---
title: "Competition and the Future"
book: "The Desk and the Firm"
subject: quant
language: en
chapter: 30
exercises: 8
source: https://one-course.com/books/quant/16/en/chapter/30-competition-and-the-future
---

# Chapter 30 — Competition and the Future

When the US securities regulator proposed in December 2022 to make many retail orders compete in auctions, its own release found that broker-dealers sent more than 90% of individual investors’ marketable orders in listed stocks to six off-exchange dealers, the wholesalers, and that two of them handled about 66% of the wholesalers’ volume. The proposal was withdrawn in June 2025. Trading looks like a market of many firms; business by business it is often a market of a few. This last chapter asks why, what protects the few, and what three changes now under way (tokenised assets, round-the-clock markets and machine-learning tooling) do to the answer.

## 30.1 Moats in trading

**Definition 30.1 (Economic moat).**

An *economic moat* is a lasting advantage that lets a firm earn returns above its cost of capital in a business without competitors entering until those returns are gone: a cost advantage from scale, proprietary information or order flow, customers’ [switching costs](https://one-course.com/books/quant/16/en/chapter/20-build-against-buy#def-fm-build-against-buy-lockin), network effects, or a licence or relationship others cannot obtain quickly.

Book 11 showed that a trading edge decays as others find it: capture falls as competitors enter. The durable advantages are therefore rarely the signals. They are the fixed costs a new entrant must pay before its first trade (chapter 1’s [fixed cost base](https://one-course.com/books/quant/16/en/chapter/1-the-economics-of-a-trading-firm#def-fm-the-economics-of-a-trading-firm-fixed), chapter 2’s [technology treadmill](https://one-course.com/books/quant/16/en/chapter/2-the-proprietary-market-making-firm#def-fm-the-proprietary-market-making-firm-treadmill), chapter 19’s [latency arms race](https://one-course.com/books/quant/16/en/chapter/19-technology-strategy#def-fm-technology-strategy-race)), the order flow that comes through relationships and contracts (chapter 23), and the data and history a firm has accumulated. Sutton’s work on sunk costs and market structure separates two cases. When the fixed cost of entry is exogenous, a larger market supports more firms and concentration falls as it grows. When firms can spend to be better (faster, better data, better models) and customers reward the best, the spending itself rises with the market, and concentration need not fall at all.

**Definition 30.2 (Market concentration, Herfindahl–Hirschman index).**

*Market concentration* is the degree to which a business’s volume or revenue is held by a few firms, measured by concentration ratios (the $k$ largest firms’ combined share, $\mathrm{CR}_k$) or by the *Herfindahl–Hirschman index*, the sum of the squared market shares in percent,

$$
\mathrm{HHI}=\sum_{i=1}^n(100\,s_i)^2,
$$

from near 0 for many small firms to 10 000 for one (Book 1’s Herfindahl index of venues, on a 0 to 10 000 scale).

## 30.2 Consolidation and market structure

The public record rarely gives every firm’s share; the release gives two numbers. They bound the index.

**Proposition 30.3 (Bounds from partial shares).**

If a business has $n$ firms whose $k$ largest hold a combined share $S_k$, the index is smallest when the $k$ leaders are equal and the other firms are equal, $\mathrm{HHI}_{\min}=10^4\bigl(S_k^2/k+(1-S_k)^2/(n-k)\bigr)$, provided $(1-S_k)/(n-k)\le S_k/k$. For $n=6$, $k=2$ and $S_2=0.66$ it lies between 2 467 and 3 668.

**Proof.** For a fixed total, a sum of squares is smallest when the parts are equal; applying this to the leaders and to the others separately gives the minimum, which is feasible when each other firm is no larger than each leader. For the maximum, fix the smaller leader’s share $b$: the larger leader holds $S_2-b$, and the others, each at most $b$, hold $1-S_2$; with $b=(1-S_2)/4=0.085$ all four others must equal $b$, and the leader holds 0.575, giving $10^4(0.575^2+5\times0.085^2)=3\,668$. A search over $b$ (`firm.moats.hhi_bounds`) confirms that larger $b$ gives less. ∎

