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 unique 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 and loss rates that are 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 $n=3$ core-periphery equilibrium, 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 $n=3$: unique core-periphery equilibrium for $a\varepsilon_I \in (a_l, a_h)$ with $a_l = 0.031$, $a_h = 0.974$; unique symmetric equilibrium for $a\varepsilon_I \geq a_s = 0.733$; no equilibrium for $a\varepsilon_I < a_l$
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)

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) the cross-dealer differences in bid-ask spreads, trading margins, trading frequencies, and loss rates documented in U.S. fixed-income markets. 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 model has $n \geq 2$ dealers indexed by $\mathcal{N} = {1, \ldots, n}$, ordered so dealer 1 has the lowest uncertainty level ($\varepsilon_1 \leq \varepsilon_j$ for all $j$), and one investor (p. 4). The asset has a common value $\theta$ for dealers and a private value $\theta_I$ for the investor. The investor’s private value is drawn from $\theta_I \sim U[\theta - \varepsilon_I, \theta + \varepsilon_I]$. Dealer $i$ observes a private signal $\theta_i \sim U[\theta - \varepsilon_i, \theta + \varepsilon_i]$, where $\varepsilon_i \in (0, \varepsilon_I/2]$ is dealer $i$‘s uncertainty level (inverse signal accuracy). Both $\theta$ and $\theta_I$ are unknown to the dealers; this is the common-value auction environment.

The investor asks all $n$ dealers simultaneously to quote a binding bid price $B_i(\theta_i)$ (the price at which dealer $i$ will buy) and ask price $A_i(\theta_i)$ (the price at which dealer $i$ will sell). The investor accepts the best bid $\bar{B} \equiv \max{B_i(\theta_i) : i \in \mathcal{N}}$ if $\bar{B} \geq \theta_I$, or the best ask $\underline{A} \equiv \min{A_i(\theta_i) : i \in \mathcal{N}}$ if $\underline{A} \leq \theta_I$. Dealer $i$ earns trading margin $\theta - B_i(\theta_i)$ when buying, or $A_i(\theta_i) - \theta$ when selling (p. 4).

The bid and ask problems are mathematically symmetric; the paper solves the bid side. Lemma 1 (p. 5) establishes that all equilibrium bid strategies are linear with slope $c_i = 1$ in the dealer’s signal, so $B_i(\theta_i) = b_i + \theta_i$ and it suffices to find the normalized bid prices $b_i = B_i(\theta_i) - \theta_i$ (each a scalar independent of $\theta_i$). Letting the normalized common value be $\bar{\theta}^i \equiv \theta - \theta_i$, dealer $i$‘s expected bid-price profit simplifies to (eq. 4, p. 5):

$$\pi_i^B(b_i, b_{-i}) \equiv \frac{1}{2\varepsilon_i} \int_{-\varepsilon_i}^{\varepsilon_i} (\bar{\theta}^i - b_i) \, f_i(b_i, b_{-i} \mid \bar{\theta}^i) \, d\bar{\theta}^i, \tag{4}$$

where the conditional buying-probability factor is $f_i(b_i, b_{-i} \mid \bar{\theta}^i) \equiv g_i(b_i - \bar{\theta}^i) \prod_{k \in \mathcal{N} \setminus {i}} g_k(b_i - b_k - \bar{\theta}^i)$, and the function $g_j$ (eq. 5, p. 5) is:

$$g_j(x) \equiv \begin{cases} 1, & x > \varepsilon_j, \\ \dfrac{\varepsilon_j + x}{2\varepsilon_j}, & -\varepsilon_j < x \leq \varepsilon_j, \\ 0, & x \leq -\varepsilon_j. \end{cases} \tag{5}$$

The four dealer statistics derived from the equilibrium (pp. 6-7) are:

• Bid-ask spread: $A_i(\theta_i) - B_i(\theta_i) = -2b_i > 0$ (always positive by Lemma A.1 in Appendix).
• Trading margin (eq. 8): $\Delta_i(\varepsilon_i, \varepsilon_{-i}) \equiv R_i(\varepsilon_i, \varepsilon_{-i}) / P_i(\varepsilon_i, \varepsilon_{-i})$, where $R_i = 2\pi_i^B$ is expected revenue.
• Trading probability (eq. 9): $P_i(\varepsilon_i, \varepsilon_{-i}) \equiv 2 \int_{-\varepsilon_i}^{\varepsilon_i} f_i(b_i, b_{-i} \mid \bar{\theta}^i) , d\bar{\theta}^i / (2\varepsilon_i)$.
• Loss probability (eq. 10): $P_i^L(\varepsilon_i, \varepsilon_{-i})$, the probability that dealer $i$ buys (sells) the asset and later resells (buys back) at a loss.

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).

Method

The model is solved via backward induction through a two-stage game (p. 7). Stage 2 (price competition): dealers simultaneously quote bid and ask prices given fixed uncertainty levels $(\varepsilon_1, \ldots, \varepsilon_n)$. Stage 1 (information acquisition): dealers choose $\varepsilon_i \in (0, \varepsilon_I/2]$ anticipating the Stage-2 equilibrium.

