arxiv: 2605.12559 · v1 · submitted 2026-05-11 · 💰 econ.TH

Recognition: no theorem link

Coordination Failures and Stackelberg Leadership in Housing Development with Network Effects

Vaibhav Rangan

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:38 UTC · model grok-4.3

classification 💰 econ.TH

keywords coordination failuresnetwork effectsStackelberg leadershiphousing developmentmultiple equilibriawelfare analysis

0 comments

The pith

A large first-moving developer always commits to at least the high-supply equilibrium, eliminating coordination failures in housing markets with network effects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

When network effects make the value of new housing rise with total supply, atomistic developers face multiple equilibria: a low-supply coordination failure and a high-supply outcome separated by an unstable threshold. The paper models a Stackelberg game in which one large developer commits to its supply level before smaller developers decide whether to enter. It proves that the large developer will always select a supply at or above the high equilibrium, pushing the market past the threshold no matter which continuation equilibrium occurs afterward. This holds for arbitrary demand functions and cost distributions, and it reverses the usual welfare effect of first-mover commitment.

Core claim

The large developer always commits at least to the high-supply equilibrium, eliminating the coordination failure by pushing past the unstable threshold that separates the low and high outcomes. The result is unconditional; it holds for general demand functions and cost distributions, and does not depend on which stable continuation equilibrium materializes. The leader's commitment inverts standard monopoly intuition: first-mover commitment can improve welfare by resolving a coordination problem that atomistic markets cannot solve on their own.

What carries the argument

Stackelberg commitment by the large developer to a supply level before atomistic developers choose entry, selecting a quantity that exceeds the unstable threshold between the low- and high-supply equilibria.

If this is right

The market underprovides housing relative to the social optimum even after the leader moves.
The leader sometimes builds beyond the high equilibrium into a monopoly region.
First-mover commitment raises total welfare by resolving coordination rather than by restricting output as in standard monopoly models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same first-mover logic may apply to other network-good markets such as broadband or charging infrastructure where scale creates value.
Empirical comparisons of supply outcomes in concentrated versus fragmented local housing markets could test the mechanism.
Zoning or permitting policies that favor large-scale commitments might replicate the coordination benefit without requiring a single private leader.

Load-bearing premise

Network effects are strong and convex enough to produce multiple equilibria with an unstable threshold, and the large developer can credibly commit to its supply before the smaller developers move.

What would settle it

Observe a housing market with convex network effects in which a dominant developer commits to a total supply strictly below the high equilibrium threshold.

Figures

Figures reproduced from arXiv: 2605.12559 by Vaibhav Rangan.

**Figure 1.** Figure 1: Timing of the game. 1Formally, the leader chooses a measurable subset AL ⊆ [0, c¯] with G(AL) = SL. Since sites are homogeneous in output and payoffs are decreasing in cost, any optimal choice is equivalent to the lowest-cost interval. The leader’s action can therefore be summarized by the scalar SL without loss of generality. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗

**Figure 2.** Figure 2: Plot of the response curve G(P(S, S)) against the 45-degree line. Intersections are equilibria. At Slow and Shigh, the curve crosses from above, so perturbations are self-correcting and these equilibria are stable. At Smid, the curve crosses from below so perturbations are selfreinforcing and this equilibrium is unstable. A Stage 2 equilibrium given SL is a total supply level S ∗ satisfying: S ∗ = max SL,… view at source ↗

**Figure 3.** Figure 3: Equilibrium correspondence as a function of the large developer’s commitment SL. For SL ≤ Slow and Slow < SL < Sunstable, multiple equilibria exist, including a low equilibrium, a high equilibrium, and (in the intermediate region) a corner equilibrium at S ∗ = SL. For SL ≥ Sunstable, the correspondence becomes single-valued with S ∗ = Shigh. For SL > Shigh, atomistic entry ceases and the market enters the … view at source ↗

