Dealer Competition in OTC Markets: Singer (2026)

What this is. The paper’s core results, the game-theoretic model of OTC dealer competition, and the main propositions with their formal equations: enough to know what it finds and how, without reading all 23 pages. To replicate or extend, read the full source at the original.

TL;DR

The paper models dealer competition in over-the-counter (OTC) markets as a first-price sealed-bid common-value auction under endogenous uncertainty. An investor simultaneously asks $n$ dealers to quote bid and ask prices for one unit of a risky asset. Neither the asset’s true value nor rivals’ private signals are observed by any dealer, creating a winner’s curse problem: the dealer whose quote is accepted is most likely to have overestimated (underestimated) the value. Dealers mitigate this by investing in costly information acquisition, raising signal accuracy. However, when dealer 1 (the most-informed) tightens its bid-ask spread, this intensifies price competition for others, deterring them from matching dealer 1’s accuracy. Equilibrium information heterogeneity emerges endogenously: for intermediate information-acquisition costs, a core-periphery equilibrium exists in which one well-informed core dealer coexists with less-informed peripheral dealers. The core dealer quotes the tightest bid-ask spread to individual investors yet earns the highest trading margins. With resale-price fluctuations set to \\varepsilon_\\sigma=\\varepsilon_I/10, its loss probability is zero for a wide range of cost parameters. This is consistent with centrality premia documented in U.S. municipal bond markets (Li and Schürhoff (2019)) and U.S. corporate bond markets.

Core results

Locators point into the source PDF (23 pages). All results are theoretical propositions and theorems; no empirical data was used.

#	Result	Locator	Magnitude
R1	Better-informed dealers quote tighter bid-ask spreads (Proposition 2, part i)	Prop. 2, §2.2, p. 7; Prop. 1, p. 6	Bid-ask spread equals $-2b_i$; normalized bid $b_i$ is strictly decreasing in uncertainty level $\varepsilon_i$ (Proposition 1): better-informed dealers set lower $b_i$, narrowing their spread
R2	Better-informed dealers earn higher expected trading margins (Proposition 2, part ii)	Prop. 2, §2.2, p. 7; Fig. 4, p. 10	Expected trading margin $\Delta_i = R_i / P_i$ is strictly decreasing in $\varepsilon_i$; in the $n=3$ core-periphery equilibrium, core dealer margin exceeds peripheral margin by up to a factor of 2 (Fig. 4, left panel)
R3	Better-informed dealers trade more frequently (Proposition 2, part iii)	Prop. 2, §2.2, p. 7; Fig. 4, p. 10	Trading probability $P_i(\varepsilon_i, \varepsilon_{-i})$ strictly decreasing in $\varepsilon_i$; core dealer trading probability exceeds peripheral dealer’s (Fig. 4, right panel)
R4	Better-informed dealers incur fewer trading losses (Proposition 2, part iv)	Prop. 2, §2.2, p. 7; Fig. 5, p. 11	Loss probability $P^L_i(\varepsilon_i, \varepsilon_{-i})$ strictly increasing in $\varepsilon_i$; in the $n=3$ core-periphery equilibrium, with $\varepsilon_\sigma=\varepsilon_I/10$, core dealer loss probability is zero for a wide range of the cost parameter $a$ (Fig. 5)
