Mathematical Economics 2: Chapter 1 Overview

What is the primary assumption in the basic random network formation model discussed in the text?

What serves as a key purpose of studying random networks within the context described?

Which of the following properties are typically studied in random networks?

According to the model described by the text, what does the probability '$p$' represent when creating random networks?

What does it mean to say that link formation is 'independent' across links in the model?

Who provided seminal studies of random networks as described in the text?

Which of the following is a key goal of comparing observed networks with random networks?

Which scenario is considered in the models alongside the probability model described in the text?

In the context of network analysis, what does P(ij) represent?

What does Pk(ij) signify in the context of network paths?

If there are two shortest paths between families A and B, and family C is on one of them, what would be the value of P_C(AB)?

How is the betweenness centrality measure calculated for a family?

In the betweenness formula, what does the term (n-1)(n-2)/2 represent?

If a family lies on all shortest paths between two other families, what would be the fraction of paths that family lies on, for that particular pair?

What would be the betweenness value of a family that is not on any shortest path between any two families?

What is the betweenness measure of the Medici family?

What does the betweenness measure of a family in the marriage network indicate?

What was the betweenness centrality of the Strozzi family in the marriage network?

According to the analysis, what does the Medici family's high betweenness suggest about their position?

What, besides circumstance, contributed to the Medici family's consolidation of power?

According to the provided figure, what is the total utility of the network with a line structure at time t=3?

The analysis of the marriage network suggests that network structure is important for understanding the social dynamics, and that:

What is a 'network disjuncture', as mentioned in the context of the Medici family?

What is the primary focus of the models discussed in the text regarding network efficiency?

What is a key characteristic of the efficient networks discussed in the context?

What aspect of the marriage arrangements is highlighted by the text?

The analysis uses a subset of families to conduct the calculations. How does this affect the results?

What is the main factor that determines agent's utilities in the network models?

What does the concept of 'pairwise stability' aim to capture in the study of networks?

What condition would cause a link to be removed based upon the concept of pairwise stability?

According to the pairwise stability concept, when is a link added between two agents?

What is the meaning of network 'completeness' within the studied models?

What does the factor between 0 and 1 signify in the context of network relationships?

In the connections model, what determines a player's net utility from a network?

In the connections model, which factor is represented by d_i(g)?

What is the impact of raising the benefit factor to higher powers in more distant relationships?

What determines if a network is considered efficient?

In the context of network formation, what is the main difference between benefits and costs?

What happens to the benefit factor as relationships become more distant?

Considering self-interested players, what is the focus of the connections model?

In a binomial model of link formation, what does the probability $p$ represent?

What does the term 'degree' of a node refer to in the context of network analysis?

According to the formula provided, what is the probability of a specific network with $m$ links forming in a network of $n$ nodes?

What does the degree distribution of a random network describe?

What happens to the correlation of degree between any two nodes as n (the number of nodes) becomes large?

In a binomial model with n = 3, what is the probability of forming a network with two links if the probability of link formation is p?

In the context of the binomial model, the formula that describes the probability of a node having exactly d links is:

Consider a random network with 4 nodes. If the probability of a link forming is p, what is the probability of the 'empty network' forming (zero links)?