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...

- 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

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

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 $\frac{(J-1)(J-2)}{(J^2K^2)}$

- 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

- 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

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

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]:

In [2]:

```
0.9-0.9^2
```

Out[2]: