Ramesh Johari
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Assistant Professor Management Science and Engineering Computer Science (by courtesy) Electrical Engineering (by courtesy) School of Engineering, Stanford University |
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Assistant Professor Management Science and Engineering Computer Science (by courtesy) Electrical Engineering (by courtesy) School of Engineering, Stanford University |
Abstract: Motivated by market design for electric power systems, we consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for the product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit maximizers. We consider a uniform price market design that uses supply function bidding (Klemperer and Meyer, 1989): firms declare the amount they would supply at any positive price, and a single price is chosen to clear the market. We are interested in evaluating the impact of price anticipating behavior both on the allocative efficiency of the market, and on the prices seen at equilibrium. We show that by restricting the strategy space of the firms to parameterized supply functions, we can provide upper bounds on both the inflation of aggregate cost at the Nash equilibrium relative to the socially optimal level, as well as the markup of the Nash equilibrium price above the competitive level: as long as N > 2 firms are competing, these quantities are both upper bounded by 1 + 1/(N-2). This result holds even in the presence of asymmetric cost structure across firms. We also discuss several extensions, generalizations, and related issues.
Abstract: We study competition between wireless devices with incomplete information about their opponents. We model such interactions as Bayesian interference games. Each wireless device selects a power profile over the entire available bandwidth to maximize its data rate (measured via Shannon capacity), which requires mitigating the effect of interference caused by other devices. Such competitive models represent situations in which several wireless devices share spectrum without any central authority or coordinated protocol. In contrast to games where devices have complete information about their opponents, we consider scenarios where the devices are unaware of the interference they cause to other devices. Such games, which are modeled as Bayesian games, can exhibit significantly different equilibria. We first consider a simple scenario where the devices select their power profile simultaneously. In such simultaneous move games, we show that the unique Bayes-Nash equilibrium is where both devices spread their power equally across the entire bandwidth. We then extend this model to a two-tiered spectrum sharing case where users act sequentially. Here one of the devices, called the primary user, is the owner of the spectrum and it selects its power profile first. The second device (called the secondary user) then responds by choosing a power profile to maximize its Shannon capacity. In such sequential move games, we show that there exist equilibria in which the primary user gets a higher data rate by using only a part of the bandwidth. In a repeated Bayesian interference game, we show the existence of reputation effects: an informed primary user can ``bluff'' to prevent spectrum usage by a secondary user who suffers from lack of information about the channel gains. The resulting equilibrium newrj can be highly inefficient, suggesting that competitive spectrum sharing is highly suboptimal. This observation points to the need for some regulatory protocol to attain a more efficient spectrum sharing solution.
Abstract: We consider a network formation game where nodes wish to send traffic to each other. Nodes contract bilaterally with each other to form bidirectional communication links; once the network is formed, traffic is routed along shortest paths (if possible). Cost is incurred to a node from four sources: (1) routing traffic; (2) maintaining links to other nodes; (3) disconnection from destinations the node wishes to reach; and (4) payments made to other nodes. We assume that a network is stable if no single node wishes to unilaterally deviate, and no pair of nodes can profitably deviate together (a variation on the notion of pairwise stability). We study such a game under a form of myopic best response dynamics. In choosing their action, nodes optimize their single period payoff only. We characterize a simple set of assumptions under which these dynamics converge to a stable network; we also characterize an important special case, where the dynamics converge to a star centered at a node with minimum cost for routing traffic. In this sense, our dynamics naturally select an efficient equilibrium. Further, we show that these assumptions are satisfied by a contractual model motivated by the bilateral Rubinstein bargaining model.
Abstract: We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we construct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.
Abstract: We analyze investment incentives and market structure under oligopoly competition in service industries with congestion effects. Firms compete by choosing prices and investments; increasing investment reduces the congestion disutility experienced by consumers. We investigate this model through the Nash equilibria of the pricing and investment game played by firms. We find that returns to investment and the timing of strategic decisions are critical determinants of the outcome of the game. For a broad range of models for which (1) firms choose prices and investments simultaneously, and (2) the model exhibits nonincreasing returns to investment, we show that if a pure strategy Nash equilibrium exists, it is unique and efficient; we also establish conditions for existence of pure strategy Nash equilibrium. This result does not hold if either (1) or (2) are violated; we show that highly inefficient outcomes can be obtained in these scenarios. In addition, we investigate several extensions, including modeling the entry of firms into the market. Our model and results provide a framework through which a range of service industries and network technologies can be studied, offering guidance for policy analysis.
