# Economic analysis of DMA-constrained data sharing strategies among platforms

Patrick Maillé, Bruno Tuffin

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Patrick Maillé, Bruno Tuffin. Economic analysis of DMA-constrained data sharing strategies among platforms. 2025. hal-05110537

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# Economic analysis of DMA-constrained data sharing strategies among platforms

Patrick Maillé<fnref n="1" />[000-0003-1064-5948] and Bruno Tuffin<fnref n="2" />[0000-0001-9415-1130]

**Abstract.** To stimulate innovation and competition in the digital sector, the European Commission has adopted the Digital Markets Act (DMA), that aims at limiting the gatekeeping power of the biggest actors. For instance, such prevailing platforms may be forced to share with their competitors some, or all, of the data they collected on users that can help improve service quality. This paper proposes a model to analyze the impacts of such a regulation, by comparing (i) a laisser-faire situation where prevailing platforms are free to sell data to newcomer service providers, (ii) the case when platforms can decide to share data but charging newcomers is prohibited, and (iii) a scenario where data sharing is imposed and enforced by the regulator. We investigate the impacts of those scenarios on key metrics like User Welfare, provider revenues, and user demand repartition.

As a response to the digital sector being more and more controlled by a small number of (mostly US-based) giant companies, the European Commission newly adopted the Digital Markets Act (DMA), “the EU’s law to make the markets in the digital sector fairer and more contestable” [5]. The law aims in particular at preventing actors with a powerful position, labeled *gatekeepers*, from stifling competition regarding services that they themselves propose. The gatekeeper position can indeed provide a significant advantage with respect to newcomer competitors, e.g., thanks to the access to user-specific information collected through the (often numerous) services those powerful actors offer.

The powerful companies targeted by the DMA are those satisfying three conditions: (i) a sufficiently significant size in terms of revenue, and an operation in at least three EU member states; (ii) a gateway position between businesses and consumers, concerning more than 45 million monthly active consumers and more than 10 thousand yearly active businesses established in the EU; and (iii) a durable such position, i.e., the previous condition being satisfied for at least three years. For such actors, the DMA imposes some obligations, like data sharing with other businesses in order to prevent lock-in situations, and stimulate innovation and competition [3].

The objective of this paper is to provide a modeling methodology to investigate the influence of regulations based on those principles. More specifically,

<footnote n="1">¹ IMT Atlantique, IRISA, UMR CNRS 6074, Rennes, France
patrick.maille@imt.fr</footnote>

<footnote n="2">² Inria, Univ. Rennes, CNRS, IRISA, Rennes, France
bruno.tuffin@inria.fr</footnote>
we consider a new service (say, app), for which two service providers compete to attract users. The first is a gatekeeper or incumbent platform, as those targeted by the DMA, that already has as customers (for its other services) a significant proportion (even possibly 100%) of the target population of the new service; The other is a newcomer to the market, that therefore has no customer base but is highly innovative and could provide the new service with higher quality of experience.

Without any regulation, the incumbent platform already uses the user data collected to provide good service, hence attracting demand, and make revenue by introducing user-targeted ads within its service. By contrast, the newcomer would not benefit from that knowledge, hence a poorer service and/or less ad revenue. To limit the advantage of the incumbent over potential competitors, the regulator can intervene with regard to that use of user personal data. For example, the use of user data collected through the incumbent platform can be regulated, i.e., limited to a certain range. The enforcement of GDPR (for General Data Protection Regulation) can be thought of this way (although its main goal is to let users control how their data is used) as it limits what platforms can do with user personal data. Another possibility to approach a level playing field could be to impose the incumbent platform to share (some of) its user information, that the newcomer could use to improve its service (and get more demand) and/or make more revenue from better-targeted ads. This can be part of what the DMA intends to do.

Our goal is to investigate the data sharing decisions that are made, depending of who makes those decisions, and how they can be enforced. Then the consequences on demands, providers’ revenues, and user welfare are considered. More specifically, we compare the following scenarios:

• The incumbent chooses the level of data sharing with the newcomer, but is not allowed to charge the newcomer for it;

• The incumbent is free to choose the data sharing level, and to charge the newcomer;

• The level of data sharing is imposed by the regulator, who then suffers some costs to enforce that policy.

Note that some contributions in the literature evoke the economic questions around the DMA and user data sharing [7, 8], sometimes altogether with legal implications [1, 6, 4], but to the best of our knowledge this is the first concrete mathematical modeling of the problem.