![The two share vectors that bound the index for six wholesalers whose two largest hold 66%, the figures in the SEC’s 2022 release. Either way the business is highly concentrated under the 2023 merger guidelines’ threshold of 1 800. Data: fm_competition.public_bounds.](https://one-course.com/images/onecourse/chapters/quant-16/fm-competition-and-the-future/fig-6b04c31cbd43.svg)

***Figure 30.1.** The two share vectors that bound the index for six wholesalers whose two largest hold 66%, the figures in the SEC’s 2022 release. Either way the business is highly concentrated under the 2023 merger guidelines’ threshold of 1 800. Data: `fm_competition.public_bounds`.*

**As of September 2026 — The public record of the chapter.**

**Wholesaling**: the SEC’s Order Competition Rule proposal (Release 34-96495, published 3 January 2023) found more than 90% of individual investors’ marketable orders in NMS stocks routed to six wholesalers, two with about 66% of the wholesalers’ executed share volume in the first quarter of 2022; the Commission withdrew the proposal on 17 June 2025. **Merger guidelines** (DOJ and FTC, December 2023): an index above 1 800 is highly concentrated; an increase above 100 in such a market, or a merged share above 30% with an increase above 100, is presumed to lessen competition substantially. **[Tokenised fund](#def-fm-competition-and-the-future-token)**: a registered US government money-market fund’s prospectus of 1 August 2026 states that its transfer agent keeps the official record of share ownership in a blockchain-integrated system on public networks. **Round-the-clock**: the SEC registered 24X National Exchange on 27 November 2024 to trade listed stocks 23 hours a day, five days a week; NSCC extended its clearing hours to 24x5 on 29 June 2026, with exchanges expected to follow in late 2026.

**Definition 30.4 (Free-entry equilibrium).**

A *free-entry equilibrium* is the number of firms at which each firm in a business covers its fixed cost and one more entrant would not: $\pi(n)\ge F>\pi(n+1)$, where $\pi(n)$ is each firm’s operating profit when $n$ firms compete and $F$ is the fixed cost of being in the business.

In a Cournot market with linear demand $a-bQ$, a common marginal cost $c$ and $n$ identical firms, each earns $\pi(n)=S/(n+1)^2$ with $S=(a-c)^2/b$, so the free-entry number is $n^*=\lfloor\sqrt{S/F}\rfloor-1$ and the index is $10\,000/n^*$. Concentration is set by the ratio of the market’s size to the fixed cost, not by either alone.

## 30.3 Tutorial: the fixed cost falls

**Goal.** Compute the free-entry number of firms and the index at the book’s parameters; halve and double the fixed cost; merge two firms, with and without synergies; and bound the index from the public figures. **End state:** Figures [30.2](#fig-fm-competition-and-the-future-entry) and [30.4](#fig-fm-competition-and-the-future-merger).

1. **Parameters.** $S=\$3\,000$ million a year (demand intercept 10 and marginal cost 4, in basis points), and a fixed cost $F=\$50$ million a year per firm; both are illustrative.
2. **Free entry.** `free_entry(3000, 50)` gives six firms, each earning $61.2 million before and $11.2 million after its fixed cost; the index is 1 667.
3. **Halve and double.** At $25 million, nine firms (1 111); at $100 million, four (2 500).
4. **The planner.** `planner` maximises consumers’ surplus plus profits less fixed costs: three firms at $50 million.
5. **A merger.** Two of the six merge and save one fixed cost; then find the marginal-cost synergy that keeps the price unchanged.

```python
def hhi_bounds(n, top_share, k=2, grid=2001):
    """Smallest and largest index over n-firm share vectors whose k largest hold `top_share`.
    Minimum: the top k equal and the rest equal. Maximum: search over the k-th largest
    share b; one leader holds the rest of the top share, the other k - 1 hold b, and
    the remaining firms are packed at b with one remainder."""
    rest = 1 - top_share
    x = rest / (n - k)
    if x > top_share / k + 1e-12:
        raise ValueError("the others cannot all be smaller than the top firms")
    lo = hhi([top_share / k] * k + [x] * (n - k))
    best = lo
    for b in np.linspace(x, top_share / k, grid):
        full = min(n - k, int(rest / b + 1e-9))
        others = [b] * full + ([rest - full * b] if full < n - k else [])
        best = max(best, hhi([top_share - (k - 1) * b] + [b] * (k - 1) + others))
    return lo, best


def free_entry(S, F):
    """The largest n with S / (n + 1)^2 >= F: firms enter while the next covers its cost."""
    return max(0, math.floor(math.sqrt(S / F) + 1e-12) - 1)


def welfare(S, F, n):
    """Total surplus with n symmetric Cournot firms: consumers' surplus plus profits,
    less fixed costs."""
    return S * (n * n / 2 + n) / (n + 1) ** 2 - n * F


def planner(S, F, nmax=200):
    """The number of firms that maximises total surplus."""
    return max(range(1, nmax + 1), key=lambda n: welfare(S, F, n))
```

