2.1 Platform Market Power, Congestion Management, and Non-Price Control

A foundational literature models platforms as intermediaries that internalize cross-group externalities while exercising control over access and participation (Armstrong, 2006; Rochet and Tirole, 2003), and related work shows how cross-network externalities can support dominance extension through tying in platform settings (Park et al., 2020). As digital markets have matured and concentrated, platforms increasingly rely on non-price instruments, including access rules, availability constraints, and algorithmic control, rather than prices alone, consistent with evidence that platform firms differ systematically in what they provide and how they leverage connectivity and innovation (e.g., Kim et al., 2024). Platform leadership can shape ecosystem outcomes not only through pricing but also through technological and architectural control (e.g., Lee et al., 2021).

This shift has been documented in both theoretical and empirical studies. Belleflamme and Peitz (2021) argue that access design has become a core competitive instrument in platform markets. Related research links platform dominance to unilateral operational policies that are difficult to discipline through competition, particularly when users face high switching costs (Hagiu et al., 2022; Jullien and Sand-Zantman, 2021). Moreover, evidence shows that algorithmic decision-making alone can sustain anticompetitive outcomes even in the absence of explicit coordination or price fixing (Calvano et al., 2020), raising concerns that algorithmic decision-making and related non-price operational controls may generate persistent welfare distortions that standard price-based competition cannot easily correct.

Parallel to this literature, a substantial body of work examines congestion and capacity constraints in on-demand service platforms. Platforms face trade-offs between service quality, completion rates, and system stability during peak demand, and increasingly rely on quantity rationing and access restrictions rather than price adjustments to manage congestion (Bimpikis et al., 2019; Cachon et al., 2017; Taylor, 2018).

Our study contributes to this literature by modeling geographic service area restriction as a strategic non-price control chosen by a dominant platform. We show that while congestion management can be efficiency-enhancing, it creates incentives for excessive restriction when platforms do not internalize choice and access losses.

This perspective aligns closely with the information systems literature on algorithmic governance, which emphasizes how platform design choices and embedded rules shape access, participation, and economic outcomes beyond prices alone (Burtch et al., 2018; Kellogg et al., 2020; Möhlmann et al., 2021). These studies suggest that non-price operational controls increasingly function as governance mechanisms that shape market access rather than prices.

2.2 Choice, Access, and Welfare of Consumers and Small Businesses

A second strand of literature emphasizes that choice and access themselves are fundamental components of welfare. Discrete choice theory establishes that the size of the choice set directly affects consumer surplus, even holding prices and qualities constant (Mc Fadden, 1977; Small and Rosen, 1981). Although this insight is well understood in theory, it has been less central in much of the platform literature.

Recent studies document that platforms actively shape effective choice sets through ranking, curation, and availability constraints, with important welfare consequences even in the absence of price changes (Nocke and Rey, 2024). Such practices can substantially reduce effective access and available options (e.g., Bourreau et al., 2017; Chiou and Tucker, 2013), and recent models formalize how intermediation and access restrictions generate first-order welfare effects (Nocke and Rey, 2024).

At the same time, a growing literature examines how platform policies affect small businesses and complementors. For example, Zhu and Liu (2018) show that Amazon’s entry into complementors’ product spaces reshaped seller performance through changes in competitive conditions rather than direct price effects. Platforms influence complementor outcomes not only through prices but also by governing access, visibility, and demand allocation, often in ways that disproportionately affect smaller firms (Cennamo et al., 2018; Kim et al., 2024). Prior research shows that platform policies can reshape complementors’ effective market access by altering competitive exposure and visibility, even when aggregate platform demand remains high (Cennamo et al., 2018; Zhu and Liu, 2018).

In the context of food delivery platforms, existing research has focused primarily on pricing, commissions, and delivery speed. Far less attention has been paid to how service availability and geographic access shape welfare for consumers and restaurants. Our study fills this gap by explicitly modeling service area restriction as a reduction in both consumer choice and restaurant market access, and by quantifying the resulting welfare loss. This highlights that access and choice are not merely outcomes of platform design, but central channels through which platform governance affects welfare.

3.1 Environment, Delivery Technology, and Consumer Choice

Consider a monopolistic food delivery platform operating in a linear city [0, 1]. Consumers are uniformly distributed along the interval. Two restaurants, A and B, are located at the endpoints 0 and 1, respectively. The platform intermediates all transactions.

The linear-city structure provides a tractable benchmark for analyzing how service area restrictions affect market access and welfare. While it abstracts from richer heterogeneity in real markets, the key mechanism operates through endogenous truncation of the consumer choice set rather than the specific spatial structure, and therefore extends naturally to richer environments with greater heterogeneity.

