Competition in Ride-Hailing Markets

Competition in Ride-Hailing Markets AmirMahdi Ahmadinejad, Hamid Nazerzadeh, Amin Saberi, Nolan Skochdopole3(B), and Kane Sweeney 1 Department of Management Science and Engineering, Stanford University, Stanford, USA {ahmadi, saberi}@stanford.edu 2 Marshall School of Business, University of Southern Califorina, Los Angeles, USA hamidnz@uber.com 3 Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA naskoch@stanford.edu 4 Uber Technologies Inc., San Francisco, USA

One of the salient and understudied features of ride-hailing markets is that riders and drivers can move between platforms with relatively low friction or have a presence on several applications at the same time. This feature of the market has created an intense competition among platforms. The goal of this paper is to understand the dynamics and outcome of this competition. We aim to answer the following questions: What is the impact of platform competition on prices as well as the overall throughput of the market? Could competition lead to a "tragedy of the commons" and market failure as the platforms compete over the shared resource of open cars?
To address these questions, building on the market dynamics framework developed in [1] for a single platform, we propose and study a game-theoretic model in which two ride-hailing platforms compete for market share via pricing. Riders and drivers seek to maximize their own utilities and can choose to be present on only a single platform or participate in both platforms simultaneously. We see that at any equilibrium, all users will patronize both platforms which must offer equal prices; an equilibrium that results in a potential market failure always exists, but we show surprisingly that under many realistic settings, other more promising equilibria also exist.
This result is additionally supported by numerical analysis, using parameters estimated from Uber data to define the demand model, and simulations. We observe that if riders are not very sensitive to waiting times, the loss of efficiency due to competition could be small, corresponding to the second equilibrium outcome of the above theorem. The shape and number of these oscillations is the object of this paper, where we provide theoretical results for the behavior of the PoA. We first present some results for general nonlinear costs, and then we focus on affine cost functions. We establish some smoothness properties of Wardrop equilibria and social optima. Under mild assumptions, we show that the price of anarchy is a smooth function of the traffic inflow, except at values of the demand where the set of paths used in equilibrium changes. We call these values break points. We then turn our attention to a class of cost functions that are heavily used in applications, namely, the ones proposed by the Bureau of Public Roads, and we show that for these costs we have a scaling law between the equilibrium and optimum flows which induces a similar scaling for the break points. Moreover, for affine cost functions we show that the number of break points is finite for any given network, and we present an example showing that this number can be exponential in the number of paths.
The relevance of break points is due to the fact that between break points the PoA is either monotone or it has a unique minimum, therefore, the PoA can have a local maximum only at a break point. The main fact that supports these results is that, with affine costs, if an equilibrium uses a certain set of paths at two different demand levels, then it uses the same set of paths at all intermediate demands. Finally, we show that this does not hold for less regular cost functions.
The details of the proofs and the relevant references can be found in [1].
Abstract. Increased availability of high-quality customer information has fueled interest in personalized pricing strategies, i.e., strategies that predict an individual customer's valuation for a product and then offer a customized price tailored to that customer. While the appeal of personalized pricing is clear, it may also incur large costs in the form of market research, investment in information technology and analytics expertise, and branding risks. In light of these trade-offs, our work studies the value of personalized pricing strategies over a simple single price strategies. We first provide tight, closed-form upper and lower bounds on the ratio between the profits of an idealized personalized pricing strategy and a single price strategy. Our upper bounds depend on simple statistics of the valuation distribution and shed light on the types of markets for which personalized pricing has the most potential. Our lower bounds depend on simple statistics as well as a unimodal assumption and shed light on which markets are ill served by a fixed price. Second, we demonstrate how to obtain bounds that depend on arbitrary moments of the valuation distribution via infinite dimensional linear programming duality. Finally, we show how to transform our upper and lower bounds on idealized personalized pricing strategies to stronger bounds on feature based personalized pricing strategies that better model current industry practices. Abstract. Voting systems based on decoy ballots aim at preventing real ballots from being bought. Decoy ballots do not count in election outcomes, but are indistinguishable from real ballots. We introduce a "Devil's Menu" consisting of several price offers and allocation rules, which can be used by a malevolent third party-called the adversary-to curb the protection offered by decoy ballots. In equilibrium, the adversary can buy the real ballots of any strict subset of voting districts at a price corresponding to the willingness to sell them. By contrast, the voters holding decoy ballots are trapped into selling them at a low or negligible price. Decoy ballots may thus be ineffective against vote-buying even if the adversary's budget is limited.

