inspiration – hopefully this book has conveyed that the range of possible applications is broad. If you do have one in mind, reading about methods of analysis can help choose a plan appropriate to the project. This chapter is designed to help select a way forward.

Once the data are collected and cleaned, we can start to explore features of the network. Taking an initial look at descriptive network statistics is a good way to take an overview of the data and to spot red flags that signal a problem with the data entry or cleaning. The earlier these can be identified, the better. This chapter serves as a tutorial for using R to do so using the igraph package. It introduces the process of importing a data file into R and walks through the first things you might do with the data, including computing descriptive statistics of the structural features, integrating substantive features of nodes and links, and visualizing the network.

The move from theory to empirics requires figuring out how to collect evidence that could support or disconfirm hypotheses derived from your theory. Empirically studying the network in your theory requires two steps: determining which nodes to include in your data and operationalizing the link type. This chapter helps a reader select the boundary that contains the nodes of interest, pointing out some subtle downsides to random sampling in network studies. It also helps readers determine whether they want to measure full networks or ego ones and offers pointers on operationalizing link types.

This chapter introduces some technical details about networks. Although they may seem like a complication that could be saved for later, the details presented here are actually a useful starting point. They will provide a sense of the many options for ways that a network can matter, which is helpful to have in mind when constructing a theory that will guide data collection. A social network is a record of a set of relationships – links – among actors in a group of interest. Depending on which relationships are present, an individual may find herself in a very different network position than someone else. Different groups can have different patterns of relationships, which means there can also be variation across networks. This chapter will help us be precise in these comparisons across actors and across networks and will highlight why they can be relevant to empirical research.

An empirical social networks study is concerned with what a well-defined social network is like, and whether and how it matters in some context of interest. Designing a successful one requires serious thinking on the front end about what the network is and what it does in theory. This book aims to help researchers do just that. To begin, this chapter motivates this research area with examples from political science, explains why the topic is unique enough to warrant a whole book, and offers guidance on how to know if your research should incorporate networks.

Once the theory is specified and an operationalization has been chosen for the nodes and links, the next step is to acquire the data. This chapter goes deep into issues that arise when designing surveys to collect data. Although this is not the only method of data collection, it is one that illuminates issues that pertain to all others. This chapter covers the practical question of how to use surveys to elicit network information. The advice leans heavily on a well-formulated theory.