Games on Endogenous Networks

We study network games in which players both create spillovers for one another and choose with whom to associate. The endogenous outcomes include both the strategic actions (e.g., effort levels) and the network in which spillovers occur. We introduce a framework and two solution concepts that extend standard approaches -- Nash equilibrium in actions and pairwise (Nash) stability in links. Our main results show that under suitable monotonicity assumptions on incentives, stable networks take simple forms. Our central conditions concern whether actions and links are strategic complements or substitutes, as well as whether links create positive or negative payoff spillovers. We apply our model to understand the consequences of competition for status, to microfound matching models that assume clique formation, and to interpret empirical findings that highlight unintended consequences of group design

Pairwise stable networks in homogeneous societies

Hellmann T, Landwehr J. Pairwise stable networks in homogeneous societies. Center for Mathematical Economics Working Papers. Vol 517 Version Januar 2018. Bielefeld: Center for Mathematical Economics; 2018.We study general properties of pairwise stable networks in homogeneous societies, i.e. when agents' utilities differ only with respect to their network position while their names do not matter. Rather than assuming a particular functional form of utility, we impose general link externality conditions on utility such as ordinal convexity and ordinal strategic complements. Depending on these rather weak notions of link externalities, we show that pairwise stable networks of various structure exist. For stronger versions of the convexity and strategic complements conditions, we are even able to characterize all pairwise stable networks: they are nested split graphs (NSG). We illustrate these results with many examples from the literature, including utility funtions that arise from games with strategic complements played on the network and utility funtions that depend on centrality measures such as Bonacich centrality

The computation of pairwise stable networks

One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in the network and adapt the linear tracing procedure for non-cooperative games to the network formation problem. As a by-product of our main result, we obtain that the number of pairwise stable networks is generically odd. We apply the algorithm to the connections model and obtain a number of novel insights

A strategic model for network formation

We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for game-theoretic network formation models in which links are formed due to strategic behaviors of individuals, rather than based on probabilities. Inspired by Even-Dar and Kearns' model [8], we consider a more realistic framework in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation and maintenance of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most 4 in the general set of equilibrium networks in our model. We achieved an economic mechanism and its dynamic process for individuals which firstly; unlike the earlier model, the outcomes of players' interactions or the equilibrium networks are guaranteed to exist. Furthermore, these networks coincide with the outcome of pairwise Nash equilibrium in network formation. Secondly; it generates large-scale networks that have a rational and strategic microfoundation and demonstrate the main characterization of small degree of separation in real-life social networks. Furthermore, we provide a network formation simulation that generates small-world networks

Competition for the access to and use of information in networks

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2016.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2016.33 - ISSN : 1955-611XIn a network formation framework, where payoffs reflect an agent's ability to access information from direct and indirect contacts, we integrate negative externalities due to connectivity associated with two types of effects: competition for the access to information, and rivalrous use of information. We consider two separate models to capture the first and the second situations, respectively. In the first model, we assume that information is a non-rivalrous good but that there is competition for the access to information, for example because an agent with many contacts must share his time between them and thus has fewer opportunities to pass on information to each particular contact. The main idea is that the probability that each neighbor receives the information decreases with the number of contacts the sender has. In the second model, we assume that there is not competition for the access to information but that the use of information is rivalrous. In this case, it is assumed that when people receive the information before me, the harmful effect is greater than when others receive the information at the same time as myself. Our results concern pairwise stability and efficiency in both models and allow us to compare and contrast the effects of two kinds of competition for information.Dans un cadre de formation de réseau, où les gains reflètent la capacité d'un agent pour accéder aux informations de contacts directs et indirects, nous intégrons des externalités négatives dues à la connectivité associé à deux types d'effets : la concurrence pour l'accès à l'information, et l'utilisation de la rivalité de l'information. Nous considérons deux modèles distincts pour capturer la première et la seconde situation, respectivement. Dans le premier modèle, nous supposons que l'information est un bien non-rivalité, mais qu'il existe une concurrence pour l'accès à l'information, par exemple en raison d'un agent avec de nombreux contacts qui doit partager son temps entre eux et a donc moins d'occasions de transmettre des informations à chaque contact. L'idée principale est que la probabilité que chaque voisin reçoit l'information diminue avec le nombre de contacts qu'a l'expéditeur. Dans le second modèle, nous supposons qu'il n'y a pas de concurrence pour l'accès à l'information, mais que l'utilisation de l'information est compétitive. En outre, il est supposé que les personnes qui reçoivent l'information avant moi ont un effet plus néfaste sur mon utilité que les personnes qui reçoivent l'information en même temps que moi. Nos résultats concernent la stabilité par paire et l'efficacité dans les deux modèles et nous permettent de comparer et contraster les effets de deux types de concurrence pour obtenir des informations

