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