ECC3841 Chap.3 Peer Effects and Network Games
Peer Effects and Network Games
Peer effects require a channel and an identification strategy. Endogenous effects run from peers outcomes, contextual effects from peers characteristics and correlated effects from shared environments. Network games then model how actions interact. Strategic complements create feedback and walk-based amplification, while strategic substitutes offset neighbors actions.
In the quadratic local-aggregate model, equilibrium activity relates to Katz-Bonacich centrality, but policy still requires a counterfactual rather than a centrality label.
What this chapter covers
- 01
Endogenous, contextual and correlated effects
- 02
Reflection and friendship selection
- 03
Strategic complements and substitutes
- 04
Best replies and simultaneous equilibrium
- 05
Katz-Bonacich centrality
- 06
Positive spillovers and planner solutions
- 07
Key-player removal counterfactuals
- 08
Local aggregate versus local average
Worked example · free
Solve complementary best replies
- +1Substitute x2 into x1 to obtain x1=2.2+0.04x1.
- +1Rearrange to 0.96x1=2.2.
- +1Calculate x1=2.2917.
- +1Back-substitute to get x2=1.4583.
- +1Check both original equations within rounding.
Key terms
- Endogenous peer effect
- An effect of peers outcomes or actions on the focal individuals outcome.
- Contextual effect
- An effect of peers observed characteristics on the focal individual.
- Correlated effect
- Similarity created by shared environments or unobserved factors.
- Strategic complements
- Interaction in which higher neighbor action raises the best reply.
- Local-average model
- A model responding to friends average behavior or deviation from that average.
- Key player
- The node whose removal causes the largest fall in total equilibrium activity.
Peer Effects and Network Games FAQ
What is the reflection problem?
My action can affect peers while peers actions affect mine, creating simultaneity. A within-group correlation alone cannot reveal the causal direction. Show the simultaneous equations or identifying variation explicitly so the claimed network mechanism can be audited.
Why does Bonacich centrality enter equilibrium?
Positive feedback travels along walks. The centrality sums direct and increasingly attenuated indirect exposure, matching the repeated best-reply multiplier. Show the simultaneous equations or identifying variation explicitly so the claimed network mechanism can be audited.
Is highest degree the key player?
Not necessarily. Removal changes the remaining graph and all equilibrium choices, so the reduced system must be solved for each candidate. Show the simultaneous equations or identifying variation explicitly so the claimed network mechanism can be audited.
Why distinguish aggregate from average?
The aggregate model responds mechanically to the number and total action of friends. The average model normalizes by degree and supports different policy comparisons. Show the simultaneous equations or identifying variation explicitly so the claimed network mechanism can be audited.
Exam move
Derive best replies from payoffs rather than memorizing a solution. Differentiate carefully, collect the agents own action and label the neighbor term. The sign of that term determines whether actions are strategic complements or substitutes. Stack the equations only after checking that each row of the adjacency matrix reproduces the intended neighbor sum.
Check interaction strength and the uniqueness condition before inverting a matrix. Solve the simultaneous system and substitute every value back into the original best replies. A numerical answer that fails one equation is not an equilibrium. Contrast local aggregate and local average on the same graph. Use two nodes with equal friend averages but different degrees to see why normalization changes the peer input.
For welfare, write the planner condition beside the private condition and circle the spillover term the individual ignores. That missing marginal effect explains the sign of a corrective instrument. For key-player policy, solve the baseline and every reduced network. Delete the candidate, remove incident links, recompute all remaining choices and compare total activity.
Do not replace this counterfactual with degree or centrality ranking. For evidence questions, create three headings: endogenous, contextual and correlated effects. Add reflection and friendship selection before proposing a design. Random assignment, fixed effects, instruments and timing solve different problems, so state the threat each addresses and the assumption it requires.
Practise interpreting coefficients with units and without causal language until the design justifies it. On the last pass, move between words, best replies and matrix form. If you can explain why Katz-Bonacich centrality summarizes repeated feedback, solve a small system by hand and identify the policy counterfactual, the chapter is exam-ready.
Working through Peer Effects and Network Games in ECC3841? Sia is AskSia’s AI Economics tutor — ask any ECC3841 Peer Effects and Network Games question and get a clear, step-by-step explanation grounded in how ECC3841 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
