Sergio Currarini

An Economic Model of Friendship: Homophily, Minorities and Segregation

We develop a model of friendship formation that sheds light on segregation patterns observed in social and economic networks. Individuals come in different types and have type-dependent benefits from friendships; we examine the properties of a steady-state equilibrium of a matching process of friendship formation. We use the model to understand three empirical patterns of friendship formation: (i) larger groups tend to form more same-type ties and fewer other-type ties than small groups, (ii) larger groups form more ties per capita, and (iii) all groups are biased towards same-type relative to demographics, with the most extreme bias coming from middle-sized groups. We trace each of these empirical observations to specific properties of the theoretical model and highlight the role of choice and chance in generating homophilous behavior. Finally we discuss welfare implications of the model.

Identifying the roles of race-based choice and chance in high school friendship network formation

Homophily, the tendency of people to associate with others similar to themselves, is observed in many social networks, ranging from friendships to marriages to business relationships, and is based on a variety of characteristics, including race, age, gender, religion, and education. We present a technique for distinguishing two primary sources of homophily: biases in the preferences of individuals over the types of their friends and biases in the chances that people meet individuals of other types. We use this technique to analyze racial patterns in friendship networks in a set of American high schools from the Add Health dataset. Biases in preferences and biases in meeting rates are both highly significant in these data, and both types of biases differ significantly across races. Asians and Blacks are biased toward interacting with their own race at rates >7 times higher than Whites, whereas Hispanics exhibit an intermediate bias in meeting opportunities. Asians exhibit the least preference bias, valuing friendships with other types 90% as much as friendships with Asians, whereas Blacks and Hispanics value friendships with other types 55% and 65% as much as same-type friendships, respectively, and Whites fall in between, valuing other-type friendships 75% as much as friendships with Whites. Meetings are significantly more biased in large schools (>1,000 students) than in small schools (<1,000 students), and biases in preferences exhibit some significant variation with the median household income levels in the counties surrounding the schools.

Network formation with sequential demands

This paper introduces a non-cooperative game-theoretic model of sequential network formation, in which players propose links and demand payoffs. Payoff division is therefore endogenous. We show that if the value of networks satisfies size-monotonicity, then each and every equilibrium network is efficient. Formation of networks satisfies size-monotonicity, then each and equilibrium network is efficient. Formation of networks through bilateral every negotiations (link-specific demands) and through absolute participation demands turn out to have the same efficiency properties. The result do not extend to the case in which players can only demand relative shares

Homophily and Long-Run Integration in Social Networks

We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is “long-run integration”, whereby the composition of types in sufficiently old nodesʼ neighborhoods approaches the global type-distribution, provided that the network-based search is unbiased. However, younger nodesʼ connections still reflect the biased meetings process. We derive the type-based degree distributions and group-level homophily patterns when there are two types and location-based biases. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals.

Bilateral Information Sharing in Oligopoly

We study the problem of information sharing in oligopoly, when sharing decisions are taken before the realization of private signals. Using the general model developed by Raith (1996), we show that if firms are allowed to make bilateral exclusive sharing agreements, then some degree of information sharing is consistent with equilibrium, and is a constant feature of equilibrium when the number of firms is not too small. Our result is to be contrasted with the traditional conclusion that no information is shared in common values situations with strategic substitutes - such as Cournot competition with demand shocks - when firms can only make industry-wide sharing contracts (e.g., a trade association).

A Sequential Approach to the Characteristic Function and the Core in Games with Externalities

This paper proposes a formulation of coalitional payoff possibilities in games with externalities, based on the assumption that forming coalitions can exploit a ”first mover advantage”. We derive a characteristic function and show that when outside players play their best response noncooperatively, the core is nonempty in games with strategic complements. We apply this result to Cournot and Bertrand games and to public goods economies.

A conjectural cooperative equilibrium for strategic form games

This paper presents a new cooperative equilibrium for strategic form games, denoted Conjectural Cooperative Equilibrium (CCE). This concept is based on the expectation that joint deviations from any strategy profile are followed by an optimal and noncooperative reaction of non deviators. We show that CCE exist for all symmetric supermodular games. Furthermore, we discuss the existence of a CCE in specific submodular games employed in the literature on environmental agreements.

Information sharing networks in linear quadratic games

We study the bilateral exchange of information in the context of linear quadratic games. An information structure is here represented by a non directed network, whose nodes are agents and whose links represent sharing agreements. We first study the equilibrium use of information given the network, finding that the extent to which a piece of information is observed by others affects the equilibrium use of it, in line with previous results in the literature. We then study the incentives to share information ex-ante, highlighting the role of the elasticity of payoffs to the equilibrium volatility of one’s own strategy and of opponents’ strategies. For the case of uncorrelated signals we fully characterise pairwise stable networks for the general linear quadratic game. For the case of correlated signals, we study pairwise stable networks for three specific linear quadratic games—Cournot Oligopoly, Keynes’ Beauty Contest and a Public Good Game—in which strategies are substitute, complement and orthogonal, respectively. We show that signals’ correlation favours the transmission of information, but may also prevent all information from being transmitted.

Network design in games with spillovers

How should an organization be designed in order to provide its members with minimal incentives to defect? And how does the optimal design depend on the type of strategic interaction between defectors and remaining organizational members? This paper addresses such issues in a game theoretic model of cooperation, in which an organization is formally represented by a connected network, and where gains from cooperation are given by a partition function. We show that critical structural features of the organization depend in a clear-cut way on the sign of spillovers. In particular, positive spillovers favor the adoption of dispersed and centralized forms, while negative spillovers favor cohesive and horizontal ones. Moreover, if the organizational form determines all the communication possibilities of members, a highly centralized organization - the star - emerges under positive spillovers, whereas two horizontal architectures - the circle and the complete - emerge under negative spillovers.

Stable Organizations with Externalities

We study the stability properties of organizations in partition function games, describing cooperative situations with externalities. An organization is defined as a group of agents, together with a set of bilateral relations, formally, a connected graph. Because of the presence of externalities, the profitability of coalitional threats to an organization depend on the reaction of non coalitional members. This reaction is likely to depend on the links that non coalitional members maintain in the organization. We show that this directly implies that minimally connected organizations emerge under positive externalities, while the fully connected organization emerges under negative. This result is shown to hold independently of the adopted payoff imputation rule. Sharper predictions are possible for the specific case of the egalitarian rule. Here, if only coalitions that are connected in the organization can effectively object to it, the star organization prevails under positive externalities, and the wheel, a non fully connected organization, prevails under negative.