**Figure 4.** Figure 4: Plot of large developer profit against SL in high (blue) and low/corner (red) equilibrium continuation. High equilibrium continuation strictly dominates low equilibrium continuation for all SL < Sunstable. Figure illustrates sufficiently strong and convex network effects, with S ∗ L = S mon L . Remark 2 (Application to Specified Demand). Under P(QD, S) = Qmax+γSα−QD β , the condition in part (c) becomes γ… view at source ↗

**Figure 5.** Figure 5: Market underprovision due to network externalities. The market equilibrium S ∗ equates private marginal benefit P(S, S) with marginal cost G−1 (S), while the social planner accounts for the additional benefit R S 0 ∂P ∂S dQD. This creates a wedge between private and social marginal benefit, leading to underprovision relative to the first-best S F B. The implication dW dS > 0 =⇒ S F B > S∗ requires that W i… view at source ↗

**Figure 6.** Figure 6: Welfare effects of Stackelberg leadership under weak and strong network effects. In both cases, eliminating the low equilibrium generates a coordination gain by increasing supply from Slow to Shigh. When network effects are weak (left panel), the large developer implements Shigh, leaving a residual inefficiency relative to the social optimum S F B. When network effects are strong (right panel), the develop… view at source ↗

read the original abstract

I study coordination failures in housing development markets with network effects, where the value of building depends on aggregate supply. When network effects are sufficiently strong and convex, multiple equilibria arise: a low-supply coordination failure and a high-supply outcome. Without a coordination mechanism, equilibrium is indeterminate. I introduce a large developer who moves first in a Stackelberg game, committing to housing supply before atomistic developers make entry decisions. The main result is that the large developer always commits at least to the high-supply equilibrium, eliminating the coordination failure by pushing past the unstable threshold that separates the low and high outcomes. The result is unconditional; it holds for general demand functions and cost distributions, and does not depend on which stable continuation equilibrium materializes. The leader's commitment inverts standard monopoly intuition: first-mover commitment can improve welfare by resolving a coordination problem that atomistic markets cannot solve on their own. I also characterize when the developer builds beyond the high equilibrium into a monopoly region, and show that the market underprovides housing relative to the social optimum.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows that a Stackelberg leader in housing with network effects always commits to at least the high-supply equilibrium, resolving the coordination failure unconditionally within the convexity class.

read the letter

The main result is that the large developer, moving first, will always pick a supply level at or above the unstable threshold, so the atomistic followers coordinate on the high equilibrium no matter the exact demand curve or cost distribution. This turns first-mover advantage into a coordination device rather than a quantity restriction, which is the new angle relative to earlier work on multiple equilibria in network markets. The setup is clean: the leader anticipates that anything below the threshold triggers the low continuation payoff, which is dominated, so the optimum lies safely in the high region. The paper also notes that total output still falls short of the social planner's level, which keeps the welfare claim modest and grounded. The argument stays general and does not rely on fitted parameters or self-referential equations, which is a plus for checking robustness. The soft spots are the maintained assumptions rather than gaps in the logic. Credible commitment by the large player is taken as given, but real-world enforcement in housing development is not obvious and could limit how far the mechanism travels. The convexity condition on network effects is doing the heavy lifting to create the threshold in the first place; without it the multiple-equilibria structure disappears and the result does not apply. The stress-test note found no internal contradictions, so the derivation appears consistent on its own terms. This is for researchers working on industrial organization, strategic complementarities, and policy in sectors like housing or infrastructure where coordination matters. A reader who wants to see how market power can sometimes improve equilibrium selection would get value from it. It deserves a serious referee because the claim is sharp enough to merit checking the full proofs and continuation equilibria.

Referee Report

2 major / 2 minor

Summary. The paper studies coordination failures in housing development with network effects, where strong convex network effects lead to multiple equilibria: a low-supply coordination failure and a high-supply outcome. A large developer acts as a Stackelberg leader by committing to a supply level before atomistic developers decide. The central claim is that the leader's profit-maximizing commitment is always at or above the high-supply equilibrium threshold, selecting the high equilibrium and resolving the coordination problem. This holds for arbitrary demand functions and cost distributions, and the leader may sometimes build beyond the high equilibrium into a monopoly region. The market is shown to underprovide housing relative to the social optimum.

