First-price vs second-price ad auctions: an interactive bidding simulator

Every time a search or feed page loads, an ad auction decides in milliseconds which ad to show and what it costs. Ads are ranked not by bid alone but by expected revenue: the bid per click times the predicted chance of a click. The pricing rule then changes how advertisers should bid. In a first-price auction the winner pays its bid; in a second-price auction it pays the least it could have bid and still won, which makes bidding what a click is truly worth the best strategy.

The playground has one ad slot and four advertisers. Move your bid, switch the pricing rule, and watch your profit at every possible bid.

Ranking by expected revenue

Rival B bids the most, $4 a click, but its ad is clicked by only 1.2% of viewers, so it is worth $48 per thousand impressions to the ad server. Rival A bids half as much on an ad clicked by 3%, worth $60, and ranks above it. Ranking by bid times click-through rate, often adjusted by a wider quality score, maximises revenue and keeps irrelevant ads off the page: a less relevant ad of yours, at 1.2%, would need a bid of over $5 to win the slot.

First price, second price, and how to bid

If a click is worth $3 to you and you bid $3 in a second-price auction, you win and pay $2.41, just enough to beat Rival A, for a profit of $14.75 per thousand impressions. Bidding $2.50 or $4 changes nothing, since the price depends on the runner-up, not on you; bidding below $2.41 just loses the slot. So the best bid is your true value, and nobody needs to guess what others will do. The one danger is overbidding: if a rival’s ad becomes stronger, a $4.50 bid still wins but pays $3.85 for a $3 click.

In a first-price auction, bidding $3 wins and earns nothing, so advertisers shade their bids and try to guess where the threshold is. Ad exchanges moved to first price in 2019, partly because header bidding made second-price prices easy to game, and bidders responded with automated bid shading. Search ads with several slots use a generalised second-price auction, where each advertiser pays what is needed to hold its position; unlike the single-slot version, it no longer makes truthful bidding the best strategy.

A single-slot auction in code

def run_auction(ads, kind="second"):
    """ads: [{"id", "bid" (per click), "ctr" (predicted)}], one slot."""
    for ad in ads:
        ad["ecpm"] = ad["bid"] * ad["ctr"] * 1000      # expected revenue per 1,000 impressions
    ranked = sorted(ads, key=lambda a: a["ecpm"], reverse=True)
    winner = ranked[0]
    if kind == "first" or len(ranked) == 1:
        price = winner["bid"]
    else:
        runner_up = ranked[1]
        # the least the winner could have bid and still ranked first
        price = min(winner["bid"], runner_up["ecpm"] / (winner["ctr"] * 1000) + 0.01)
    return winner["id"], round(price, 2)                # charged only if the ad is clicked

In a system design interview

For an ad server, the auction is the core of the request path: “Candidate ads come from an index matched on targeting, a few hundred per request. A model predicts each one’s click-through rate, we rank by bid times predicted CTR, apply budget pacing so campaigns spend evenly through the day, and price the winner at second price. All of it has to finish within about 50 ms. Impressions and clicks flow to an aggregation pipeline that updates budgets and billing.” Expect the follow-ups: pacing, click fraud, and keeping CTR predictions calibrated, since prices depend on them.

Read the guide to ad serving and auctions, see multi-armed bandits for exploring new ads, or watch a strong candidate design an ad click aggregator.

Questions people ask