# 1 Modeling data sharing among providers

This section introduces the mathematical model we consider to represent how data sharing from an incumbent provider with a newcomer affects service qualities, and as a consequence user demands, provider revenues, and user welfare.
## 1.1 The providers and their qualities

Throughout the whole paper, we use the index $I$ (resp., $N$) to refer to the incumbent platform (resp., newcomer service provider). Those indices will also be used as labels to specify the choice made by users regarding the provider they choose for that service; finally we add the label “0” for users preferring not to use that service at all.

Let us denote by $\alpha \in [0, 1]$ the proportion of user-related data controlled by the incumbent that the newcomer is able to access, and by $q_N(\alpha)$ the corresponding quality of the service that the newcomer can offer if accessing that amount of data, assumed non-decreasing. By contrast, the quality offered by the incumbent for the similar service is independent of $\alpha$, and denoted by $q_I$. Finally, the quality experienced by users not considering any service is $q_0 = 0$.

We assume that the target population of the newcomer is included in the population already using some service(s) from the incumbent platform, so the incumbent already has the user-specific information, and the quality $q_N(\alpha)$ is considered the same for each potential user of the newcomer service. A larger $\alpha$ will make the newcomer more attractive, at the expense of the incumbent that will lose some users for that specific service (or get less traffic from users, who will partially turn to the newcomer).

We will often make the following assumption regarding the function $q_N$, which can be justified by considering that any extra information can yield some quality improvement, but that there are diminishing returns.

**Assumption A** The quality function $q_N(\cdot)$ of the newcomer's service is differentiable, strictly increasing and concave over $[0, 1]$.

## 1.2 User options and choices

To represent the impact of quality on demands, we assume that each user $i$ has a utility for each choice $C \in \{I, N, 0\}$ regarding the service (respectively, the incumbent, the newcomer, or no service), of the form

$$U_{i,C} = \ln(1 + q_C) + \kappa_{i,C}, \quad (1)$$

where $q_C$ is the quality for the choice $C$, and $\kappa_{i,C}$ is a user-specific value that represents some other aspects affecting that user's perception of each choice. Each user then selects the highest-utility choice for them. When all $\kappa_{i,C}$ are independent random variables following a standard Gumbel distribution, an assumption often made in discrete-choice models [2], then choices spread proportionally to the exponentials of the non-random parts of the utilities. In our case the proportions of users choosing each option $I$, $N$, or 0 (for which we consider the quality to be zero) then respectively equal

$$d_I = \frac{1 + q_I}{3 + q_I + q_N(\alpha)}, \quad d_N = \frac{1 + q_N(\alpha)}{3 + q_I + q_N(\alpha)}, \quad d_0 = \frac{1}{3 + q_I + q_N(\alpha)}.$$
## 1.3 Revenues for providers

We consider that both service providers make money through ads, with some revenue that is proportional to the traffic they attract, i.e., to their market share for the service.

Let us denote by $\beta_I$ (resp., $\beta_N$) the revenue per unit of market share that the incumbent platform (resp., the newcomer) can generate through the service. Their total revenue $R_I$ (resp., $R_N$) can then be expressed as a function of $\alpha$:

$$R_I = \beta_I \frac{1 + q_I}{3 + q_I + q_N(\alpha)} \qquad (2)$$

$$R_N = \beta_N \frac{1 + q_N(\alpha)}{3 + q_I + q_N(\alpha)}. \qquad (3)$$

Note that we can also consider $\beta_N$ to be a non-decreasing function of $\alpha$, as more targeted ads, which we assumed are positively perceived by users, are also more likely to lead to sales and generate revenue.

## 1.4 User Welfare

Intuitively, User Welfare (UW) should be maximized when $\alpha$ is maximal, since $\alpha$ just increases the quality of Choice $N$ without affecting the others. To quantify UW, we use as a reference the situation where no service is provided (and each user $i$ has a utility $U_{i,0}$), and define UW as the average gain in utility with respect to that reference. As each user $i$ selects the highest-utility choice, their gain $G_i$ from the existence of the service is

$$G_i = \max(U_{i,I}, U_{i,N}, U_{i,0}) - U_{i,0} = \max(U_{i,I} - U_{i,0}, U_{i,N} - U_{i,0}, 0).$$

Taking the average over all users (hence removing the user index), we get

$$UW = \mathbb{E}[G] = \int_{x=0}^{\infty} \mathbb{P}(G > x)dx = \int_{x=0}^{\infty} (1 - \mathbb{P}(G \le x)) dx.$$

