Equilibria and centrality in link formation games

Salonen, Hannu

doi:10.1007/s00182-015-0514-6

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…The most closely related articles are Salonen (2015), Griffith (2017), and Brueckner (2006), which analyze the formation of weighted social networks, and Goyal et al (2008), which analyzes a two‐stage game in which firms first form weighted links in research and development (R&D) networks and then compete in a market. These authors focus on symmetric equilibria.…”

Section: Introductionmentioning

confidence: 99%

A model of weighted network formation

Baumann¹

2021

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This paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either “reciprocal” or “nonreciprocal.” In a reciprocal equilibrium, any two agents invest equally in the link between them. In a nonreciprocal equilibrium, agents are partitioned into “concentrated” and “diversified” agents, and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and are not efficient due to the positive externalities of investing in a link.

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Section: Introductionmentioning

confidence: 99%

A model of weighted network formation

Baumann¹

2021

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“…Boucher (2015) considers a model where individuals with a limited budget derive utility from selfinvestment and from direct connections, assuming the utility of a direct link to be a convex function of the investments of the two players involved, whose distance also enters as an argument in their utility. In Salonen (2015), Baumann (2021) and Griffith (2019) individuals with limited resources derive utility from self-investment and from direct connections, but assuming that the utility of a link is a strictly concave function of the investments of the two players. Ding (2019) considers a constant elasticity of substitution link-formation technology that nests unilateral and bilateral network formation.…”

Section: Related Literaturementioning

confidence: 99%

A connections model with decreasing returns link-formation technology

Olaizola

Valenciano

2022

SERIEs

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We study a connections model where the strength of a link depends on the amount invested in it and is determined by an increasing strictly concave function. The revenue from investments in links is the value (information, contacts, friendship) that the nodes receive through the network. First, assuming that links are the result of investments by the node-players involved, there is the question of stability. We introduce and characterize a notion of marginal equilibrium, where all nodes play locally best responses, and identify different marginally stable structures. This notion is based on weak assumptions about node-players’ information and is necessary for Nash equilibrium and for pairwise stability. Second, efficient networks in absolute terms are characterized. Efficiency and stability are shown to be incompatible, but partial subsidizing is shown to be able to bridge the gap.

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“…Accommodating the idea of mutual consent requires an equilibrium concept which allows for a certain degree of cooperative behavior (e.g., pairwise stability). Readers who are interested in this line of research can consult Baumann [17] and Salonen [18]. Both papers are variations of Jackson and Wolinsky [7]'s symmetric connections model in their relaxation of the assumption of exogenous link strength.…”

Section: [Assumption 1] Strength Technologymentioning

confidence: 99%

Network Formation with Endogenous Link Strength and Decreasing Returns to Investment

2016

Games

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We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the direct link between any pair of agents is a concave function of their investments towards each other. In comparison with some existing models of network formation where the strength technology is a convex function of investment, we find that (i) the symmetric complete network can dominate the star architecture in terms of total utility; (ii) a dominating symmetric complete network needs not be stable; and, (iii) star and complete networks can be dominated by small-world networks.

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Equilibria and centrality in link formation games

Cited by 7 publications

References 21 publications

A model of weighted network formation

A model of weighted network formation

A connections model with decreasing returns link-formation technology

Network Formation with Endogenous Link Strength and Decreasing Returns to Investment

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