R5	Core-periphery dealer structures emerge endogenously for intermediate information-acquisition costs (Result 2)	Result 2, §3.2, p. 9; Table 1, p. 9; Fig. 2, p. 9	For $n=3$: a unique core-periphery equilibrium exists for $a\varepsilon_I \in (a_l, a_h)$, with $a_l = 0.031$ and $a_h = 0.974$; it coexists with the unique symmetric equilibrium for $a\varepsilon_I \in [a_s,a_h)$, where $a_s=0.733$; the symmetric equilibrium is unique for $a\varepsilon_I \geq a_h$; no equilibrium exists for $a\varepsilon_I \leq a_l$
R6	Investor transaction costs decrease monotonically in the number of competing dealers (Section 5, Fig. 7)	§5, Fig. 7, p. 12-13; Table A.1, p. 22	At $a\varepsilon_I = 0.2$: $C_I(2) / C_I(10) \approx 4.05$; ratio is above 1 for all $n \in \{2, \ldots, 10\}$ (Fig. 7)
R7	The best-informed dealer tightens its spread when rivals become better informed, while peripheral spreads do not respond to other dealers’ information (Proposition 3)	Proposition 3, §3.1, p. 7	$\partial b_1 / \partial \varepsilon_k \leq 0$ for $k \ne 1$; $\partial b_i / \partial \varepsilon_k = 0$ for $i \ne 1, k \ne i$ (Eq. 12)
R8	In the two-dealer price-insensitive-investor case, information advantage produces higher core revenue and margins	Theorem 4, §3.1, p. 8	$R_1 > R_2$ and $\Delta_1 > \Delta_2$; as $a \to 0$, the core margin exceeds the peripheral margin by a factor of 2
R9	Peripheral information acquisition is non-monotonic in cost within the three-dealer core-periphery equilibrium	Result 2 discussion, Fig. 2, p. 9	$\varepsilon_2=\varepsilon_3$ increases with $a$ for $a\varepsilon_I \in (0.031,0.55)$ and decreases for $a\varepsilon_I \in [0.55,0.974)$
R10	Equilibrium dealers overinvest in information relative to the planner; the welfare-optimal structure changes with acquisition cost	§4, Fig. 6, pp. 11-12	For $n=3$, symmetric uncertainty is welfare-optimal for $a\varepsilon_I \geq 0.23$; $\varepsilon_1=\varepsilon_2<\varepsilon_3$ is optimal below 0.23; equilibrium information investment exceeds the planner’s
R11	Transaction taxes lower welfare, while small transaction subsidies increase it but introduce inefficient trade and arbitrage opportunities	§4, p. 12; Eq. 19	At $c=\varepsilon_I/100$, welfare falls by 0.34%-0.53% over $a\varepsilon_I \in (a_l,5)$; small transaction subsidies increase welfare
R12	With uncertainty about which competitors are contacted, equilibrium heterogeneity and the core dealer’s ranking persist at sufficiently high acquisition costs	§6.1, Eq. 21, pp. 13-14; Figs. 8-9, p. 13	For $q=0$, equilibria exist when acquisition costs are sufficiently high; no equilibrium is found at low costs; for $\varepsilon_\sigma=\varepsilon_I/10$ the best-informed dealer retains the tightest spread, highest margin and trading probability, and lowest loss probability
R13	Heterogeneous inventory valuations increase price competition and lower investor transaction costs in the three-dealer example	§6.2, p. 14	At $a\varepsilon_I=0.2$, the three valuation cases reduce transaction costs by 6%, 11%, and 15%, respectively
R14	Non-uniform signal distributions may increase information heterogeneity; uniform signals can limit it	§6.3, pp. 14-15	Under non-uniform signals, peripheral pricing may respond to rivals’ information, potentially preventing equal uncertainty levels; the paper reports no numerical estimate