Now, remark that $G = \max(\ln(1 + q_I) + \kappa_I - \kappa_0, \ln(1 + q_N(\alpha)) + \kappa_N - \kappa_0, 0)$, so that for any $x \ge 0$ we have

$$\{G \le x\} = \{\kappa_0 + x \ge \ln(1 + q_I) + \kappa_I\} \cap \{\kappa_0 + x \ge \ln(1 + q_N(\alpha)) + \kappa_N\}.$$

Hence $\mathbb{P}(G \le x)$ is the probability that a user would prefer the “no service” option if that option had a non-random part of $x$ instead of 0. Applying again results from discrete-choice theory [2] gives $\mathbb{P}(G \le x) = \frac{e^x}{e^x + 2 + q_I + q_N(\alpha)}$, thus

$$UW = \int_{x=0}^{\infty} \frac{2 + q_I + q_N(\alpha)}{e^x + 2 + q_I + q_N(\alpha)} dx = \ln(3 + q_I + q_N(\alpha)). \qquad (4)$$

As expected, UW increases with $\alpha$, hence a regulator focusing only that metric would want to impose a maximum level of data sharing among service providers, as the DMA tries to enforce.
## 2 When information sharing is decided by the incumbent platform

In this section, we investigate the level of information sharing $\alpha$ that would be chosen, if the decision was taken by the incumbent platform trying to maximize its revenue.

### 2.1 No data sharing without compensation or regulation

We first assume that the incumbent platform can choose the level of data sharing with the newcomer, but that it is not allowed to ask for any (financial) compensation. In that simple case, the incumbent revenue in (2) being decreasing in $\alpha$, the optimal sharing level is just $\alpha = 0$. Note that this situation is the worst from the point of view of User Welfare, as pointed out before.

### 2.2 An all-or-nothing outcome if the incumbent can charge the newcomer

Now assume that no regulation at all applies, so that the incumbent is free to decide the data sharing level $\alpha$ but also to charge the newcomer provider any price it decides to.

In such a situation, the incumbent, having the decision power over $\alpha$, can extract all the potential benefits in ad revenues stemming from data sharing. To do so, it would charge the newcomer just so that the newcomer's net revenue is equal (or very slightly above, to introduce some minor incentive) what it would get with no user data at all.

The objective for the incumbent would then be to maximize the sum of both providers' revenues, namely

$$ 
\begin{aligned}
R_I + R_N &= \beta_I \frac{1 + q_I}{3 + q_I + q_N(\alpha)} + \beta_N \frac{1 + q_N(\alpha)}{3 + q_I + q_N(\alpha)} \\
&= \beta_N \frac{q_N(\alpha) + 1 + \frac{\beta_I}{\beta_N}(1 + q_I)}{q_N(\alpha) + 3 + q_I}.
\end{aligned}
$$

That expression is strictly increasing in $q_N(\alpha)$, if and only if $3+q_I > 1+\frac{\beta_I}{\beta_N}(1+q_I)$, i.e., if $\frac{\beta_N}{\beta_I} > \frac{1+q_I}{2+q_I}$, that is, if the newcomer ad profitability relative to the incumbent's exceeds a function of the incumbent quality.

When that inequality holds, the pair incumbent+newcomer generates the most revenue when $\alpha = 1$ (which is the only optimal solution when $q_N(\cdot)$ is strictly increasing). The extra revenue $R_{extra}$ with respect to the situation where $\alpha = 0$ is

$$ R_{extra} = \frac{\beta_I(1 + q_I) + \beta_N(1 + q_N(1))}{3 + q_I + q_N(1)} - \frac{\beta_I(1 + q_I) + \beta_N(1 + q_N(0))}{3 + q_I + q_N(0)}. $$
To keep all this benefit to itself, the incumbent could present the newcomer with a take-it-or-leave-it offer, adjusting the price $p$ it charges the newcomer to have it exactly indifferent between accepting and refusing, i.e.,

$$ \beta_N \frac{1 + q_N(1)}{3 + q_I + q_N(1)} - p = \beta_N \frac{1 + q_N(0)}{3 + q_I + q_N(0)}. $$

Alternatively, the newcomer could be aware that it has some bargaining power, as the benefit only materializes when the newcomer accepts the offer, and could choose to refuse such an offer. The resulting outcome, seen either as the Nash Bargaining Solution [10] with equal bargaining power, or a Shapley value [9], would then consist in both providers sharing that benefit evenly. In that case the price $\bar{p}$ paid by the newcomer to the incumbent would be such that

$$ \beta_N \frac{1 + q_N(1)}{3 + q_I + q_N(1)} - \bar{p} = \beta_N \frac{1 + q_N(0)}{3 + q_I + q_N(0)} + \frac{1}{2} R_{\text{extra}}. $$