***Listing 30.1.** Bounds on the index from partial shares, the free-entry number of firms, total surplus and the planner’s number. code/firm/moats/firm_moats.py*

![The free-entry index against the fixed cost at S=\$3\,000 million: six firms and 1 667 at $50 million (circled), nine and 1 111 at $25 million, four and 2 500 at $100 million. The shaded band is the range the public wholesaler figures allow. Data: fm_competition.entry.](https://one-course.com/images/onecourse/chapters/quant-16/fm-competition-and-the-future/fig-387f7de7d6b8.svg)

***Figure 30.2.** The free-entry index against the fixed cost at $S=\$3\,000$ million: six firms and 1 667 at $50 million (circled), nine and 1 111 at $25 million, four and 2 500 at $100 million. The shaded band is the range the public wholesaler figures allow. Data: `fm_competition.entry`.*

The symmetric model at the book’s parameters gives six firms and an index of 1 667, below the guidelines’ threshold; the public wholesaler figures imply at least 2 467. The gap is the model’s symmetry: the real firms differ in cost, and a firm with lower costs takes a larger share. Halving the fixed cost, as cloud computing and open-source tooling do for research and infrastructure, raises the free-entry number from six to nine; doubling it, as a new speed tier does for the firms that must buy it, lowers it to four.

**Remark 30.5 (Excess entry).**

The planner would choose three firms at $50 million, not six: each entrant takes business from the others, and its private gain exceeds the surplus it adds. Total surplus is $1 169 million at free entry against $1 256 million at three firms. This is Mankiw and Whinston’s excess-entry result in the chapter’s model; it is not an argument for fewer firms in any real business, where entrants also bring new products and lower costs.

Consolidation in trading has followed the arithmetic of fixed costs. Knight Capital and GETCO merged under KCG Holdings on 1 July 2013; Virtu Financial acquired KCG on 20 July 2017 for $20.00 a share in cash, and Investment Technology Group on 1 March 2019 for about $1.0 billion ([Figure 30.3](#fig-fm-competition-and-the-future-chain)). Each deal combined firms whose fixed costs (technology, connectivity, data, compliance) overlapped; chapter 20 read the second as a build-against-buy decision.

![A consolidation chain from the public filings: two firms merged in 2013, the combined firm was acquired in 2017, and the acquirer bought Investment Technology Group in 2019.](https://one-course.com/images/onecourse/chapters/quant-16/fm-competition-and-the-future/fig-e9de6cf30a57.svg)

***Figure 30.3.** A consolidation chain from the public filings: two firms merged in 2013, the combined firm was acquired in 2017, and the acquirer bought Investment Technology Group in 2019.*

![Two of six Cournot firms merge: the price after the merger against the merged firm’s reduction in marginal cost. Without it, the price rises from 4.857 to 5.000 (2.9%); a reduction of 0.857, 21.4% of the marginal cost, restores the old price. Data: fm_competition.merger.](https://one-course.com/images/onecourse/chapters/quant-16/fm-competition-and-the-future/fig-aeb9cc9dd87b.svg)

