When governments want to raise money, they do so by issuing bills (typically short-term) and bonds (longer term maturities can reach 30 years or more). The method is usually an auction. Remember that the issuer wants to raise capital as cheaply as possible and that means at the lowest possible yield (the yield is the annual return divided by price as a percentage. So the more a bidder bids, the lower the yield will be).
A competitive auction is where institutional and individual investors fight to get the bonds. It should ensure the issuing government raises the money it needs at the lowest cost.
Once all bids have been received, bonds are allocated at a single price to all successful bidders that price is usually the one that represents the highest yield from the bids accepted (so the higher your bid price, the more likely it is you will be allocated some bonds).
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Alternatively, you may bid non-competitively and take bonds at the yield determined by the competitive bid process.
See Tim Bennett's video tutorial: Bond basics.
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