Stage 2 equilibrium. The equilibrium first-order condition for dealer $i$‘s normalized bid price (eq. 6, p. 5-6) requires marginal expected bid-price profit to be zero:

$$\frac{d\pi_i^B(b_i, b_{-i})}{db_i} = \frac{1}{2\varepsilon_i} \Big[ (-\varepsilon_i - b_i) f_i(b_i, b_{-i} \mid -\varepsilon_i) - (\varepsilon_i - b_i) f_i(b_i, b_{-i} \mid \varepsilon_i) \Big] = 0. \tag{6}$$

Theorem 1 (p. 6) establishes a unique equilibrium: for all dealers $i \in \mathcal{N} \setminus {1}$ the equilibrium is simply $b_i = -\varepsilon_i$. For dealer 1 (most-informed):

• if $\varepsilon_1 \geq \varepsilon_I/2$, then $b_1 = -\varepsilon_1$;
• otherwise $b_1 \in [-\min(\varepsilon_2, \varepsilon_I/2), -\varepsilon_1]$ satisfies eq. (6) implicitly.

Theorem 2 (p. 6): the equilibrium ask-price strategy is $A_i(\theta_i) = -b_i + \theta_i$ for all dealers.

Proposition 1 (p. 6) establishes comparative statics: $db_1/d\varepsilon_1 < 0$ (dealer 1 quotes tighter spreads when more informed) and $db_i/d\varepsilon_i = -1$ for $i \neq 1$ (peripheral dealers’ spreads move one-for-one with uncertainty). Proposition 3 (p. 7) shows dealer 1 has market power: $db_1/d\varepsilon_k \leq 0$ for $k \in \mathcal{N} \setminus {1}$, meaning dealer 1 narrows its spread as rivals become better informed, deterring rivals from information acquisition.

Stage 1 equilibrium. The information-acquisition cost for dealer $i$ is (p. 7):

$$C(\varepsilon_i) = \frac{a}{2} \left( \frac{\varepsilon_I}{2} - \varepsilon_i \right)^2,$$

with cost parameter $a > 0$. Dealer $i$‘s overall expected profit is (eq. 11, p. 7):

$$\Pi_i(\varepsilon_i, \varepsilon_{-i}) \equiv R_i(\varepsilon_i, \varepsilon_{-i}) - C(\varepsilon_i). \tag{11}$$

Theorem 3 (p. 8) establishes that symmetric equilibria in uncertainty levels (all dealers equally informed) do not exist if the cost parameter $a$ is sufficiently low: dealer 1’s market power prevents ex ante identical dealers from choosing the same information level. When a symmetric equilibrium exists (Result 1, eq. 15, p. 8), the equilibrium uncertainty ratio satisfies:

$$\frac{\varepsilon_1}{\varepsilon_I} = \frac{(n(n+1)a\varepsilon_I - 4)(n+2)}{2(n+1)(n+2)a\varepsilon_I - 8}, \tag{15}$$

valid for $a\varepsilon_I \geq a_s$ where $a_s$ is a threshold that equals 0.507 at $n=4$ and decreases as $n$ grows (Table 1, p. 9). For $a\varepsilon_I \in (a_l, a_h)$, a unique core-periphery equilibrium exists with $\varepsilon_1 < \varepsilon_j$ for all $j \neq 1$. The phase boundaries $a_l$, $a_s$, $a_h$ are derived numerically via the fixed-point procedure described in Appendices A.8-A.9 (pp. 19-21).

Empirical specifications

This is a pure-theory paper with no empirical estimation. No data was used (Data availability statement, p. 22). The paper conducts a numerical equilibrium analysis for $n \in {2, \ldots, 15}$ dealers (Table 1, p. 9; Appendices A.8-A.9) that:

1. Determines phase boundaries $(a_l, a_s, a_h)$ for each $n$ by solving for symmetric and core-periphery equilibria via a four-step best-response search over $a$ and $\varepsilon_I$ (Appendix A.8, p. 19).
2. Verifies Result 2 for the $n = 3$ case: a symmetric equilibrium exists for $a\varepsilon_I \geq 11/15$; a core-periphery equilibrium for $a\varepsilon_I \in (0.031, 0.974)$; the thresholds are $a_s = 11/15 \approx 0.733$, $a_l = 0.031$, $a_h = 0.974$ (Appendix A.9, p. 20-21).
3. Shows transaction costs $C_I(n)$ decrease monotonically in dealer count for $a\varepsilon_I \in {0.2, 0.8}$ (Table A.1, p. 22; Fig. 7, p. 12).

Model predictions are compared qualitatively with cross-dealer statistics in real OTC markets: Li and Schürhoff (2019) for U.S. municipal bond markets, Di Maggio et al. (2017) for U.S. corporate bond markets, and Hasbrouck and Levich (2021) for foreign exchange markets.

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.