Summarizing, the total utility (revenues from ads plus monetary exchanges between providers) of the incumbent and newcomer providers are respectively:

$$ \text{With no bargaining:} \quad \begin{cases} U_I = \beta_I d_{I|\alpha=0} + R_{\text{extra}} \\ U_N = \beta_N d_{N|\alpha=0} \end{cases} $$

$$ \text{At Nash Bargaining Solution (NBS):} \quad \begin{cases} U_I = \beta_I d_{I|\alpha=0} + R_{\text{extra}}/2 \\ U_N = \beta_N d_{N|\alpha=0} + R_{\text{extra}}/2. \end{cases} $$

Whether the incumbent has all the negotiating power or that power is shared so that the gain $R_{\text{extra}}$ is equally split over providers, the data sharing level $\alpha_I^*$ that should be chosen by the incumbent (hence the index $I$) is one maximizing $R_{\text{extra}}$, or equivalently $R_I + R_N$. Hence the following result.

**Proposition 1.** Under Assumption A, the data sharing level $\alpha_I^*$ that the incumbent would choose if allowed to charge the newcomer, is

$$ \alpha_I^* = \begin{cases} 1 & \text{if } \frac{\beta_N}{\beta_I} > \frac{1+q_I}{2+q_I} \\ 0 & \text{if } \frac{\beta_N}{\beta_I} < \frac{1+q_I}{2+q_I} \\ \text{any } \alpha \in [0, 1] & \text{if } \frac{\beta_N}{\beta_I} = \frac{1+q_I}{2+q_I}. \end{cases} $$

The proposition states that if the newcomer's ads are sufficiently efficient (in terms of revenue $\beta_N$ per market share unit) then it is worth maximizing the newcomer's quality to maximize total revenue. While this could be expected, the condition also specifies the threshold for data sharing to be beneficial, and surprisingly it is not even necessary to have $\beta_N > \beta_I$, although that would be sufficient: Even with equally effective advertising, i.e., $\beta_N = \beta_I$, it is optimal to select $\alpha = 1$.

Conversely, if $\frac{\beta_N}{\beta_I} < \frac{1+q_I}{2+q_I}$ then the incumbent's best strategy is to set $\alpha = 0$, i.e., share no user data with the newcomer. Indeed, for any positive $\alpha$ there would be no price the incumbent could charge the newcomer that would at the same time be accepted by the newcomer and lead to some gain (between ad revenue and selling data) to the incumbent.
## 3 When information sharing is enforced by the regulator

We already saw from (4) that User Welfare strictly increases with $q_N(\alpha)$, so a regulator focusing on UW only would want to impose the incumbent a maximum level of data sharing, without any payment from the newcomer to the incumbent, in order to stimulate innovation and competition. But that is assuming that enforcing such a rule is costless, while in practice it might be complex. In this section, we add a regulation cost component to the objective function of the regulator, to highlight the possible loss of welfare such a cost incurs.

### 3.1 Modeling the cost of enforcing data sharing

First note that for some basic pieces of data (e.g., user name or address) it may be relatively easy to determine whether they have been shared truthfully, for example the recipient (the newcomer provider) can check that information. However, more detailed information, like what the incumbent exactly learned about users from their online behavior, can be altered by the incumbent to prevent its competitor from maximizing service quality, or can simply be hidden by the incumbent, the newcomer not even knowing that such information exists. It can then be extremely difficult to identify missing or deformed data.

Therefore, ordering data by increasing checking costs, we end up with a cost function $c(\alpha)$ to enforce a sharing level $\alpha$ satisfying the assumption below (where we also add differentiability).

**Assumption B** The cost function $c(\cdot)$ of enforcing some level of data sharing is differentiable, strictly increasing and convex.

### 3.2 Optimizing the regulated data sharing level

The regulator is now faced with a trade-off regarding the data sharing level $\alpha$ to set, a higher $\alpha$ meaning larger User Welfare from (4) but also higher enforcing costs. We formulate its objective function, or utility $U_R$, as

$$U_R(\alpha) = \text{UW}(\alpha) - c(\alpha) = \ln(3 + q_I + q_N(\alpha)) - c(\alpha).$$

Maximizing $U_R(\alpha)$ is a convex optimization problem under Assumptions A and B, in which case the first-order condition

$$\frac{q'_{N}(\alpha)}{3 + q_{I} + q_{N}(\alpha)} = c'(\alpha), \qquad (5)$$

has at most one solution. Therefore we have the following result.