***Figure 30.4.** Two of six Cournot firms merge: the price after the merger against the merged firm’s reduction in marginal cost. Without it, the price rises from 4.857 to 5.000 (2.9%); a reduction of 0.857, 21.4% of the marginal cost, restores the old price. Data: `fm_competition.merger`.*

```python
def cournot(a, b, costs):
    """Cournot equilibrium, inverse demand a - bQ, marginal costs `costs` (all active)."""
    c = np.asarray(costs, float)
    n = len(c)
    price = (a + c.sum()) / (n + 1)
    q = (price - c) / b
    if (q <= 0).any():
        raise ValueError("a firm would not produce; drop it and recompute")
    return {"price": price, "q": q, "profit": b * q * q, "shares": q / q.sum(), "hhi": hhi(q),
            "cs": b * q.sum() ** 2 / 2}


def merge(a, b, costs, i, j, synergy=0.0):
    """Firms i and j merge into one with marginal cost min(c_i, c_j) - synergy."""
    c = [x for k, x in enumerate(costs) if k not in (i, j)] + [min(costs[i], costs[j]) - synergy]
    return cournot(a, b, c)


def synergy_for_price(a, costs, i, j):
    """The marginal-cost synergy that leaves the Cournot price unchanged after i and j merge."""
    n = len(costs)
    before = (a + sum(costs)) / (n + 1)
    others = sum(x for k, x in enumerate(costs) if k not in (i, j))
    return a + others + min(costs[i], costs[j]) - n * before
```

***Listing 30.2.** Cournot equilibrium with unequal costs, a merger with a marginal-cost synergy, and the synergy that keeps the price unchanged. code/firm/moats/firm_moats.py*

The merger in the model shows why consolidation happens even when it raises prices. Without a marginal-cost synergy, the price rises 2.9% and the index from 1 667 to 2 000, but the merged firm saves one fixed cost: the two firms’ profit after fixed costs rises from $22.4 million to $33.3 million, while consumers lose $60 million of surplus. With the synergy that holds the price, the merged firm’s share is 33.3% and the index 2 222, above both of the guidelines’ presumptions, although buyers pay no more: concentration measures structure, not harm, which is why the guidelines treat their thresholds as presumptions to be tested.

## 30.4 Tokenised assets

**Definition 30.6 (Asset tokenisation, tokenised fund).**

*Asset tokenisation* records ownership of a financial asset (a fund share, a bond, a deposit) as tokens on a blockchain, with the issuer, its transfer agent or a [custodian](https://one-course.com/books/quant/16/en/chapter/4-the-asset-manager-and-the-fund#def-fm-the-asset-manager-and-the-fund-admin) keeping legal responsibility for the record. A *tokenised fund* is a fund whose official register of share ownership is kept, wholly or partly, in such a system.

The registered money-market fund in the dated box shows what the record currently looks like: its transfer agent keeps the official register in a permissioned system on public blockchains, with a whitelist of approved wallets in a smart contract (Book 3), the power to correct errors and to limit transfers, and peer-to-peer transfers of shares between approved wallets. For a trading firm the change is operational before it is strategic. A share that can move between wallets at any hour can serve as collateral outside banking hours, which bears on chapter 14’s margin and funding; its records sit with a transfer agent that can reverse transfers, so it is not a bearer asset. Whether tokenisation lowers the fixed cost of entering a business (by removing intermediaries) or raises it (new custody, controls and connections) is the question the model above makes precise.

## 30.5 Round-the-clock markets

**Definition 30.7 (Round-the-clock trading).**

*Round-the-clock trading* extends a market’s trading sessions to most or all hours of the week, in the listed equity case to 23 or 24 hours on business days, with the clearing, market data and surveillance that the sessions need running over the same hours.

The Commission’s order registering 24X National Exchange describes the structure: the usual pre-market, core and post-market sessions from 4 a.m. to 7 p.m., and an overnight session from 8 p.m. to 4 a.m. on the nights before business days, weekends and holidays having been removed from the proposal. The clearing house moved first: NSCC’s clearing runs from Sunday 8 p.m. to Friday 8 p.m. For a firm, longer hours raise fixed costs (staffing, monitoring, incident response through the night, chapter 21’s on-call design) while the overnight volume, at first, is thin. In the chapter’s model that is a rise in $F$ for every firm that chooses to be present, and a smaller $S$ per session: the overnight business will support fewer firms than the day.

## 30.6 What machine-learning tooling changes

Book 12’s machine-learning platforms and large language models cut two costs at once. The cost of research infrastructure falls: open-source libraries, rented accelerators and pretrained models do what a team once built. So does the cost of routine work (reconciliations, documentation, code review, first drafts of research), chapter 21’s organisation with fewer people per function. Both lower $F$, and the free-entry model says more firms. Sutton’s second case says to look further: if the tools also let the best firms spend to be better (more data, larger models, faster iteration), and the business rewards being best, the spending rises with the market and the leaders’ share need not fall. The two effects can be told apart in a firm’s own numbers: which costs fell (chapter 1’s [fixed cost base](https://one-course.com/books/quant/16/en/chapter/1-the-economics-of-a-trading-firm#def-fm-the-economics-of-a-trading-firm-fixed)), and whether its capture held against the best competitor or against the average one.