Significance. If the result holds, it offers a novel mechanism for resolving coordination failures through Stackelberg leadership in network-effect markets, inverting the usual first-mover disadvantage intuition. The generality to arbitrary demand and costs is a strength, as it avoids reliance on specific functional forms. This has potential implications for understanding large-scale housing development and policy interventions to encourage coordination. The paper provides falsifiable predictions about when large developers will lead supply.

major comments (2)

The main result (abstract and §3) asserts that the leader always commits at or above the unstable threshold for general demand and costs. The argument compares leader payoffs under low vs. high continuation equilibria, but the manuscript does not explicitly derive or state the condition ensuring the threshold is strictly unstable under the maintained convexity assumption; without this, the selection of the high equilibrium is not guaranteed for all admissible functions.
§4 (welfare section): the claim that the market underprovides relative to the social optimum relies on the high equilibrium being the relevant benchmark, but the comparison does not address cases where the leader's optimum lies strictly inside the monopoly region; this could reverse the underprovision conclusion depending on the curvature of the social welfare function.

minor comments (2)

Notation for the network-effect function and the unstable threshold should be defined in the model section before the main theorem to improve flow.
The abstract's phrasing that the result is 'unconditional' should include a brief qualifier noting dependence on the convexity condition that generates multiple equilibria.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment below, indicating the revisions we will incorporate to strengthen the rigor and clarity of the manuscript.

read point-by-point responses

Referee: The main result (abstract and §3) asserts that the leader always commits at or above the unstable threshold for general demand and costs. The argument compares leader payoffs under low vs. high continuation equilibria, but the manuscript does not explicitly derive or state the condition ensuring the threshold is strictly unstable under the maintained convexity assumption; without this, the selection of the high equilibrium is not guaranteed for all admissible functions.

Authors: We appreciate the referee highlighting the need for greater explicitness here. While the maintained assumptions of sufficiently strong and convex network effects are intended to ensure an unstable threshold separating the low- and high-supply equilibria, we agree that deriving the instability condition formally would make the selection argument fully rigorous. In the revised version, we will insert a new lemma in §2 that derives the strict instability of the threshold directly from the positive second derivative of the network benefit function (under the convexity maintained throughout). This lemma will confirm that the leader's payoff comparison always selects the high equilibrium for the entire class of admissible demand and cost functions, without changing the statement or proof strategy of the main result. revision: yes
Referee: §4 (welfare section): the claim that the market underprovides relative to the social optimum relies on the high equilibrium being the relevant benchmark, but the comparison does not address cases where the leader's optimum lies strictly inside the monopoly region; this could reverse the underprovision conclusion depending on the curvature of the social welfare function.

Authors: The referee correctly identifies a case that requires additional attention. When the leader's optimum lies in the monopoly region, the welfare comparison must be handled separately. We will revise §4 to add an explicit proposition addressing this case. The proposition will show that underprovision relative to the social optimum continues to hold, because the social planner internalizes the full marginal network externality while the leader captures only the private marginal benefit; this comparison is robust to standard concavity of the social welfare function and does not reverse the underprovision conclusion. We will also clarify that the high equilibrium serves as the lower bound for the relevant benchmark in all cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central result—that the Stackelberg leader commits at or above the unstable threshold for general demand functions and cost distributions—follows directly from the sequential-move game structure and the maintained assumption of sufficiently strong convex network effects. No step reduces a prediction to a fitted parameter, renames a known result, or relies on a load-bearing self-citation whose content is itself unverified within the paper. The derivation is self-contained against the stated assumptions and does not invoke prior author work to force the outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard game-theoretic assumptions for equilibrium existence and selection in games with strategic complementarities. No free parameters are fitted to data and no new entities are postulated; the result is stated to hold generally.