The analysis focuses on peak hours. During this period, the platform chooses a delivery service radius r ∈ [1/2, 1]. A consumer located at x can order from restaurant A if x ≤ r, and from restaurant B if 1 - x ≤ r. The condition r ≥ 1/2 ensures full market coverage, so that each consumer has access to at least one restaurant.

Menu prices are identical across restaurants and normalized to p. Production costs are normalized to zero.

Delivery time for an order with distance d is given by

where τ'(d) > 0 captures distance-related travel time, and H'(r) > 0 captures congestion in the platform’s dispatch system. A larger service area increases routing complexity and congestion during peak demand.

There exists a delivery time threshold T such that if T(d, r) > T, the consumer cancels the order and no transaction occurs, consistent with waiting-sensitive demand (Allon et al., 2011).

If an order is completed, a consumer located at x who orders from restaurant j ∈ {A, B} obtains utility

where V is baseline valuation, α > 0 measures disutility from delivery time, and ε_j is a restaurant-specific taste shock.

Taste shocks ε_A and ε_B are independently and identically distributed according to a Gumbel distribution with unit scale. This assumption implies that when both restaurants are available, consumers enjoy a positive choice value. Under the standard logit model with i.i.d. Gumbel taste shocks and symmetric deterministic utility components, the expected maximum utility increases by ln 2 when the number of available alternatives increases from one to two¹. When only one restaurant is available, the incremental choice value from having an additional alternative disappears. This formulation captures the welfare value of choice in a reduced-form manner, and the associated welfare loss from access restriction would be larger in environments with a richer set of differentiated alternatives.

To clarify the scope and interpretation of the model, we note the following. The model adopts a stylized structure to isolate the core mechanism of service area restriction. In particular, the monopolistic platform should be interpreted as a reduced-form representation of strong market power rather than the literal absence of competition. In highly concentrated platform markets, even limited competition may not fully discipline platform behavior due to network effects and switching frictions. This interpretation is particularly relevant in highly concentrated platform markets such as the Korean food delivery industry, where a small number of dominant platforms can shape market access and participation.

In addition, rider supply is treated as exogenous to focus on the demand-side distortion arising from access restriction. Allowing for endogenous supply would introduce an additional adjustment margin, potentially mitigating congestion. However, the platform’s incentive to restrict access in order to improve operational performance would remain. We return to these considerations in the discussion section.

3.2 Platform Payoffs, Transaction Volume, and Social Welfare

Consumers choose among available restaurants to maximize utility. Let d*(x, r) denote the delivery distance chosen by consumer x, conditional on availability. An order is completed if and only if

Aggregate completed transaction volume during peak hours is therefore

Because reducing the service area lowers congestion, a decrease in r may increase transaction volume by preventing cancellations, despite reducing the choice set.

The platform earns a per-transaction margin m(r) ≥ 0, which may depend on the service area through delivery fees, commissions, or operational costs. Platform profit during peak hours is

The platform chooses r to maximize Π(r), internalizing the effect of congestion on delivery times and order completion but not the welfare loss from reduced consumer choice.

We define social welfare, denoted by W(r), as the sum of consumer surplus net of delivery disutility and the intrinsic value of consumer choice. This welfare function serves as the objective of the social planner in Section V.

where s̄(r) denotes the average completion probability among consumers who retain access to both restaurants.

This welfare measure is intentionally parsimonious. It captures completed-transaction surplus, delivery-time disutility, and the intrinsic value of consumer choice, but does not separately model seller-side payoff. Incorporating seller payoff based on accessible market reach or exposure would reinforce the access-related mechanism, while seller payoff based solely on realized transactions could partially offset it. The central point is therefore not that all seller-side effects necessarily strengthen the result, but that reduced choice and access create a welfare component that the platform does not fully internalize.

We assume that the access-expansion effect of a wider service radius dominates any reduction in completion probability due to congestion, so that the choice-value term (2r - 1) ln 2 is strictly increasing in r over the interior of [1/2, 1]. This condition ensures that a marginal reduction in the service radius always generates a strictly positive welfare loss through reduced consumer choice, and is satisfied when congestion effects on completion probability are sufficiently mild relative to the direct gain in consumer access from expanding the service radius.

A social planner chooses r to maximize W(r), fully internalizing both the congestion relief benefits of service area reduction and the welfare loss arising from reduced consumer choice.

4.1 The Platform’s Problem

During peak hours, the monopolistic platform chooses the delivery service radius $r \in [1/2, 1]$ to maximize peak-period profit. Let $Q(r)$ denote the measure of completed transactions, as defined in Section 3, and let $m(r) \geq 0$ denote the platform’s per-transaction margin, which may depend on the service area through delivery fees, commissions, or operational costs.

