Networks pervade social and economic life, and they play a prominent role in explaining a huge variety of social and economic phenomena. Standard economic theory did not give much credit to the role of networks until the early 1990s, but since then the study of the theory of networks has blossomed. At the heart of this research is the idea that the pattern of connections between individual rational agents shapes their actions and determines their rewards. The importance of connections has (...) in turn motivated the study of the very processes by which networks are formed. In Connections, Sanjeev Goyal puts contemporary thinking about networks and economic activity into context. He develops a general framework within which this body of research can be located. In the first part of the book he demonstrates that location in a network has significant effects on individual rewards and that, given this, it is natural that individuals will seek to form connections to move the network in their favor. This idea motivates the second part of the book, which develops a general theory of network formation founded on individual incentives. Goyal assesses the robustness of current research findings and identifies the substantive open questions. Written in a style that combines simple examples with formal models and complete mathematical proofs, Connections is a concise and self-contained treatment of the economic theory of networks, one that should become the natural source of reference for graduate students in economics and related disciplines. (shrink)

Modal logics for reasoning about social networks is currently an active field of research. There is still a gap, however, between the state of the art in logical formalisations of concepts related to social networks and the much more mature field of social network analysis. In this paper we take a step to bridge that gap. One of the key foundations of social network analysis is balance theory, which is used to analyse signed social networks where agents can have positive (...) or negative relationships. Certain combinations of positive and negative relationships are considered to be unbalanced, or unstable—in particular the occurrence of cycles with an odd number of negative relationships. Especially relatively short cycles with an odd number of negative relationships are thought to put pressure on the agents to change one or more of the involved relationships from negative to positive or the other way around. Most existing logics for reasoning about social networks are defined for unsigned networks. In this paper we develop a modal logic for reasoning about structural properties of signed social networks, and give a sound and complete Hilbert-style axiomatic system. Furthermore, we completely axiomatise classes of signed social networks that are balanced to a certain degree n, in the sense that there are no cycles of length up to n with an odd number of negative relationships. Finally, we completely axiomatise the class of all fully balanced complete signed social networks, i.e., networks where everyone is connected with everyone else. Axiomatic completeness is non-trivial because neither the balance properties, nor the dichotomy between positive and negative relations, are modally definable. The paper thus provides a logical basis for reasoning about signed social networks in general and balanced networks in particular. (shrink)