Markets on geopolitical events

Six statements, each about the model under the card above; the mapping to regulated event markets is a reconstruction R, and no statement estimates any real market's informativeness or the extent of insider trading on it.

• A subsidised market buys resolution. Whatever the traders know and however they behave, the sponsor's expected payment equals the resolution of the closing price minus its reliability, plus the opening price's distance from the base rate (Proposition 10.12 (p. 419)(a)). The budget of a market maker is therefore a measure of how sharply the closing price separates the outcomes, and miscalibration hands part of it back. This joins the chapter's two halves: the telescoping subsidy of Proposition 10.4 (p. 415) is Murphy's resolution in money D [Proposition 10.12 (p. 419)].

• An insider is paid by the subsidy, not by the other traders. In the insider variant the insider's expected profit is $\rho \cdot \frac{1}{4}$ and the analyst never loses money: at $\rho =\frac{1}{2}$ the sponsor pays $\frac{5}{32}$, of which $\frac{1}{8}$ goes to the insider (Table 10.2 (p. 402)). Question 29's “public-interest utility” has an exact form here: every unit the insider is paid is a unit of resolution delivered to readers of the price. The statement depends on the sponsor being the counterparty; in a market where traders trade against each other the insider's profit is someone else's loss (item 4) D [Proposition 10.12 (p. 419)(b)].

• An insider can make the price less informative. The insider also takes the reward for research: the analyst's signal is worth $\frac{1}{16}$ only if no insider has moved the price first, so the analyst researches only while $(1-\rho )\frac{1}{16}\ge \frac{1}{32}$, that is up to ${\rho }^{\ast }=\frac{1}{2}$. Past that point the analyst stays out, and the expected Brier score of the price jumps from $\frac{3}{32}$ to $\frac{1}{8}$; it returns to $\frac{3}{32}$ only at ${\rho }^{\circ }=\frac{5}{8}$ (Figure 10.4 (p. 403)a). On $(\frac{1}{2},\frac{5}{8})$ the forecast is worse than at ${\rho }^{\ast }$, although within that interval it still improves as $\rho$ rises: in the states without an insider the price now carries no information at all. The answer to question 29 in this model is therefore not monotone in $\rho$: insiders add information where they trade and remove it where they would have been outbid. The theme is familiar for securities markets (Fishman and Hagerty 1992); the instance is the book's derivation within the model D [Proposition 10.12 (p. 419)(b)].

• Calibration cannot see any of this. At every $\rho$ the closing price is perfectly calibrated (the last column of Table 10.2 (p. 402)): whenever it says $\frac{3}{4}$, the event occurs three times in four. Only resolution moves. An audit of a market's record by calibration alone (“events priced at $p$ happened a fraction $p$ of the time”) cannot detect insiders, crowding-out, or their balance; this is the climatology lesson of Proposition 10.10 (p. 417) applied to markets D [prop:agg-insider,prop:agg-murphy].

• A stake in the published number bunches beliefs on thresholds. A price-setter who gains $K$ when the price reaches $\tau$ (a campaign that benefits from being shown as the favourite, a party whose position is helped by a headline) reports $\tau$ whenever $K>b(\tau -q{)}^2$. At the base values every belief in $(\frac{3}{8},\frac{1}{2})$ is reported as $\frac{1}{2}$; a belief of $\frac{2}{5}$ gains $\frac{9}{1600}$ by doing so. Removing the distortion at distance $g$ requires a payment scale of at least $K/g^2$, a worst-case liability of $K/(4g^2)$: $\frac{1}{16}$ at $g=\frac{1}{4}$, $\frac{25}{16}$ at $g=\frac{1}{20}$ (Figure 10.4 (p. 403)b). Distortion is cheapest exactly where a contest is close, and a price that sits on a salient threshold says less than a price elsewhere D [Proposition 10.12 (p. 419)(c)].

• The meaning of a price is conditional on who trades. In both variants the price is a forecast in the sense of the chapter only relative to the population of traders — the probability of an insider, the analysts' research incentives, the outside stakes. Rules on insider trading, surveillance, and listing decisions change that population; they therefore change what the price means, not only whether trading on it is fair. “Honesty properties are design properties” is, in this case, a statement about the regulator's levers R.

The registered exchanges in the record run order books, not a sponsor's scoring rule. There an insider's profit is paid by whoever took the other side of its trades, so item (ii) does not transfer: the cost of insider trading falls on other traders and on whoever provides liquidity, who respond by widening spreads or withdrawing. This is the adverse-selection layer of microstructure, which the second worked case takes up in its smallest instance (Section 10.8 (p. 404); the author's earlier monograph treats that layer for leveraged prediction markets; Nechepurenko 2026). Insiders rarely know the outcome for certain, rarely trade first and once, and in an order book trade gradually to hide; there are many analysts with correlated research, not one. The legal notion in the record — misappropriation of confidential information in breach of a duty — is not the model's “trader who knows the outcome”: a well-informed analyst is an informed trader and breaks no rule, and the model cannot say what is lawful. Several of the documented cases concern events that one person controls (a candidate's trades on his own race, words in a speech), where the price is a signal inside a game and Chapter 4's commitment and Chapter 6's inspection mathematics apply. And the outside stake of item (v) is a step at one known threshold; real stakes in published prices are continuous, several and unknown.