The platform’s optimization problem is

The platform takes consumer choice behavior and the congestion technology as given. Importantly, while the platform internalizes the effect of $r$ on congestion, delivery times, and order completion, it does not internalize the welfare loss associated with reduced consumer choice and contracted restaurant market access.

Assuming an interior solution, the first-order condition is

This condition characterizes the platform’s privately optimal peak-hour service radius, denoted $r^P$.

4.2 Comparative Statics and Interpretation

The first-order condition highlights two opposing forces. First, reducing the service area decreases congestion, lowers delivery times, and prevents order cancellations. This effect increases the volume of completed transactions, implying $Q'(r) \leq 0$ over ranges where congestion relief dominates the loss of availability.

Second, reducing the service area contracts the set of available restaurants for some consumers, but this effect enters the platform’s problem only indirectly through its impact on completed transactions. The platform does not account for the direct utility loss from reduced consumer choice or the contraction of effective market access for restaurants.

As a result, whenever congestion relief is sufficiently strong, the platform has an incentive to reduce the service area even if such reductions substantially diminish consumer choice and restaurant exposure. Formally, because the platform’s objective function depends on $r$ only through $m(r)$ and $Q(r)$ any welfare effect that does not affect completed transactions or margins is ignored. The following proposition summarizes the platform’s incentives.

Proposition 1 (Private Incentives for Service Area Restriction) Suppose there exists a range of $r$ over which congestion relief dominates availability loss, so that $Q'(r) < 0$. Then the platform optimally reduces the peak-hour service radius over that range. Moreover, the platform’s privately optimal service radius $r^P$ is weakly decreasing in the severity of congestion, as captured by the slope of the congestion function $H'(r)$.

Proof. From the platform’s first-order condition, a marginal reduction in $r$ is profitable if and only if

To isolate the congestion channel, we consider local deviations holding per-transaction margins fixed, so that $m'(r) = 0$. Under this restriction, the profitability condition reduces to

Reducing the service radius alleviates congestion and improves delivery performance. When congestion sensitivity is higher, that is, when $H'(r)$ is larger, a given reduction in $r$ yields a greater improvement in delivery times and a larger reduction in cancellations.

Under mild regularity conditions on demand and cancellation behavior, higher congestion sensitivity magnifies the transaction-volume response to service area reductions. Consequently, the marginal effect of reducing $r$ on completed transactions becomes more negative, implying that $Q'(r)$ is more negative. Higher congestion severity therefore strengthens the platform’s incentive to restrict the service area, resulting in a weakly smaller privately optimal service radius $r^P$.

Proposition 1 formalizes the platform’s operational logic. When congestion is severe, restricting service areas improves delivery performance and raises completed transactions, increasing profit. This incentive exists regardless of the magnitude of consumer choice loss or restaurant market contraction, as long as these effects do not reduce transaction volume sufficiently.

This observation is critical for the regulatory analysis that follows. The platform’s first-order condition contains no term reflecting the direct welfare cost of reduced choice. In contrast, the social planner’s problem explicitly incorporates this cost. The wedge between the platform’s private optimum and the social optimum arises precisely from this missing term, which we analyze in the next section.

5.1 Social Planner’s Problem

We consider a social planner who chooses the peak-hour delivery service area r &in; [1/2, 1] to maximize social welfare. Social welfare incorporates three components. First, it includes surplus from completed transactions net of delivery time disutility. Second, it captures the extensive-margin effect arising from order cancellations when delivery times exceed a threshold. Third, and critically, it incorporates the intrinsic welfare value of consumer choice and restaurant access.

Let d*(x, r) denote the delivery distance chosen by a consumer located at x, conditional on restaurant availability. An order is completed if delivery time satisfies

Using the social welfare function W(r) defined in Section III, the social planner chooses the peak-hour service radius r to maximize welfare,

The first term in W(r) captures congestion relief and order completion effects, which the platform also internalizes through transaction volume. The second term reflects the welfare value of consumer choice and restaurant access, which is not internalized by the platform.

Taking the derivative of the W(r) with respect to r yields the social first-order condition

The first term captures the marginal welfare effect of congestion relief and reduced cancellations. The remaining terms capture the marginal welfare loss from shrinking consumer choice sets and effective restaurant access. These latter terms do not appear in the platform’s first-order condition, generating a wedge between the private and social optima. This wedge constitutes the central mechanism underlying our main results.

5.2 Divergence Between Private and Social Optima and Regulatory Implications

Comparing the social first-order condition with the platform’s first-order condition in Section 4 reveals a key difference. The platform’s condition, depends only on margins and completed transactions. By contrast, the social planner’s condition includes the additional choice-loss term proportional to ln 2, which the platform does not internalize. This yields the central result.

