Violations of Uniform Partner Ranking Condition in Two-way Flow Strict Nash Networks

The paper of Charoensook ((2015), [3]) extends the results of the original model of two-way flow information sharing network of Bala and Goyal ((2000),[1]), given that a condition called Uniform Partner Ranking is satisfied. In this technical note, we study what happen to these results when this condition is violated. By providing some examples, we conclude that a certain degree of agent homogeneity needs to exist in order that the results of [3] remains satisfied

Network Formation with Productivity as Decay

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is built upon Bala and Goyal. A unique assumption is that the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided

On the Interaction between Player Heterogeneity and Partner Heterogeneity in Two-way Flow Strict Nash Networks

This paper brings together analyses of two-way flow Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption. This is achieved through examining how the interactions between these two assumptions influence important properties of Strict Nash networks. Built upon the findings of Billand et al (2011) and Galeotti et al (2006), which assume exclusive partner heterogeneity and exclusive player heterogeneity respectively, I provide a proposition that generalizes the results of these two models by stating that: (i) Strict Nash network consists of multiple non-empty components as in Galleotti et al (2006), and (ii) each non-empty component is a branching or Bi network as in Billand et al (2011). This proposition requires that a certain restriction on link formation cost (called Uniform Partner Ranking), which encloses exclusive partner heterogeneity and exclusive player heterogeneity as a specific case, is satisfied. In addition, this paper shows that value heterogeneity plays a relatively less important role in changing the shapes of Strict Nash networks

On the Interaction between Player Heterogeneity and Partner Heterogeneity in Strict Nash Networks

This paper brings together analyses of Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption. This is achieved through examining how the interactions between these two assumptions influence important properties of Strict Nash networks. Built upon the findings of Billand et al (2011) and Galleotti et al (2006), which assume exclusive partner hetero- geneity and exclusive player heterogeneity respectively, I provide a proposition that generalizes the results of these two models by stating that: (i) Strict Nash network consists of multiple non-empty components as in Galleotti et al (2006), and (ii) each non-empty component is a branching or Bi network as in Billand et al (2011). This proposition requires that a certain restriction on link formation cost (called Uniform Partner Rankng), which encloses exclusive partner heterogeneity and exclusive player heterogeneity as a specific case, is satisfied. In addition, this paper shows that value heterogeneity plays a relatively less important role in changing the shapes of Strict Nash networks

Network Formation with Productivity as Decay

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is built upon Bala and Goyal. A unique assumption is that the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided

A noncooperative model of network formation with decreasing productivity

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is based on Bala and Goyal (2000) with the following difference in assumption: the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided

Violations of Uniform Partner Ranking Condition in Two-way Flow Strict Nash Networks

The paper of Charoensook ((2015), [3]) extends the results of the original model of two-way flow information sharing network of Bala and Goyal ((2000),[1]), given that a condition called Uniform Partner Ranking is satisfied. In this technical note, we study what happen to these results when this condition is violated. By providing some examples, we conclude that a certain degree of agent homogeneity needs to exist in order that the results of [3] remains satisfied

A noncooperative model of network formation with decreasing productivity

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is based on Bala and Goyal (2000) with the following difference in assumption: the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided

A noncooperative model of network formation with decreasing productivity

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is based on Bala and Goyal (2000) with the following difference in assumption: the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided.Social Networks; Game Theory; Network Formation

On the Interaction between Player Heterogeneity and Partner Heterogeneity in Two-way Flow Strict Nash Networks

This paper brings together analyses of two-way flow Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption. This is achieved through examining how the interactions between these two assumptions influence important properties of Strict Nash networks. Built upon the findings of Billand et al (2011) and Galleotti et al (2006), which assume exclusive partner heterogeneity and exclusive player heterogeneity respectively, I provide a proposition that generalizes the results of these two models by stating that: (i) Strict Nash network consists of multiple non-empty components as in Galleotti et al (2006), and (ii) each non-empty component is a branching or Bi network as in Billand et al (2011). This proposition requires that a certain restriction on link formation cost (called Uniform Partner Ranking), which encloses exclusive partner heterogeneity and exclusive player heterogeneity as a specific case, is satisfied. In addition, this paper shows that value heterogeneity plays a relatively less important role in changing the shapes of Strict Nash networks