**Method 30.8 (Reading a business’s structure).**

1. Measure concentration from what is public: counts, top shares, bounds on the index.
2. Estimate the business’s size and the fixed cost of being in it; compare the free-entry number with the firms observed.
3. Ask which costs are exogenous and which the firms choose to spend to be better; the second kind sustains concentration as the market grows.
4. For each change (a tool, a market structure, a rule), ask whether it moves $S$ , $F$ or the spending race, and for whom.

## 30.7 Build: the moats model

**Purpose.** Concentration from shares or partial shares, the free-entry number of firms, the planner’s number, and Cournot mergers with fixed- and marginal-cost synergies.

**Interface.** `firm.moats`: `hhi`, `cr`, `hhi_bounds`, `free_entry`, `welfare`, `planner`, `cournot`, `merge`, `synergy_for_price`, `scenarios`.

**Rules.** Shares are normalised; a Cournot firm with no output raises an error rather than silently dropping out; the bounds reject share data that cannot be ordered.

**Acceptance tests.** `code/firm/moats/tests/`: the index on hand examples; bounds that bracket random feasible share vectors; the free-entry condition and excess entry; the merger’s price rise and the synergy that removes it.

**Stretch.** Endogenous sunk costs (firms choose quality at a cost); entry with asymmetric costs; two sessions (day and overnight) with different sizes and a shared fixed cost.

Sources and further reading

- US Securities and Exchange Commission, Order Competition Rule, Release 34-96495, 88 FR 128 (2023); Withdrawal of Proposed Regulatory Actions, 90 FR 25531 (2025).
- US Department of Justice and Federal Trade Commission, *Merger Guidelines* , 18 December 2023.
- KCG Holdings, Form 8-K12G3, 1 July 2013; Virtu Financial, Forms 8-K, 21 July 2017 and 1 March 2019.
- Franklin OnChain U.S. Government Money Fund, prospectus, 1 August 2026.
- SEC, In the Matter of the Application of 24X National Exchange LLC, Release 34-101777, 27 November 2024; DTCC, press release, 29 June 2026.
- J. Sutton, *Sunk Costs and Market Structure* , MIT Press, 1991.
- N. G. Mankiw and M. D. Whinston, “Free entry and social inefficiency”, *RAND Journal of Economics* , 1986.

## 30.8 Exercises

**Exercise 30.1 ★.**

Compute the index of six equal firms, and of shares 33, 33, 8.5, 8.5, 8.5 and 8.5%.

**Solution of Exercise 30.1.**

$6\times16.67^2=1\,667$; $2\times33^2+4\times8.5^2=2\,178+289=2\,467$.

**Exercise 30.2 ★.**

Define an [economic moat](#def-fm-competition-and-the-future-moat) and give three sources of one in trading.

**Solution of Exercise 30.2.**

See [Definition 30.1](#def-fm-competition-and-the-future-moat). Fixed costs an entrant must pay first (technology, connectivity, compliance), order flow held by relationships and contracts, and accumulated data and history; a licence or clearing access can be another.

**Exercise 30.3 ★.**

With $S=\$3\,000$ million, how many firms does free entry support at a fixed cost of $25 million, $50 million and $100 million?

**Solution of Exercise 30.3.**

$\lfloor\sqrt{120}\rfloor-1=9$, $\lfloor\sqrt{60}\rfloor-1=6$ and $\lfloor\sqrt{30}\rfloor-1=4$.

**Exercise 30.4 ★★.**

Prove [Proposition 30.3](#prop-fm-competition-and-the-future-bounds). Why must each other firm be no larger than each leader?

**Solution of Exercise 30.4.**

See the proof of [Proposition 30.3](#prop-fm-competition-and-the-future-bounds). If another firm were larger than a leader, it would itself be among the $k$ largest, and the leaders’ combined share would not be $S_k$.

**Exercise 30.5 ★★.**

Two of the six firms merge without a marginal-cost synergy. Would the merger be presumed to lessen competition under the 2023 guidelines, and is it profitable for the merging firms?

