A model for sharing advertising audiences without sacrificing merchants’ baseline clicks

Protecting clicks, not exclusive audiences

Merchants can be both buyers of advertising and suppliers of the customer audiences that make targeting possible. That dual role creates a problem: joining a shared audience pool may improve a merchant’s advertising opportunities while exposing its existing audience to competitors.

In the theoretical preprint Targeted Advertising Platforms: Pooling Audiences Despite Poaching Risk, Klajdi Hoxha develops a mechanism for encouraging voluntary participation. The central idea is to preserve a merchant’s baseline expected clicks—or compensate it for surrendering them—without preserving exclusive access to the same customers. These are mathematical results, not measured outcomes from a platform rollout.

The paper uses Shopify Audiences as a motivating example of voluntary pooling. It places such programs in the context of restrictions on third-party tracking, which have increased interest in using audiences contributed within platforms.

Three choices for participating merchants

The model gives each merchant a privately known value per click. Customers have observable, merchant-specific probabilities of clicking an ad. Advertising only to its initial audience establishes each merchant’s baseline expected clicks and its alternative to joining the platform.

The designer maximizes a weighted combination of platform revenue, merchants’ surplus and customer engagement, measured by expected clicks. Participation must leave merchants at least as well off as their outside option, and the mechanism must give them incentives to report their private information truthfully.

The simplest implementation emerges in a limit model with a continuum of merchants grouped into observable categories, called tags. Tags can capture characteristics such as product category, price tier or audience contribution. Under the paper’s assumptions, each tag receives a menu:

• Keep a campaign delivering baseline expected clicks, with no payment.
• Buy additional expected clicks at a posted buying price.
• Give up baseline expected clicks and receive compensation at a posted selling price.

The selling price is no higher than the buying price. Because merchants’ payoffs are linear in clicks up to a capacity limit, low-value merchants sell their entire baseline allocation, high-value merchants expand to capacity, and intermediate merchants retain their baseline clicks for free.

That middle option matters: merchants can exchange audience access for advertising rather than becoming cash-paying buyers or compensated sellers.

Where the gains come from

Pooling creates two distinct opportunities in the model. Clicks can move toward merchants who value them more. Better targeting can also generate more clicks from the same customer pool, potentially delivering baseline clicks with fewer ad impressions and freeing other advertising opportunities for buyers.

In one worked example with two symmetric product tags and specified uniform distributions, the optimal mechanism raises total expected clicks from 8/15 to 2/3—a 25% increase. This is an illustrative model calculation, not an estimate of what an actual pooling program would achieve.

Targeting is coordinated through tag-specific “virtual prices”: internal values representing the designer’s marginal value of supplying another click to a tag. Each customer goes to the tag with the highest virtual price multiplied by her click probability for that tag.

Consequently, the chosen ad need not be the one she is most likely to click. A higher internal value for clicks in another tag can outweigh its lower click probability. The same virtual prices determine merchants’ posted buying and selling prices, with supply equaling demand in every tag.

From finite platforms to large markets

For finitely many merchants, the optimal mechanism instead uses a merchant-specific score combined with each customer’s click probability. A single merchant score governs the whole campaign, addressing the opposing incentives merchants face when buying additional clicks and selling baseline ones.

The paper connects this mechanism to the large-market menu through a convergence proof. Under symmetry within tags and a statistical assumption that relabeling merchants within a tag leaves the joint click-probability distribution unchanged, suitably normalized optimal allocations and payments converge to their limit-market counterparts. The analysis also constructs finite-market mechanisms that become asymptotically optimal; it does not specify a practical merchant-count threshold.

Efficiency and repeat advertising

The preprint separately examines efficient allocations. Within the limit model, maximizing merchants’ surplus can be implemented without an outside subsidy. When efficiency also gives weight to customer engagement, self-financing is not guaranteed: aggregate buyer payments must cover seller compensation, although surpluses in one tag can finance deficits in another.

An extension allows a second ad from a different tag after no click on the first. Click probabilities help determine the selected pair, but the tag with the higher virtual price is shown first.

The conclusions depend on the model’s structure, including observable click probabilities, private values per click and campaign capacity limits. Expected clicks serve as the engagement measure; their connection to consumer surplus requires additional assumptions about fixed prices and willingness to pay. The practical proposal is therefore a design principle, not demonstrated commercial performance: reward merchants for contributing audiences, even when they do not want to buy ads.