Abstract: Most large-scale communication networks, such as the Internet, consist of interconnected administrative domains. While source (or selfish) routing, where transmission follows the least cost path for each source, is reasonable across domains, service providers typically engage in traffic engineering to improve operating performance within their own network. Motivated by this observation, we develop and analyze a model of partially optimal routing, where optimal routing within subnetworks is overlaid with selfish routing across domains. We demonstrate that optimal routing within a subnetwork does not necessarily improve the performance of the overall network. In particular, when Braess' paradox occurs in the network, partially optimal routing may lead to worse overall network performance. We provide bounds on the worst-case loss of efficiency that can occur due to partially optimal routing. For example, when all congestion costs can be represented by affine latency functions and all administrative domains have a single entry and exit point, the worst-case loss of efficiency is no worse than 25% relative to the optimal solution. In the presence of administrative domains incorporating multiple entry and/or exit points, however, the performance of partially optimal routing can be arbitrarily inefficient even with linear latencies. We also provide conditions for traffic engineering to be individually optimal for service providers.
Abstract: Thousands of competing autonomous systems must cooperate with each other to provide global Internet connectivity. Each autonomous system (AS) encodes various economic, business, and performance decisions in its routing policy. The current interdomain routing system enables each AS to express policy using rankings that determine how each router in the AS chooses among different routes to a destination, and filters that determine which routes are hidden from each neighboring AS. Because the Internet is composed of many independent, competing networks, the interdomain routing system should provide autonomy, allowing network operators to set their rankings independently, and to have no constraints on allowed filters. This paper studies routing protocol stability under these conditions. We first demonstrate that ``next-hop rankings,'' commonly used in practice, may not ensure routing stability. We then prove that, when providers can set rankings and filters autonomously, guaranteeing that the routing system will converge to a stable path assignment imposes strong restrictions on the rankings ASes are allowed to choose. We discuss the implications of these results for the future of interdomain routing.
Abstract: The design of pricing mechanisms for network resource allocation has two important objectives: 1) a simple and scalable end-to-end implementation and 2) efficiency of the resulting equilibria. Both objectives are met by certain recently proposed mechanisms when users are price taking, but not when users can anticipate the effects of their actions on the resulting prices. In this paper, we partially close this gap, by demonstrating an alternative resource allocation mechanism which is scalable and guarantees a fully efficient allocation when users are price taking. In addition, when links have affine marginal cost, this mechanism has efficiency loss bounded by 1/3 when users are price anticipating. These results are derived by studying Cournot games, and in the process we derive the first nontrivial constant factor bounds on efficiency loss in these well-studied economic models.
Abstract: We consider a network game where the nodes of the network wish to form a graph to route traffic between themselves. We present a model where costs are incurred for routing traffic, as well as for a lack of network connectivity. We focus on directed links and the link stability equilibrium concept, and characterize connected link stable equilibria. The structure of connected link stable networks is analyzed for several special cases.
Abstract: We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on prices, a simple proportional pricing mechanism can maximize the sum of users' utilities minus the cost (called aggregate surplus). Continuing previous efforts to quantify the effects of selfish behavior in network pricing mechanisms, we consider the possibility that users anticipate the effect of their actions on link prices. Under the assumption that the links' marginal cost functions are convex, we establish existence of a Nash equilibrium. We show that the aggregate surplus at a Nash equilibrium is no worse than a factor of 4*sqrt(2) - 5 times the optimal aggregate surplus; thus, the efficiency loss when users are selfish is no more than approximately 34%.
Abstract: We explore the properties of a congestion game where users of a congested resource anticipate the effect of their actions on the price of the resource. When users are sharing a single resource, we establish that the aggregate utility received by the users is at least 3/4 of the maximum possible aggregate utility. We also consider extensions to a network context, where users submit individual payments for each link in the network which they may wish to use. In this network model, we again show that the selfish behavior of the users leads to an aggregate utility which is no worse than 3/4 the maximum possible aggregate utility. We also show that the same analysis extends to a wide class of resource allocation systems where end users simultaneously require multiple scarce resources. These results form part of a growing literature on the ``price of anarchy,'' i.e., the extent to which selfish behavior affects system efficiency.
Abstract: Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of end-to-end Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end system needs knowledge only of its own round-trip delay. Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where all users share the same round-trip delay. Numerical experiments investigate extensions to more general networks. Through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. Finally, we suggest how these results may be used to design network resources.