Keywords
Keywords: Voting · Decoy ballots · Adversary · Mechanism design · Attacks · Adverse selection JEL Classifications: C72 · D4 · D82 · D86 We would like to thank David Basin, Afsoon Ebrahimi, Georgy Egorov, Lara Schmid, Larry Samuelson, Salvador Barberà and seminar participants at ETH Zurich for valuable comments. All errors are ours. The authors declare that they have no relevant or material financial interests that relate to the research described in this paper. A full draft of the paper is available at https://papers.ssrn.com/sol3/papers.cfm? abstract id=3088508.

Markets Beyond Nash Welfare for Leontief Utilities
Ashish Goel, Reyna Hulett, and Benjamin Plaut (B) Stanford University, Stanford, USA {ashishg, rmhulett, bplaut}@stanford.edu Abstract. We study the allocation of divisible goods to competing agents via a market mechanism, focusing on agents with Leontief utilities. The majority of the economics and mechanism design literature has focused on linear prices, meaning that the cost of a good is proportional to the quantity purchased. Equilibria for linear prices are known to be exactly the maximum Nash welfare allocations.
Price curves allow the cost of a good to be any (increasing) function of the quantity purchased. We show that price curve equilibria are not limited to maximum Nash welfare allocations with two main results. First, we show that an allocation can be supported by strictly increasing price curves if and only if it is group-domination-free. A similar characterization holds for weakly increasing price curves. We use this to show that given any allocation, we can compute strictly (or weakly) increasing price curves that support it (or show that none exist) in polynomial time. These results involve a connection to the agent-order matrix of an allocation, which may have other applications. Second, we use duality to show that in the bandwidth allocation setting, any allocation maximizing a CES welfare function can be supported by price curves.
The full version of the paper can be found at https://arxiv.org/pdf/ 1807.05293.pdf. We study oligopolistic competition in service markets where firms offer a service to customers. The service quality of a firm -from the perspective of a customerdepends on the level of congestion and the charged price. A firm can set a price for the service offered and additionally decides on the service capacity in order to mitigate congestion. The total profit of a firm is derived from the gained revenue minus the capacity investment cost. Firms simultaneously set capacities and prices in order to maximize their profit and customers subsequently choose the services with lowest combined cost (congestion and price). For this basic model, Johari, Weintraub and Van Roy [1] derived the first existence and uniqueness results of pure Nash equilibria (PNE) assuming mild conditions on congestion functions. Their existence proof relies on Kakutani's fixed-point theorem and a key assumption for the theorem to work is that demand for service is elastic, that is, there is a smooth inverse demand function determining the volume of customers given the effective customers' costs.

Capacity and Price Competition in Markets with Congestion Effects
In this paper, we consider the case of perfectly inelastic demand. This scenario applies to realistic cases where customers are not willing to drop out of the market, e.g., if prices are regulated by reasonable price caps. We investigate existence, uniqueness and quality of PNE for models with inelastic demand and price caps. We show that for linear congestion cost functions, there exists a PNE. This result requires a completely new proof approach compared to previous approaches, since the best response correspondences of firms may be empty, thus standard fixed-point arguments are not directly applicable. We show that the game is C-secure (see Reny [3], and McLennan, Monteiro and Tourky [2]), which leads to the existence of PNE. We furthermore show that the PNE is unique, and that the efficiency compared to a social optimum is unbounded in general.
A full version of this paper is available at https://arxiv.org/abs/1905.05683.