**Proposition 2.** The maximization problem for the regulator $\max_{\alpha \in [0,1]} U_R(\alpha)$ has a unique solution $\alpha_R^*$, that is

$$\alpha_R^* = \begin{cases} 0 & \text{if } c'(0) > \frac{q_N'(0)}{3+q_I+q_N(0)}, \\ 1 & \text{if } c'(1) < \frac{q_N'(1)}{3+q_I+q_N(1)}, \\ \text{the only value } x \in [0,1] \text{ such that } \frac{q_N'(x)}{3+q_I+q_N(x)} = c'(x) \text{ otherwise.} \end{cases}$$
The first and second cases in the proposition above respectively correspond to situations where controls are just too expensive to impose any level of data sharing, and where on the opposite those costs are negligible with respect to the gains in User Welfare.

## 4 Numerical Analysis

In this section, we provide a quantitative analysis for some specific functions $q_N(\cdot)$ and $c(\cdot)$. While any functions satisfying Assumptions A and B are easy to deal with numerically (as (5) can be solved by dichotomy), we take here some functions allowing to solve (5) analytically, namely we consider quadratic checking costs for the regulator, and a service quality for the newcomer that increases linearly with the level of data sharing:

$$q_N(\alpha) = \gamma + M\alpha$$
$$c(\alpha) = K\alpha^2$$

for some constants $\gamma \ge 0$, $M > 0$, and $K > 0$.

With those functions, the first-order condition (5) of the regulator's problem leads to the second-degree equation $\alpha^2 + \frac{3+q_I+\gamma}{M}\alpha - \frac{1}{2K} = 0$, which has a unique non-negative solution. As per Proposition 2, the sharing level imposed by the regulator would then be $\alpha_R^* = \min(1, \sqrt{\left(\frac{3+q_I+\gamma}{2M}\right)^2 + \frac{1}{2K} - \frac{3+q_I+\gamma}{2M}})$.

On the other hand, note that Proposition 1 implies that the data sharing level, if chosen by the incumbent, is independent of the functions we consider, as it only depends on ad efficiencies $\beta_I, \beta_N$ and incumbent service quality $q_I$.

In Figure 1, we vary individual parameters of the model, keeping the other parameters to the default values below:

$$\frac{\beta_I \beta_N q_I \gamma M K}{1 1 1 0.5 1 0.5}$$

The plots illustrate the threshold effect for $\alpha_I^*$ regarding newcomer ad profitability $\beta_N$: below a threshold (here 2/3), an incumbent allowed to charge the newcomer prefers not to share anything, while it would share all of its data above that threshold, even if some bargaining takes place between both providers. Without bargaining, the incumbent takes all the benefits of the sharing, while this benefit is shared equally with the provider in the Nash Bargaining Solution outcome.

As could be expected, from the incumbent's point of view, the preferred situation is the “no bargaining” outcome, then the bargaining one, then the situation with no sharing ($\alpha = 0$), its least-preferred being the regulated scenario, where it is forced to share some amount $\alpha_R^*$ of data without any compensation. But for the newcomer, while the “no bargaining” solution yields the lowest utility, exactly as the “$\alpha = 0$” situation, the best scenario can either be the Nash Bargaining Solution or the regulated one, the latter being preferred for high values of $K$ (regulation is so costly that the imposed sharing level is insufficient), or low values of $M$ where the imposed sharing level is also small, as the curves of $\alpha_R^*$ show.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Impact of model parameters on the selected data sharing level $\alpha$ (top), User Welfare (center), and providers' utilities (bottom).</figcaption></figure>

In terms of User Welfare (or UW minus the regulation cost), the best situation can either be the laisser-faire (i.e., letting the incumbent decide the sharing level, with or without bargaining) when $\alpha_I^* = 1$, which can be at the expense of the newcomer, or some regulatory intervention even if imposing $\alpha_R^*$ is costly.

# 5 Conclusions

This paper proposes a simple mathematical model to analyze the economic implications of regulating the sharing of user data that powerful platforms control, one key component of the DMA. The model encompasses competition between incumbent and newcomer actors, and the feasibility of regulation. Our results suggest that while preventing payments from newcomers to incumbents is sim-
ple to implement, it would not lead to data sharing or stimulate innovation by helping newcomers if data sharing is not imposed. Then, facing the reality of enforcing such regulation leads to tradeoffs about what level of sharing can be imposed: in the end, from a user welfare point of view, or even for a newcomer with bargaining power, a regulatory intervention is not always beneficial.

The model presented in this paper can be enriched in several directions, for example by considering more complex relations between data sharing and quality, with data sharing not being limited to one number, or by introducing different demand models, possibly with several newcomers.

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