axioms (2)

domain assumption Network effects are sufficiently strong and convex to generate multiple equilibria separated by an unstable threshold
Invoked to create the coordination failure scenario described in the abstract.
domain assumption The large developer can credibly commit to supply before atomistic developers move in the continuation game
Standard Stackelberg timing assumption required for the leader to influence the threshold.

pith-pipeline@v0.9.0 · 5474 in / 1469 out tokens · 55172 ms · 2026-05-14T21:38:21.223366+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

Journal of the European Economic Association , volume =

Rochet, Jean-Charles and Tirole, Jean , title =. Journal of the European Economic Association , volume =

work page
[2]

The RAND Journal of Economics , volume =

Armstrong, Mark , title =. The RAND Journal of Economics , volume =

work page
[3]

The RAND Journal of Economics , volume =

Rochet, Jean-Charles and Tirole, Jean , title =. The RAND Journal of Economics , volume =

work page
[4]

Glen , title =

Weyl, E. Glen , title =. American Economic Review , volume =

work page
[5]

Michael , title =

Spence, A. Michael , title =. The Bell Journal of Economics , volume =

work page
[6]

European Journal of Political Economy , volume =

Economides, Nicholas , title =. European Journal of Political Economy , volume =

work page
[7]

The Quarterly Journal of Economics , volume =

Card, David and Mas, Alexandre and Rothstein, Jesse , title =. The Quarterly Journal of Economics , volume =

work page
[8]

The Quarterly Journal of Economics , volume =

Cooper, Russell and John, Andrew , title =. The Quarterly Journal of Economics , volume =

work page
[9]

and Shleifer, Andrei and Vishny, Robert W

Murphy, Kevin M. and Shleifer, Andrei and Vishny, Robert W. , title =. Journal of Political Economy , volume =

work page
[10]

and Shapiro, Carl , title =

Katz, Michael L. and Shapiro, Carl , title =. The American Economic Review , volume =

work page
[11]

and Shapiro, Carl , title =

Katz, Michael L. and Shapiro, Carl , title =. Journal of Political Economy , volume =

work page
[12]

The RAND Journal of Economics , volume =

Caillaud, Bernard and Jullien, Bruno , title =. The RAND Journal of Economics , volume =

work page
[13]

Journal of Political Economy , volume =

Rossi-Hansberg, Esteban and Sarte, Pierre-Daniel and Owens, Raymond , title =. Journal of Political Economy , volume =

work page
[14]

2017 , url =

Owens, Raymond and Rossi-Hansberg, Esteban and Sarte, Pierre-Daniel , title =. 2017 , url =

work page 2017
[15]

and Kolko, Jed and Saiz, Albert , title =

Glaeser, Edward L. and Kolko, Jed and Saiz, Albert , title =. Journal of Economic Geography , volume =

work page
[16]

Journal of Urban Economics , volume =

Couture, Victor and Handbury, Jessie , title =. Journal of Urban Economics , volume =

work page
[17]

, title =

Schelling, Thomas C. , title =

work page
[18]

and Geanakoplos, John D

Bulow, Jeremy I. and Geanakoplos, John D. and Klemperer, Paul D. , title =. Journal of Political Economy , volume =

work page
[19]

Lipsey, R. G. and Lancaster, Kelvin , title =. The Review of Economic Studies , volume =

work page
[20]

and Strange, William C

Helsley, Robert W. and Strange, William C. , title =. Regional Science and Urban Economics , volume =

work page
[21]

Journal of Public Economics , volume =

Guerrieri, Veronica and Hartley, Daniel and Hurst, Erik , title =. Journal of Public Economics , volume =

work page
[22]

Urban Affairs Review , volume =

Freemark, Yonah , title =. Urban Affairs Review , volume =

work page
[23]

Greenaway-McGrevy, Ryan and Phillips, Peter C. B. , title =. Journal of Urban Economics , volume =

work page