Who Matters to Whom? Identifying Peer Effects with Propagation Geometry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908855361863680 |
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| author | Tchuente, Guy |
| author_facet | Tchuente, Guy |
| contents | This paper develops a unifying theory of peer effects that treats the peer aggregator (the social norm mapping peers' actions into a scalar exposure) as the central behavioral primitive. We formulate peer influence as a norm game in which payoffs depend on own action and an exposure index, and we provide equilibrium existence and uniqueness for a broad class of aggregators. Using economically interpretable axioms, we organize commonly used exposure maps into a small taxonomy that nests linear-in-means, CES (peer-preference) norms, and smooth ``attention-to-salient-peers'' aggregators; rank-based quantile norms are treated as a complementary class. Building on this unification, we show that each aggregator induces an operator that governs how exogenous variation propagates through the network. Linear-in-means corresponds to constant transport (adjacency matrix), recovering the classic (friends-of-friends) instrument families. For nonlinear norms, operator becomes state- and preference-dependent and is characterized by the Jacobian of the exposure map evaluated at an exogenous predictor. This perspective yields geometry-induced instrument that exploit heterogeneity in marginal influence and nonredundant paths, and can remain informative when one-step moments or adjacency-power instruments become weak. Monte Carlo evidence and an application to NetHealth illustrate the practical implications across alternative aggregators and outcomes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Who Matters to Whom? Identifying Peer Effects with Propagation Geometry Tchuente, Guy Econometrics This paper develops a unifying theory of peer effects that treats the peer aggregator (the social norm mapping peers' actions into a scalar exposure) as the central behavioral primitive. We formulate peer influence as a norm game in which payoffs depend on own action and an exposure index, and we provide equilibrium existence and uniqueness for a broad class of aggregators. Using economically interpretable axioms, we organize commonly used exposure maps into a small taxonomy that nests linear-in-means, CES (peer-preference) norms, and smooth ``attention-to-salient-peers'' aggregators; rank-based quantile norms are treated as a complementary class. Building on this unification, we show that each aggregator induces an operator that governs how exogenous variation propagates through the network. Linear-in-means corresponds to constant transport (adjacency matrix), recovering the classic (friends-of-friends) instrument families. For nonlinear norms, operator becomes state- and preference-dependent and is characterized by the Jacobian of the exposure map evaluated at an exogenous predictor. This perspective yields geometry-induced instrument that exploit heterogeneity in marginal influence and nonredundant paths, and can remain informative when one-step moments or adjacency-power instruments become weak. Monte Carlo evidence and an application to NetHealth illustrate the practical implications across alternative aggregators and outcomes. |
| title | Who Matters to Whom? Identifying Peer Effects with Propagation Geometry |
| topic | Econometrics |
| url | https://arxiv.org/abs/2602.23594 |