Online platforms, such as Airbnb, this http URL, Amazon, Uber and Lyft, can control and optimize many aspects of product search to improve the efficiency of marketplaces. Here we focus on a common model, called the discriminatory control model, where the platform chooses to display a subset of sellers who sell products at prices determined by the market and a buyer is interested in buying a single product from one of the sellers. Under the commonly-used model for single product selection by a buyer, called the multinomial logit model, and the Bertrand game model for competition among sellers, we show the following result: to maximize social welfare, the optimal strategy for the platform is to display all products; however, to maximize revenue, the optimal strategy is to only display a subset of the products whose qualities are above a certain threshold. We extend our results to Cournot competition model, and show that the optimal search segmentation mechanisms for both social welfare maximization and revenue maximization also have simple threshold structures. The threshold in each case depends on the quality of all products, the platform's objective and seller's competition model, and can be computed in linear time in the number of products.
Cournot competition, introduced in 1838 by Antoine Augustin Cournot, is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility—naturally a function of the production cost as well as market price of the product—by deciding on the amount of production. This problem has been studied comprehensively in Economics and Game Theory; however, in today’s dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game Network Cournot Competition (NCC). Computation of equilibrium, taking into account a network of markets and firms and the different forms of cost and price functions, makes challenging and interesting new problems. This paper studies how the efficiency of an online platform is impacted by the degree to which access of platform participants is open or controlled. The study is motivated by an emerging trend within platforms to impose increasingly finegrained control over the options available to platform participants. While early online platforms allowed open access, e.g., Ebay allows any seller to interact with any buyer; modern platforms often impose matches directly, e.g., Uber directly matches drivers to riders. This control is performed with the goal of achieving more efficient market outcomes. However, the results in this paper highlight that imposing matches may create new strategic incentives that lead to increased inefficiency. In particular, in the context of networked Cournot competition, we prove that open access platforms guarantee social welfare within 7 16 of the optimal; whereas controlled allocation platforms can have social welfare unboundedly worse than optimal. This paper studies network design and efficiency loss in online platforms using the model of networked Cournot competition. We consider two styles of platforms: open access platforms and discriminatory access platforms. In open access platforms, every firm can connect to every market, while discriminatory access platforms limit connections between firms and markets in order to improve social welfare. Our results provide tight bounds on the efficiency loss of both open access and discriminatory access platforms. For open access platforms, we show that the efficiency loss at a Nash equilibrium is upper bounded by 3 2. In the case of discriminatory access platforms, we prove that, under an assumption on the linearity of cost functions, a greedy algorithm for optimizing network connections can guarantee the efficiency loss at a Nash equilibrium is upper bounded by 4 3. The paper considers a model of competition among firms that produce a homogeneous good in a networked environment. A bipartite graph determines which subset of markets a firm can supply to. Firms c...