Equality of Power and Fair Public Decision-Making
Nicole Immorlica 1 , Benjamin Plaut 2(B) , and E. Abstract. Ronald Dworkin's equality of resources and the closely related concept of envy-freeness, are two of the fundamental ideas behind fair allocation of private goods. The appropriate analog to these concepts in a public decision-making environment is unclear, since all agents consume the same "bundle" of resources (though they may have different utilities for this bundle). Drawing inspiration from equality of resources and the Dworkin quote below, we propose that equality in public decision-making should allow each agent to cause equal cost to the rest of society, which we model as equal externality. We term this equality of power. The first challenge here is that the cost to the rest of society must be measured somehow, and it is generally impossible to elicit the scale of individual utilities (in the absence of monetary payments). Again drawing inspiration from foundational literature for private goods economies, we normalize each agent's utility so that every agent's marginal utility for additional power is the same. We show that for quadratic utilities, in the large market limit, there always exists an outcome that simultaneously satisfies equal power, equal marginal utility for additional power, and social welfare maximization with respect to the normalized utilities. The full version of the paper can be found at: https://papers.ssrn. com/sol3/papers.cfm?abstract id=3420450.

"Equality of resources supposes that the resources devoted to each person's life should be equal. That goal needs a metric. The auction proposes what the envy test in fact assumes, that the true measure of the social resources devoted to the life of one person is fixed by asking how important, in fact, that resource is for others. It insists that the cost, measured in that way, figure in each person's sense of what is rightly his and in each person's judgment of what life he should lead, given that command of justice."
We think these two insights, considering the utility as a representation and not as the preference itself (which is common in the economic community) and considering utilities which represent the preference only for the relevant domain, would turn out to fruitful in other domains as well.
Keywords: Mechanism design · Strategy-proofness · Dominant strategy incentive compatibility · Non Quasi-linear Utilities · Positive-representation · Roberts' Theorem Abstract. We consider information design in spatial resource competition, motivated by ridesharing platforms sharing information with drivers about rider demand. Each of N co-located agents (drivers) decides whether to move to another location with an uncertain and possibly higher resource level (rider demand), where the utility for moving increases in the resource level and decreases in the number of other agents that move. A principal who can observe the resource level wishes to share this information in a way that ensures a welfare-maximizing number of agents move. Analyzing the principal's information design problem using the Bayesian persuasion framework, we study both private signaling mechanisms, where the principal sends personalized signals to each agent, and public signaling mechanisms, where the principal sends the same information to all agents. We show:

Information Design in Spatial Resource Competition
(1) For private signaling, computing the optimal mechanism using the standard approach leads to a linear program with 2 N variables, rendering the computation challenging. We instead describe a computationally efficient two-step approach to finding the optimal private signaling mechanism. First, we perform a change of variables to solve a linear program with O(N 2 ) variables that provides the marginal probabilities of recommending each agent move. Second, we describe an efficient sampling procedure over sets of agents consistent with these optimal marginal probabilities; the optimal private mechanism then asks the sampled set of agents to move and the rest to stay. (2) For public signaling, we first show the welfare-maximizing equilibrium given any common belief has a threshold structure. Using this, we show that the optimal public mechanism with respect to the sender-preferred equilibrium can be computed in polynomial time. (3) We support our analytical results with numerical computations that show the optimal private and public signaling mechanisms achieve substantially higher social welfare when compared with noinformation and full-information benchmarks.

Keywords: Bayesian persuasion · Spatial resource competition
The full paper is available at http://arxiv.org/abs/1909.12723. K. Iyer gratefully acknowledges support from the NSF under grants CMMI-1462592 and CMMI-1633920. P. Frazier gratefully acknowledges support from NSF and AFOSR.