Theorem 1 (Excessive Service Area Restriction) Suppose there exists a range of r over which congestion relief is sufficiently strong so that Q'(r) < 0. Then the platform’s privately optimal service radius rP is weakly smaller than the socially optimal service radius rS, i.e., rP &le; rS.

Proof. At any r such that Q'(r) < 0, a marginal reduction in r increases completed transactions through congestion relief, giving the platform an incentive to reduce the service radius to increase profits, as shown in Section 4. The social planner faces the same congestion-relief and cancellation benefits but, in addition, internalizes the marginal welfare loss from reduced consumer choice and restaurant access.

Specifically, shrinking the service radius reduces the measure of consumers who retain access to both restaurants and lowers the expected utility derived from choice. Under the standard logit model with symmetric alternatives and unit-scale Gumbel taste shocks, the expected utility gain from having two available options rather than one equals ln 2. As a result, the marginal welfare loss from reduced choice is given by

which is strictly positive under the assumption stated in Section III.

Because this choice-and-access loss does not enter the platform’s objective function, the platform’s first-order condition omits a strictly positive term that appears in the social planner’s first-order condition. Under the maintained regularity condition that the relevant marginal objective functions satisfy a standard single-crossing property in the service radius, this additional marginal choice-and-access term shifts the planner’s optimum weakly upward relative to the platform’s private optimum. Consequently, the planner’s condition is satisfied at a weakly larger service radius than the platform’s, implying rP &le; rS.

Theorem 1 formalizes the intuition that a dominant platform restricts service areas too aggressively during peak hours. The inefficiency arises not from congestion management per se, but from the platform’s failure to internalize the welfare loss associated with reduced consumer choice and restaurant market access.

This wedge provides a foundation for regulatory design. Directly mandating service areas may not be necessary when performance-based rules are appropriately structured. Instead, regulation can target performance outcomes while restricting when service area reductions are permissible.

Proposition 2 (Access-Preserving Performance Regulation) Consider a regulator who imposes the following two-part rule. First, the platform must satisfy a publicly announced delivery performance standard E[T(r)] &le; T^. Second, any reduction in the peak-hour service radius relative to the prior period must be accompanied by a demonstrated performance necessity. The platform must show that maintaining the current radius (rcurrent) would violate the standard, that is E[T(rcurrent)] > T^.

This rule permits service area reductions only when necessary to satisfy performance constraints and prevents further reductions once the standard is met.

Let rP denote the platform’s unregulated optimum and rS the social optimum, with rP &le; rS by Theorem 1. Define r~ as the largest service radius at which the performance standard is satisfied with equality so that E[T(r~)] = T^.

Suppose the regulator sets T^ such that rP < r~ &le; rS. Then under the two-part rule and the maintained verifiability and regularity conditions, the platform’s regulated optimum satisfies r* = r~ > rP, and social welfare increases relative to the unregulated outcome.

Proof. Since E[T(r)] is strictly increasing in r because H'(r) > 0, the performance standard E[T(r)] &le; T^ is satisfied for all r &le; r~. Without the justification requirement, the platform could freely reduce r below r~, as doing so strictly improves the performance metric. The two-part rule eliminates this possibility. A reduction in the service radius is permitted only when the current radius violates the performance standard, that is when E[T(rcurrent)] > T^. By construction, this condition never holds for any r &le; r~. Therefore, once the service radius reaches r~, further reductions are not admissible under the rule, and r~ acts as a lower bound that the platform cannot cross through permissible adjustments.

The platform chooses r to maximize &Pi;(r) subject to the admissibility implied by the rule. The unconstrained optimum rP lies strictly below r~ by assumption. Since rP satisfies the interior first order condition, &Pi;'(rP) = 0 and is a local optimum, &Pi;'(r) < 0 for all r in a right neighborhood of rP. We assume that &Pi;(r) has no local maximum in the interval (rP, 1], so that the platform's globally optimal feasible choice is the smallest admissible r.

By the assumption stated in Section III, the choice-value term (2r - 1) ln 2 s(r) is strictly increasing in r over [1/2, 1], and this term is not internalized by the platform. It follows that W(r) is strictly increasing in r over the interval [rP, rS]. Since r* = r~ > rP and r~ &le; rS, it follows that W(r*) > W(rP).

Theorem 1 and Proposition 2 imply that the primary regulatory concern is not delivery speed itself, but how performance considerations are used to justify reductions in choice and access induced by peak-hour restrictions. By focusing on performance outcomes rather than operational inputs, regulators can correct the inefficiency while maintaining platform adaptability.