arXiv subjects

Adam Wierman

Publications and source records attributed to Adam Wierman.

152 records · Page 9Linked to original sources

arXiv2014

The Role of a Market Maker in Networked Cournot Competition

We study the role of a market maker (or market operator) in a transmission constrained electricity market. We model the market as a one-shot networked Cournot competition where generators supply quantity bids and load serving entities provide downward sloping inverse demand functions. This mimics the operation of a spot market in a deregulated market structure. In this paper, we focus on possible mechanisms employed by the market maker to balance demand and supply. In particular, we consider three candidate objective functions that the market maker optimizes - social welfare, residual social welfare, and consumer surplus. We characterize the existence of Generalized Nash Equilibrium (GNE) in this setting and demonstrate that market outcomes at equilibrium can be very different under the candidate objective functions.

cs.GT↗

arXiv2014

Potential Games are Necessary to Ensure Pure Nash Equilibria in Cost Sharing Games

We consider the problem of designing distribution rules to share "welfare" (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games, which includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions W, we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some "ground" welfare functions W', which can be distinct from W. However, if budget-balance is required in addition to the existence of a Nash equilibrium, then W' must be the same as W. We also provide an alternate characterization of this space in terms of "generalized" marginal contributions, which is more appealing from the point of view of computational tractability. A possibly surprising consequence of our result is that, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is necessary to work within the class of potential games.

cs.GT↗

arXiv2014

The Empirical Implications of Privacy-Aware Choice

This paper initiates the study of the testable implications of choice data in settings where agents have privacy preferences. We adapt the standard conceptualization of consumer choice theory to a situation where the consumer is aware of, and has preferences over, the information revealed by her choices. The main message of the paper is that little can be inferred about consumers' preferences once we introduce the possibility that the consumer has concerns about privacy. This holds even when consumers' privacy preferences are assumed to be monotonic and separable. This motivates the consideration of stronger assumptions and, to that end, we introduce an additive model for privacy preferences that does have testable implications.

cs.GT↗

arXiv2013

The Cost of an Epidemic over a Complex Network: A Random Matrix Approach

In this paper we quantify the total economic impact of an epidemic over a complex network using tools from random matrix theory. Incorporating the direct and indirect costs of infection, we calculate the disease cost in the large graph limit for an SIS (Susceptible - Infected - Susceptible) infection process. We also give an upper bound on this cost for arbitrary finite graphs and illustrate both calculated costs using extensive simulations on random and real-world networks. We extend these calculations by considering the total social cost of an epidemic, accounting for both the immunization and disease costs for various immunization strategies and determining the optimal immunization. Our work focuses on the transient behavior of the epidemic, in contrast to previous research, which typically focuses on determining the steady-state system equilibrium.

cs.SI↗

arXiv2013

Approximate dynamic programming using fluid and diffusion approximations with applications to power management

Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only within a prescribed finite-dimensional function class. Thus, the question that always arises is how should the function class be chosen? The goal of this paper is to propose an approach using the solutions to associated fluid and diffusion approximations. In order to illustrate this approach, the paper focuses on an application to dynamic speed scaling for power management in computer processors.

cs.LG↗

arXiv2013

The Empirical Implications of Rank in Bimatrix Games

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant payoff functions. We prove that high complexity (high rank) has empirical consequences when arbitrary data is considered. Additionally, we prove that, in more restrictive classes of data (termed laminar), any observation is rationalizable using a low-rank game: specifically a zero-sum game. Hence complexity as a structural property of a game is not always testable. Finally, we prove a general result connecting the structure of the feasible data sets with the highest rank that may be needed to rationalize a set of observations.

cs.GT↗

arXiv2012

Incentives for P2P-Assisted Content Distribution: If You Can't Beat 'Em, Join 'Em

The rapid growth of content distribution on the Internet has brought with it proportional increases in the costs of distributing content. Adding to distribution costs is the fact that digital content is easily duplicable, and hence can be shared in an illicit peer-to-peer (P2P) manner that generates no revenue for the content provider. In this paper, we study whether the content provider can recover lost revenue through a more innovative approach to distribution. In particular, we evaluate the benefits of a hybrid revenue-sharing system that combines a legitimate P2P swarm and a centralized client-server approach. We show how the revenue recovered by the content provider using a server-supported legitimate P2P swarm can exceed that of the monopolistic scheme by an order of magnitude. Our analytical results are obtained in a fluid model, and supported by stochastic simulations.

cs.SI↗

arXiv2011

Peer Effects and Stability in Matching Markets

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. The key feature of our model is that it captures peer effects and complementarities using utility functions, rather than traditional preference ordering. With this model and considering a weaker notion of stability, namely two-sided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a two-sided exchange stable matching. To assess the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we provide general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

cs.SI↗