**Solution of Exercise 30.5.**

The index rises from 1 667 to 2 000, an increase of 333 into a highly concentrated market: presumed to lessen competition. The merged firm’s profit after its one fixed cost is $33.3 million against $22.4 million for the two before, so it is profitable, through the saved fixed cost; the price rises 2.9%.

**Exercise 30.6 ★★.**

How does overnight trading change a market-making firm’s fixed costs, and what does the free-entry model predict for the overnight session?

**Solution of Exercise 30.6.**

Staff, monitoring, incident response and support through the night, and connections to the overnight venues and clearing: a higher fixed cost for each firm present. With thin volume ($S$ small) and a higher $F$, the model predicts fewer firms overnight than in the day, and a more concentrated session.

**Exercise 30.7 ★★★.**

*Coding.* Compute total surplus at free entry and at the planner’s number for $F=\$50$ million. By how much does free entry fall short?

**Solution of Exercise 30.7.**

$1 169 million at six firms against $1 256 million at three: free entry reaches 93.1% of the planner’s surplus, $87 million short.

**Exercise 30.8 ★★★.**

*Find the flaw.* “Machine-learning tools make research cheap, so the business will become competitive and the leaders’ share will fall.”

**Solution of Exercise 30.8.**

Lower fixed costs raise the free-entry number only if the cost of competing is exogenous. If the tools also let the leaders spend to be better and the business rewards the best, the spending race sustains concentration (Sutton’s second case), and the leaders may gain share.

## 30.9 Problem: The Fixed Cost Falls

**Problem 30.1.**

Weekend problem — the fixed cost falls

A firm’s strategy committee asks what cheaper research tools, tokenised collateral and round-the-clock markets will do to the businesses it is in.

**Part I — The concepts.**

1. Define an [economic moat](#def-fm-competition-and-the-future-moat) .
2. Define [market concentration](#def-fm-competition-and-the-future-hhi) and the [Herfindahl–Hirschman index](#def-fm-competition-and-the-future-hhi) .
3. Define a [free-entry equilibrium](#def-fm-competition-and-the-future-freeentry) .
4. What distinguishes Sutton’s two cases?

**Part II — The record.**

5. What did the SEC’s 2022 release find about wholesaling, and what happened to the proposal?
6. State the 2023 merger guidelines’ thresholds.
7. Describe the consolidation chain of [Figure 30.3](#fig-fm-competition-and-the-future-chain) .
8. What do the [tokenised fund](#def-fm-competition-and-the-future-token) ’s prospectus, the 24X order and NSCC’s announcement establish?

**Part III — The model.**

9. State and prove [Proposition 30.3](#prop-fm-competition-and-the-future-bounds) ; give the bounds for the wholesalers.
10. Derive the free-entry number of firms in the symmetric Cournot model.
11. Give the number of firms and the index at $25, 50 and 100 million.
12. Give the planner’s numbers and explain the gap.
13. Give the merger’s effect on price, index and profits, and the synergy that holds the price.
14. Why does the model’s index fall short of the public bounds?

**Part IV — The strategy.**

15. Which of the firm’s fixed costs do cheaper tools lower, and which do round-the-clock markets raise?
16. In which of the firm’s businesses is the fixed cost chosen (a spending race)?
17. How would you tell, from the firm’s own numbers, whether its moat is shrinking?
18. What would you watch in the record over the next two years?
19. State the *named result* : the free-entry number of firms and the index at the book’s parameters, and how both move when the fixed cost halves.
20. In two sentences, write the recommendation.

