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AbstractWe establish a relationship between decay centrality and two widely used measures of centrality, namely degree and closeness. We show that for low values of the decay parameter the nodes with maximum decay centrality also have maximum degree, whereas for high values of the decay parameter they also maximize closeness. For intermediate values, we provide sufficient conditions that allow the comparison of decay centrality of different nodes and we show via numerical simulations that in the vast majority of networks, the nodes with maximum decay centrality are characterized by a threshold on the decay parameter below which they belong to the set of nodes with maximum degree and above which they belong to the set of nodes with maximum closeness. We also propose a simple rule of thumb that ensures a nearly optimal choice with very high probability.

AbstractWe investigate the effect of potential entry on the formation and stability of R&D networks considering farsighted firms. The presence of a potential entrant often alters the incentives of incumbents to collaborate. Incumbent firms may form an otherwise undesirable collaboration to deter entry of a new firm. Moreover, an incumbent may refrain from establishing an otherwise desirable collaboration, expecting to form a more profitable link with the entrant. Finally, potential entry may lead an inefficient incumbent to exit the market. Welfare analysis shows market and social incentives to be often misaligned. We propose a subsidy scheme that encourages welfare‐improving entry.

Abstract
Vote trading in power-sharing systems—i.e., systems in which a voter's utility with respect to the election's outcome is proportional to the vote share of her favourite party—is, in theory, welfare improving. However, trading votes for money in majoritarian systems may have detrimental welfare effects, especially when voters' preference intensities are similar (Casella et al., 2012). We use a laboratory experiment to test the effect of vote trading in each of these popular electoral systems on voter welfare and find strong evidence in support of the above intuitions: vote trading in power-sharing systems boosts aggregate welfare across all considered specifications, but it is not welfare improving in majoritarian systems. Importantly, and contrary to theoretical predictions, a substantial share of subjects consistently loses from vote trading even in power-sharing systems, indicating that its welfare effects are not unambiguous.