“Friends Are Thieves of Time": Heuristic Attention Sharing in Stable Friendship Networks

This paper studies a model of network formation in which agents create links following a simple heuristic -- they invest their limited resources proportionally more in neighbours who have fewer links. This decision rule captures the notion that when considering social value more connected agents are on average less beneficial as neighbours and node degree is a useful proxy when payoffs are difficult to compute. The decision rule illustrates an externalities effect whereby an agent's actions also influence his neighbours' neighbours. Besides complete networks and fragmented networks with complete components, the pairwise stable networks produced by this model include many non-standard ones with characteristics observed in real life networks like clustering and irregular components. Multiple stable states can develop from the same initial structure -- the stable networks could have cliques linked by intermediary agents while sometimes they have a core-periphery structure. The observed pairwise stable networks have close to optimal welfare. This limited loss of welfare is due to the fact that when a link is established, this is beneficial to the linking agents, but makes them less attractive as neighbours for others, thereby partially internalising the externalities the new connection has generated

Incentive-Aware Models of Financial Networks

Financial networks help firms manage risk but also enable financial shocks to spread. Despite their importance, existing models of financial networks have several limitations. Prior works often consider a static network with a simple structure (e.g., a ring) or a model that assumes conditional independence between edges. We propose a new model where the network emerges from interactions between heterogeneous utility-maximizing firms. Edges correspond to contract agreements between pairs of firms, with the contract size being the edge weight. We show that, almost always, there is a unique "stable network." All edge weights in this stable network depend on all firms' beliefs. Furthermore, firms can find the stable network via iterative pairwise negotiations. When beliefs change, the stable network changes. We show that under realistic settings, a regulator cannot pin down the changed beliefs that caused the network changes. Also, each firm can use its view of the network to inform its beliefs. For instance, it can detect outlier firms whose beliefs deviate from their peers. But it cannot identify the deviant belief: increased risk-seeking is indistinguishable from increased expected profits. Seemingly minor news may settle the dilemma, triggering significant changes in the network

Structural estimation of pairwise stable networks with nonnegative externality

This paper develops a framework to structurally estimate pairwise stable networks with nonnegative externality. We characterize pairwise stable equilibria as a fixed point of a certain mapping and show that the set of pairwise stable equilibria with nonnegative externality is a complete lattice. We extend the characterization to an econometric framework for structural estimation based on the moment inequality model. We apply our methodology to friendship networks of students in the United States, using data from Add-Health. We find that the preference toward racial homophily is overestimated if we do not control for the preference toward clustering.First author draf

Evolution of Social networks

Hellmann T, Staudigl M. Evolution of Social networks. Working Papers. Institute of Mathematical Economics. Vol 470. Bielefeld: Universität Bielefeld; 2012.Modeling the evolution of networks is central to our understanding of modern large communication systems, such as theWorld-Wide-Web, as well as economic and social networks. The research on social and economic networks is truly interdisciplinary and the number of modeling strategies and concepts is enormous. In this survey we present some modeling approaches, covering classical random graph models and game-theoretic models, which may be used to provide a unified framework to model and analyze the evolution of networks