**Solution of Problem 30.1.**

1. See [Definition 30.1](#def-fm-competition-and-the-future-moat) .
2. See [Definition 30.2](#def-fm-competition-and-the-future-hhi) .
3. See [Definition 30.4](#def-fm-competition-and-the-future-freeentry) .
4. Whether the fixed cost is given (a larger market supports more firms) or chosen by firms competing to be better (the spending rises with the market and concentration need not fall).
5. Six wholesalers received more than 90% of individual investors’ marketable orders, two with about 66% of their volume; the proposal was withdrawn on 17 June 2025.
6. Above 1 800 is highly concentrated; an increase above 100 there, or a merged share above 30% with an increase above 100, is presumed to lessen competition.
7. Knight Capital and GETCO merged under KCG Holdings in 2013; Virtu acquired KCG in 2017 at $20.00 a share and ITG in 2019 for about $1.0 billion.
8. That a registered fund keeps its official register on public blockchains through its transfer agent; that an exchange was registered to trade listed stocks 23 hours a day, five days a week; and that central clearing runs 24x5.
9. See [Proposition 30.3](#prop-fm-competition-and-the-future-bounds) : 2 467 to 3 668.
10. $\pi(n)=S/(n+1)^2\ge F$ gives $n+1\le\sqrt{S/F}$ , so $n^*=\lfloor\sqrt{S/F}\rfloor-1$ .
11. Nine and 1 111; six and 1 667; four and 2 500.
12. Four, three and two; each entrant’s profit includes business taken from others, which adds nothing to total surplus.
13. Price up 2.9%, index from 1 667 to 2 000, merging firms’ profit after fixed costs from $22.4 million to $33.3 million; a synergy of 0.857 (21.4% of marginal cost) holds the price, with a 33.3% share and an index of 2 222.
14. The model’s firms are identical; real firms differ in cost and scale, and the lower-cost firms take larger shares.
15. Research infrastructure and routine work (lower); staffing, monitoring and connectivity for the overnight sessions (higher).
16. Where being fastest or best-informed wins most of the business: [latency tiers](https://one-course.com/books/quant/16/en/chapter/19-technology-strategy#def-fm-technology-strategy-tier) , data, models.
17. Its capture against the best competitor over time, its fixed costs against entrants’, and its share of the business.
18. Rules on retail order flow and auctions, extended-hours trading and data, tokenised collateral accepted by clearing houses, and further mergers.
19. Six firms and an index of 1 667 at $50 million; nine and 1 111 when it halves.
20. Treat cheaper tools as lowering the cost of entering the firm’s businesses, and defend them where the fixed cost is a spending race the firm can win. Enter overnight sessions only where the firm can be among the few that the thinner business will support.

## 30.10 Interview questions

**Interview question 30.1 ★ researcher.**

What is the [Herfindahl–Hirschman index](#def-fm-competition-and-the-future-hhi) of a business with four equal firms, and what does a merger of two of them do to it?

**Solution of Interview question 30.1.**

2 500; the merged firm has half the business and the index becomes $50^2+2\times25^2=3\,750$, an increase of 1 250.

*What the interviewer is looking for: $2s_is_j$ as the change.*

**Interview question 30.2 ★ trader, researcher.**

What is your firm’s moat, if any?

**Solution of Interview question 30.2.**

A good answer names a lasting advantage and how it is defended (order flow, cost, data, a licence), and admits which edges are signals that decay.

*What the interviewer is looking for: honesty about decaying edges.*

**Interview question 30.3 ★★ researcher.**

In a Cournot market with linear demand and a fixed cost, how many firms enter, and how does the number scale with the market’s size?

**Solution of Interview question 30.3.**

$n^*=\lfloor\sqrt{S/F}\rfloor-1$ with $S=(a-c)^2/b$: the number grows with the square root of the market’s size, so quadrupling the market doubles it.

*What the interviewer is looking for: the square-root scaling.*

**Interview question 30.4 ★★ developer.**

What changes in a trading system when the market it trades runs 23 hours a day?

**Solution of Interview question 30.4.**

Session boundaries and date handling, market data and reference data overnight, risk limits and kill switches staffed around the clock, maintenance windows, and clearing cut-offs.

*What the interviewer is looking for: operations, not only code.*

**Interview question 30.5 ★★ risk.**

A counterparty offers tokenised money-market fund shares as collateral on a Sunday. What do you check?

**Solution of Interview question 30.5.**

Who keeps the register and whether transfers can be reversed, whether the shares can be redeemed or sold before Monday, haircuts, and that the legal documentation (chapter 18) accepts them.

*What the interviewer is looking for: legal record and liquidity.*

**Interview question 30.6 ★★★ researcher.**

You know only that six firms serve a business and that the two largest hold two thirds. Bound its concentration.

**Solution of Interview question 30.6.**

Between 2 467 (leaders equal, others equal) and 3 668 (one leader at 57.5% and five firms at 8.5%).

*What the interviewer is looking for: the feasibility constraint on the others.*