Who's Who in Networks. Wanted: The Key Player

Abstract

Finite population noncooperative games with linear-quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own-concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich-Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player's centrality and her contribution to the centrality of the others. Copyright The Econometric Society 2006.

Interrogation Methods and Terror Networks

“…This paper is also related to the literature on social networks. In particular, Ballester et al (2006), under the assumptions that the network structure is exogenously given and observed, characterize the "key player"-the player who, once removed, leads to the optimal change in aggregate activity. In this paper, instead, we start by asking how a network can be (endogenously) built to make criminal activity as efficient as possible.…”

“…This benefit can be viewed as arising from the enhanced ability of the organization to discipline such a member, leading to better outcomes from the group's perspective. 6 Here, we devote more attention to fleshing out the costs of the network, and how they respond to law enforcement policies. In particular, we suppose that individuals within the organization are directly vulnerable according to the authorities' investigation policies.…”

“…After we characterize the effect of different policies on network structure, we can turn to the assessment of the authorities' policies and, therefore, to the characterization of the 6 Such a benefit is derived endogenously in Baccara and Bar-Isaac (2008). optimal policies.…”

Changes in transport and non-transport costs: Local vs global impacts in a spatial network

“…Second, note that the equilibrium conditions (14) define a linear system with respect to the industry shares λ * . This property is particularly 3 Note that ϕ can be related to the Bonacich network centrality measure that has been recently used in non-cooperative network games (Ballester et al, 2006). To see this, note that Φ =φI + G, whereφ > 0 is the common intracountry trade cost and where G is the matrix of intercountry trade costs.…”

“…We believe that a natural way of thinking about a multi-country world is in terms of spatial network, i.e., a graph. 5 Each country can then be viewed as a node of the spatial network, which is linked to the other countries via edges (which represent transportation links). Formally, the space-economy is described by a graph (M, E), where…”