Sovereign debt is sold at auction, and the two rules that matter differ in who pays what.
Under a uniform-price rule every accepted bidder pays the same price, the one corresponding to the highest accepted yield, called the stop-out. Under a multiple-price rule each accepted bidder pays its own bid.
Both rank bids from the most aggressive to the least, fill in that order until the amount on offer is exhausted, and fill the marginal bidder pro rata.
How do US Treasury auctions work?
The United States runs single-price auctions for all marketable Treasury securities, a change made in the late 1990s after multiple-price experiments (check the current practice with the Treasury's own auction regulations). Competitive bidders submit a yield; non-competitive bidders submit only an amount, are filled in full up to a per-bidder cap, and pay the stop-out price. The coupon on a new note is then set at the highest eighth of a percent that prices the issue at or below par.
Worked Example 2 runs a $40 billion ten-year auction with $2 billion of non-competitive bids and five competitive bidders. The book fills through 4.180%, 4.195% and 4.205%, and the fourth bidder is the marginal one at 4.210%, taking $7.00 billion of an $8.00 billion bid, an 87.500000% fill. The fifth bidder gets nothing. Total tenders of $47.0 billion against $40.0 billion accepted give a bid-to-cover of 1.175000, and everyone accepted, including the non-competitive tranche, pays 99.3120545725 per 100.
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Why did the US choose uniform pricing?
The counterfactual is what makes the rule visible. Charge each accepted competitive bidder its own price and the Treasury raises $39,771,965,924.85 rather than $39,724,821,828.99, a difference of $47,144,095.85, or 11.8677 basis points of proceeds on that book. A multiple-price rule extracts more from this book, which raises the obvious question of why the United States gave it up. The answer is the winner's curse: under a multiple-price rule the bidder who wins is the one who bid most aggressively, so winning is itself bad news, and rational bidders shade their bids to compensate. Uniform pricing removes that penalty, which is meant to bring more aggressive bidding and a tighter stop-out over time. Which effect dominates is an empirical question and the literature is not unanimous.
How does India auction government bonds?
India runs both rules and announces which one applies in each auction notification (check against the current RBI auction calendar and notifications). Auctions are conducted by the Reserve Bank of India as the government's debt manager, through its own electronic bidding system. A new security is auctioned yield-based, so bidders submit yields; a reissue of an existing security is auctioned price-based, so bidders submit prices, and the price ranking runs from highest to lowest rather than the other way. A portion of the notified amount, 5% in dated-security auctions at the time of writing, is reserved for non-competitive bidders who submit only an amount and receive the weighted-average price of the accepted competitive bids (check the current reservation and eligibility under the RBI's non-competitive bidding scheme).
Worked Example 6 runs a ₹32,000 crore reissue under a multiple-price rule. The cut-off price is ₹99.41, the marginal bidder is filled at 98.333333%, the weighted-average accepted price is ₹99.5262828947 and the bid-to-cover is 1.159375. Against a uniform-price counterfactual at the cut-off, the multiple-price rule raises ₹37.210526 crore more on the same book.
Two features of the Indian arrangement have no close American analogue. Primary dealers carry an underwriting obligation, bidding in a separate underwriting auction for commission and standing ready to absorb the unsold portion, so an auction that does not clear at an acceptable yield devolves onto them rather than failing. And the states borrow through the same machinery. State Development Loans are auctioned by the central bank on behalf of individual state governments, which is why they trade at a spread to central-government paper despite an implicit federal backstop nobody has tested.
An auction that cannot fail prices differently from one that can.