## Enriching Such Models¶

• Cost depend on geography and characteristics of nodes

• easier to be friends with neighbors
• easier to relate to people with similar background
• Benefits depend on characteristics of nodes

• synergies from working together, trading, sharing risk, exchanging favors...
• complementarities: benefits from diversity...

## Can economic models match observables?¶

• Small worlds derived from costs/benefits
• low costs to local links - high clustering
• high value to distant connection - low diameter
• high cost of distant connections - few distant links

## Geographic Connections¶

Islands connections model:

• J players live on an island, K islands
• cost c of link to player on the island
• cost C > c of link to player on another island

Result:

• High clustering within islands, few links across
• small distances

## Proposition JR04¶

• Truncate connections: $u_i(g) = \sum_{j:l(i,j) \leq D} \delta^{l(i,j)} - d_i(g)c$

• If $c < \delta - \delta^2$ and $C < \delta + (J - 1)\delta^2$ then

• players on each island form a clique
• diameter is bounded by D+1
• $\delta-\delta^3<C$ implies a lower bound on individual clustering is $\frac{(J-1)(J-2)}{(J^2K^2)}$

## Summary Strategic Formation¶

• Efficient networks and stable Networks need not coincide
• Need not coincide even when transfers are possible, and with complete information
• depends on
• setting
• restrictions on transfers, endogenous transfers...
• forward looking, errors...
• Can match and explain some observations

## Strengths of an economic approach¶

• Payoffs allow for a welfare analysis
• Identify tradeoffs - incentives versus efficiency
• Tie the nature of externalities to network formation...
• Put network structures in context
• Account for and explain some observables

## Challenges to an Economic Approach¶

• Stark (overly regular) network structures emerge

• need some heterogeneity
• simulations help in fitting
• over-emphasize choice versus chance for some (especially large) applications?

• How to identify payoff structure in applications?

• relating network structure and outcomes, payoffs

## Models that marry strategic with random are needed¶

• Weaknesses of Random are Strengths of Economic approach, and vice verca.

• Mixed models

• allow for welfare/efficiency analysis
• take model to data and fit observed networks
• do so across applications
In [1]:
0.9 + 2*0.9^2

Out[1]:
2.52
In [2]:
0.9-0.9^2

Out[2]:
0.08999999999999997