Overall (paper’s conclusion). The friction of opaque market prices in OTC markets, modeled as simultaneous first-price sealed-bid common-value auctions, endogenously generates both (i) the core-periphery dealer structures observed in real markets and (ii) cross-dealer differences in bid-ask spreads, trading margins, trading frequencies, and loss rates. Core dealers earn centrality premia despite quoting tighter spreads, because their superior information leads to fewer mispriced trades offset by higher-margin trades.

Theory / model

The framing of dealers as first-price sealed-bid common-value auctioneers builds on the analysis of Milgrom and Weber (1982b) and on the information-acquisition model of Persico (2000), and is complementary to the search-and-bargaining OTC model of Duffie, Garleanu, and Pedersen (2005) and to the endogenous-structure model of Farboodi, Jarosch, and Shimer (2022).

This is a theoretical model with no empirical sample or regression design. In the main model, an investor privately values a unit of an asset at a draw around the common dealer value, and each of n dealers receives an independent noisy signal. Dealer i’s expected bid profit and ask profit are given by Eqs. (1)-(2), p. 4:

$$\pi_i^B(B_i(\theta_i),B_{-i}|\theta_i)=\frac{1}{2\varepsilon_i}\int_{\theta_i-\varepsilon_i}^{\theta_i+\varepsilon_i}(\theta-B_i(\theta_i))\left[\int_{\theta-\varepsilon_I}^{\theta+\varepsilon_I}\mathbf{1}(B_i(\theta_i)\geq\theta_I)\frac{d\theta_I}{2\varepsilon_I}\prod_{k\ne i}\int_{\theta-\varepsilon_k}^{\theta+\varepsilon_k}\mathbf{1}(B_i(\theta_i)\geq B_k(\theta_k))\frac{d\theta_k}{2\varepsilon_k}\right]\frac{d\theta}{2\varepsilon_i}. \tag{1}$$ $$\pi_i^A(A_i(\theta_i),A_{-i}|\theta_i)=\frac{1}{2\varepsilon_i}\int_{\theta_i-\varepsilon_i}^{\theta_i+\varepsilon_i}(A_i(\theta_i)-\theta)\left[\int_{\theta-\varepsilon_I}^{\theta+\varepsilon_I}\mathbf{1}(A_i(\theta_i)\leq\theta_I)\frac{d\theta_I}{2\varepsilon_I}\prod_{k\ne i}\int_{\theta-\varepsilon_k}^{\theta+\varepsilon_k}\mathbf{1}(A_i(\theta_i)\leq A_k(\theta_k))\frac{d\theta_k}{2\varepsilon_k}\right]\frac{d\theta}{2\varepsilon_i}. \tag{2}$$

With linear strategies, Lemma 1 implies unit slope and normalized bid $b_i=B_i(\theta_i)-\theta_i$. Equation (3), p. 5, is the conditional expected profit integral after normalizing the values and signals:

$$\pi_i^B(b_i,b_{-i})=\frac{1}{2\varepsilon_i}\int_{-\varepsilon_i}^{\varepsilon_i}(\tilde{\theta}_i-b_i)\left[\int_{\tilde{\theta}_i-\varepsilon_I}^{\tilde{\theta}_i+\varepsilon_I}\mathbf{1}(b_i\geq\tilde{\theta}_{Ii})\frac{d\tilde{\theta}_{Ii}}{2\varepsilon_I}\prod_{k\ne i}\int_{\tilde{\theta}_i-\varepsilon_k}^{\tilde{\theta}_i+\varepsilon_k}\mathbf{1}(b_i\geq b_k+\tilde{\theta}_{ki})\frac{d\tilde{\theta}_{ki}}{2\varepsilon_k}\right]\frac{d\tilde{\theta}_i}{2\varepsilon_i}. \tag{3}$$

Equations (4)-(6), pp. 5-6, define the profit kernel, uniform-signal probability function, and pricing first-order condition:

$$\pi_i^B(b_i,b_{-i})=\frac{1}{2\varepsilon_i}\int_{-\varepsilon_i}^{\varepsilon_i}(\tilde{\theta}_i-b_i)f_i(b_i,b_{-i}|\tilde{\theta}_i)d\tilde{\theta}_i, \quad f_i=g_I(b_i-\tilde{\theta}_i)\prod_{k\ne i}g_k(b_i-b_k-\tilde{\theta}_i). \tag{4}$$ $$g_j(x)=\begin{cases}1,&x>\varepsilon_j,\\(\varepsilon_j+x)/(2\varepsilon_j),&-\varepsilon_j<x\leq\varepsilon_j,\\0,&x\leq-\varepsilon_j.\end{cases} \tag{5}$$ $$\frac{d\pi_i^B}{db_i}=\frac{1}{2\varepsilon_i}\left[(-\varepsilon_i-b_i)f_i(b_i,b_{-i}|-\varepsilon_i)-(\varepsilon_i-b_i)f_i(b_i,b_{-i}|\varepsilon_i)\right]=0. \tag{6}$$

Theorem 1 gives a unique equilibrium in normalized bids: peripheral dealers quote $b_i=-\varepsilon_i$; dealer 1 also does so if $\varepsilon_1\geq\varepsilon_I/2$, otherwise its bid lies in $[-\min(\varepsilon_2,\varepsilon_I/2),-\varepsilon_1]$ and solves Eq. (6). Theorem 2 gives asks $A_i(\theta_i)=-b_i+\theta_i$ (both p. 6). The spread comparative static and dealer-statistic definitions are Eqs. (7)-(10), pp. 6-7:

$$\frac{db_1}{d\varepsilon_1}<0,\qquad\frac{db_i}{d\varepsilon_i}=-1\quad(i\ne1). \tag{7}$$ $$\Delta_i(\varepsilon_i,\varepsilon_{-i})=\frac{R_i(\varepsilon_i,\varepsilon_{-i})}{P_i(\varepsilon_i,\varepsilon_{-i})},\qquad R_i=2\pi_i^B(b_i,b_{-i}). \tag{8}$$ $$P_i(\varepsilon_i,\varepsilon_{-i})=2\int_{-\varepsilon_i}^{\varepsilon_i}f_i(b_i,b_{-i}|\tilde{\theta}_i)\frac{d\tilde{\theta}_i}{2\varepsilon_i}. \tag{9}$$ $$P_i^L(\varepsilon_i,\varepsilon_{-i})=\frac{2}{P_i}\int_{-\varepsilon_i}^{\varepsilon_i}\int_{-\varepsilon_\sigma}^{\varepsilon_\sigma}\mathbf{1}(\tilde{\theta}_i+\sigma-b_i<0)f_i(b_i,b_{-i}|\tilde{\theta}_i)\frac{d\sigma}{2\varepsilon_\sigma}\frac{d\tilde{\theta}_i}{2\varepsilon_i}. \tag{10}$$

Method

The paper solves a two-stage game by backward induction. Dealers first choose uncertainty levels and then simultaneously quote prices; the equilibrium revenue net of information-acquisition cost and rival-response comparative static are Eqs. (11)-(12), pp. 7-8:

$$C(\varepsilon_i)=\frac{a}{2}\left(\frac{\varepsilon_I}{2}-\varepsilon_i\right)^2,\qquad\Pi_i(\varepsilon_i,\varepsilon_{-i})=R_i(\varepsilon_i,\varepsilon_{-i})-C(\varepsilon_i). \tag{11}$$ $$\frac{db_1}{d\varepsilon_k}\leq0\quad(k\ne1),\qquad\frac{db_i}{d\varepsilon_k}=0\quad(i\ne1, k\ne i). \tag{12}$$

For the special two-dealer case with a price-insensitive investor, the revenue and marginal revenue expressions are Eqs. (13)-(14), p. 8:

$$R_i(\varepsilon_i,\varepsilon_{-i})=\begin{cases}(3\varepsilon_{-i}^2-\varepsilon_i^2)/(6\varepsilon_{-i}),&\varepsilon_i\leq\varepsilon_{-i},\\(3\varepsilon_i^2+\varepsilon_{-i}^2)/(12\varepsilon_i),&\varepsilon_i>\varepsilon_{-i}. \end{cases} \tag{13}$$ $$\frac{dR_i}{d\varepsilon_i}=\begin{cases}-\varepsilon_i/(3\varepsilon_{-i}),&\varepsilon_i\leq\varepsilon_{-i},\\(3\varepsilon_i^2-\varepsilon_{-i}^2)/(12\varepsilon_i^2),&\varepsilon_i>\varepsilon_{-i}. \end{cases} \tag{14}$$

Theorem 4 finds the unique equilibrium with dealer 2 at the investor’s maximum uncertainty and equal normalized bids. The main model’s symmetric equilibrium condition is Eq. (15), p. 8; the three-dealer thresholds and core-periphery equilibrium are Result 2, pp. 9-10:

$$\frac{\varepsilon_i}{\varepsilon_I}=\frac{(n(n+1)a\varepsilon_I-4)(n+2)}{2(n(n+1)(n+2)a\varepsilon_I-8)},\qquad a\varepsilon_I\geq a_s. \tag{15}$$

For n=3, $a_s=11/15=0.733$, $a_l=0.031$, and $a_h=0.974$; the paper reports unique symmetric equilibrium above the symmetric threshold, core-periphery equilibrium for $a\varepsilon_I\in(a_l,a_h)$, and no other equilibria in the analyzed n=3 case. The equilibrium classification for n=2,…,15 is numerical (Table 1, p. 9; Appendix A.8, pp. 19-20). There is no estimation, fixed-effects structure, standard-error procedure, or empirical sample.

Empirical specifications

The paper is theoretical and estimates no empirical specifications. For the welfare analysis, Eqs. (16)-(18), pp. 10-11, define welfare, the density of the best bid, and the reduced welfare expression:

$$W=-2\int_{-\varepsilon_I}^{\varepsilon_I}\theta_I\sum_{i\in\mathcal{N}}\int_{-\varepsilon_i}^{\varepsilon_i}\mathbf{1}(b_i+\theta_i\geq\theta_I)\prod_{k\ne i}\mathbf{1}(b_i+\theta_i\geq b_k+\theta_k)\frac{d\theta_k}{2\varepsilon_k}\frac{d\theta_i}{2\varepsilon_i}\frac{d\theta_I}{2\varepsilon_I}-\sum_i C(\varepsilon_i). \tag{16}$$ $$f_I(\bar B)=\begin{cases}\sum_i\frac{1}{2\varepsilon_i}\prod_{k\ne i}\frac{\bar B+\varepsilon_k-b_k}{2\varepsilon_k},&\bar B\in[b_1-\varepsilon_1,b_1+\varepsilon_1],\\\sum_{i\ne1}\frac{1}{2\varepsilon_i}\prod_{k\ne i,1}\frac{\bar B+\varepsilon_k-b_k}{2\varepsilon_k},&\bar B\in(b_1+\varepsilon_1,0],\\0,&\text{otherwise}. \end{cases} \tag{17}$$ $$W=2\int_{\max(b_1-\varepsilon_1,-\varepsilon_I)}^0\frac{(\varepsilon_I-\bar B)^2}{4\varepsilon_I}f_I(\bar B)d\bar B-\sum_{i\in\mathcal{N}}C(\varepsilon_i). \tag{18}$$

For a transaction tax or subsidy c, the profit kernel is changed as in Eq. (19), p. 12. The expected investor transaction cost and the unknown-competitor conditional trading probability are Eqs. (20)-(21), pp. 12-14:

$$\tilde{\pi}_i^B(b_i,b_{-i})=\frac{1}{2\varepsilon_i}\int_{-\varepsilon_i}^{\varepsilon_i}(\tilde{\theta}_i-b_i-c)f_i(b_i,b_{-i}|\tilde{\theta}_i)d\tilde{\theta}_i. \tag{19}$$ $$C_I=\frac{\int_{\max(b_1-\varepsilon_1,-\varepsilon_I)}^0(-\bar B)\frac{\bar B+\varepsilon_I}{2\varepsilon_I}f_I(\bar B)d\bar B}{\int_{\max(b_1-\varepsilon_1,-\varepsilon_I)}^0\frac{\bar B+\varepsilon_I}{2\varepsilon_I}f_I(\bar B)d\bar B}. \tag{20}$$ $$f_i(b_i,b_{-i}|\tilde{\theta}_i)=g_I(b_i-\tilde{\theta}_i)\left[\frac{3q}{2+q}g_j(b_i-b_j-\tilde{\theta}_i)g_k(b_i-b_k-\tilde{\theta}_i)+\frac{1-q}{2+q}g_j(b_i-b_j-\tilde{\theta}_i)+\frac{1-q}{2+q}g_k(b_i-b_k-\tilde{\theta}_i)\right]. \tag{21}$$

The model’s numerical equilibrium analysis reports transaction costs falling as dealer count rises (at $a\varepsilon_I=0.2$, $C_I(2)/C_I(10)=4.05$), welfare overinvestment relative to the planner, and a 0.34%-0.53% welfare loss from a transaction tax of $c=\varepsilon_I/100$ (Figs. 6-7, pp. 11-12). Robustness checks vary competitor contact uncertainty, dealer private valuations, and signal distributions (Sections 6.1-6.3, pp. 13-15). These are model exercises, not data-based estimates.

Datasets used

The paper is entirely theoretical. No empirical datasets are analyzed.

Dataset	Role in paper	Wiki page
None	Pure theory model; stylized facts from Li and Schürhoff (2019), Di Maggio et al. (2017), Hasbrouck and Levich (2021) are cited as motivation in the introduction but no data is analyzed here	n/a

When to read the full paper

Read the original if you are: (1) modeling OTC dealer competition with simultaneous price competition rather than sequential search; (2) building on the first-price common-value auction framework for market microstructure; (3) studying endogenous information acquisition in dealer markets; or (4) extending the welfare and transaction-cost analysis of Sections 4-5 to policy settings (transaction taxes, subsidies). Formal proofs of all lemmas, propositions, and theorems are in the Appendix (pp. 15-22).

Attribution and rights

Source: peer-reviewed, Journal of Financial Markets 77 (2026) 101004. This distillation was extracted by an LLM on 2026-06-25 and is not human-verified or independently reproduced. The CC BY 4.0 licence permits mirroring; the verbatim PDF is not hosted in this batch.

Attribution (CC BY 4.0). Singer, Alexander. “Dealer Competition in Over-the-Counter Markets.” Journal of Financial Markets 77 (2026) 101004. DOI: 10.1016/j.finmar.2025.101004. Copyright 2025 The Author. Published by Elsevier B.V. Licensed under CC BY 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.