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.
Bertrand competition, proposed by Joseph Bertrand in 1883, and Cournot competition, introduced in 1838 by Antoine Augustin Cournot, are fundamental economic models that represent sellers competing in a single market, and have been studied comprehensively in economics. Due to the motivation that many sellers compete in more than one market in modern dynamic and diverse economy, a recent and growing literature has studied Cournot competitions in network environments @cite_30 @cite_2 @cite_20 @cite_21 . The work @cite_30 @cite_2 focused on characterizing and computing Nash equilibria, and investigated the impact of changes in the (bipartite) network structure on seller's profit and buyer's surplus. @cite_20 and @cite_21 analyzed the efficiency loss of networked Cournot competition game via the metric of price of anarchy. While all these previous works focused on the objective of social welfare maximization in networked Cournot competition, we consider the objective of both social welfare and revenue maximization in the networked Bertrand competition, and also in the networked Cournot competition. We further provide efficient segmenting mechanisms to optimize the social welfare revenue under the Nash equilibrium.
@cite_30 @cite_21 @cite_20 @cite_2
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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. We present a two-stage model of competing ad auctions. Search engines attract users via Cournot-style competition. Meanwhile, each advertiser must pay a participation cost to use each ad platform, and advertiser entry strategies are derived using symmetric Bayes-Nash equilibrium that lead to the VCG outcome of the ad auctions. Consistent with our model of participation costs, we find empirical evidence that multi-homing advertisers are larger than single-homing advertisers. We then link our model to search engine market conditions: We derive comparative statics on consumer choice parameters, presenting relationships between market share, quality, and user welfare. We also analyze the prospect of joining auctions to mitigate participation costs, and we characterize when such joins do and do not increase welfare. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service of the agents. These environments include position auctions where slots with decreasing click-through rates are auctioned to advertisers. We generalize and characterize the envy-free benchmark from Hartline and Yan (2011) to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue. We give prior-free mechanisms that approximate these benchmarks. A building block in our mechanism is a clinching auction for position auction environments. This auction is a generalization of the multi-unit clinching auction of (2008) and a special case of the polyhedral clinching auction of (2012). For welfare maximization, we show that this clinching auction is a good approximation to the envy-free optimal welfare for position auction environments. For profit maximization, we generalize the random sampling profit extraction auction from (2002) for digital goods to give a 10.0-approximation to the envy-free optimal revenue in symmetric, downward-closed environments. The profit maximization question is of interest even without budgets and our mechanism is a 7.5-approximation which improving on the 30.4 bound of Ha and Hartline (2012).