Why prices need algorithms (invited talk)

1 Mathematical Background.- Integration of Banach-Valued Correspondences.- Set-Valued Functions of Two Variables in Economic Theory.- 2 Equilibria, Core, and Pareto Optimality.- A Theorem on the Existence of Competitive Equilibria in a Market with a Finite Number of Agents and Whose Commodity Space is L?.- The Core of an Economy Without Ordered Preferences.- Fundamental Theorems of Welfare Economics in Infinite Dimensional Commodity Spaces.- 3 Core Equivalence.- A Limit Theorem on the Core of an Economy with a Continuum of Commodities.- An Equivalence Theorem for the Core of an Economy with Commodity Space L? ? ?(L?, L1).- The Principle of Equivalence.- 4 The Existence of an Equilibrium in Economies with a Continuum of Agents.- A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many Commodities.- Equilibria in Markets with a Continuum of Agents and Commodities.- What is Perfect Competition?.- 5 Correlated Equilibria.- On the Existence of Correlated Equilibria.- Existence of Correlated Weak Equilibria in Discontinuous Games.- Communication Equilibria with Large State Spaces.- 6 Games with a Continuum of Players.- An Axiomatic Approach to the Efficiency of Non-Cooperative Equilibrium in Economies with a Continuum of Traders.- On Symmetric Cournot-Nash Equilibrium Distributions in a Finite-Action, Atomless Game.- Equilibria in Random and Bayesian Games with a Continuum of Players.- 7 Sequential Equilibria.- Recursive Utility Under Uncertainty.- Consistency and Continuity of Choice in a Sequence of Spot and Futures Markets.- 8 References.

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

Existence of non-cooperative equilibria in social systems

A remark on the existence of equilibria in markets without ordered preferences and with a Riesz space of commodities

Offloading decisions in mobile edge computing have been extended with multiple objectives, such as revenue maximization, energy conservation and latency reduction. Revenues of network/service operators, as the realistic and ultimate goal at intensive competitive markets, have not been thoroughly studied under a pricing scheme in combination with offloading decisions, especially with the aims of reducing and restricting energy consumption and latency. To bridge this important gap, this paper studies the revenue maximization of network operators through a pricing scheme in mobile edge computing, by explicitly formulating energy consumption and latency into the offloading strategy. A two-stage game-theory framework based on the Stackelberg game is established, through which the optimal price for both the network operator and the customer can be reached. The offloading data size can be dynamically adjusted according to the agreed price. The existence of equilibrium in the Stackelberg game is proved, and experiments are conducted to verify the effectiveness of our proposed model.

Joint power control and spectrum allocation for cognitive radio networks via pricing

We are grateful to Jorg Laitenberger who allow us to take this chapter from his Ph.D. Thesis, Laitenberger [1999].

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. A common feature of many of these two-sided marketplaces is that the platform has full control over search and discovery, but prices are determined by the buyers and sellers. We summarize our results from [Banerjee et al. 2017] where, motivated by this application domain, we study the algorithmic aspects of market segmentation via directed discovery in two-sided markets with endogenous prices. We consider a model where an online platform knows each buyer/seller's characteristics, and associated demand/supply elasticities. Moreover, the platform can use discovery mechanisms (search, recommendation, etc.) to control which buyers/sellers are visible to each other. We develop efficient algorithms for throughput (i.e. volume of trade) and welfare maximization with provable guarantees under a variety of assumptions on the demand and supply functions.

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. A common feature of many of these two-sided marketplaces is that the platform has full control over search and discovery, but prices are determined by the buyers and sellers. Motivated by this, we study the algorithmic aspects of market segmentation via directed discovery in two-sided markets with endogenous prices. We consider a model where an online platform knows each buyer/seller's characteristics, and associated demand/supply elasticities. Moreover, the platform can use discovery mechanisms (search, recommendation, etc.) to control which buyers/sellers are visible to each other. We develop efficient algorithms for throughput (i.e. volume of trade) and welfare maximization with provable guarantees under a variety of assumptions on the demand and supply functions. We also test the validity of our assumptions on demand curves inferred from NYC taxicab log-data, as well as show the performance of our algorithms on synthetic experiments.

Rental harmony with roommates

Mathematical inequalities are pervasive in economic theory, just as economic inequalities are pervasive in social life. The insistence that quantities (always) and prices (usually) be nonnegative, the constraint that expenditure not exceed wealth, the necessity in proving existence of competitive equilibrium that each agent's resources have positive value, are so familiar that we scarcely think of them as requirements of inequality, though that is what they are.

Infrastructure-as-a-Service cloud providers offer diverse purchasing options and pricing plans, namely on-demand, reservation, and spot market plans. This allows them to efficiently target a variety of customer groups with distinct preferences and to generate more revenue accordingly. An important consequence of this diversification however, is that it introduces a non-trivial optimization problem related to the allocation of the provider's available data center capacity to each pricing plan. The complexity of the problem follows from the different levels of revenue generated per unit of capacity sold, and the different commitments consumers and providers make when resources are allocated under a given plan. In this work, we address a novel problem of maximizing revenue through an optimization of capacity allocation to each pricing plan by means of admission control for reservation contracts, in a setting where aforementioned plans are jointly offered to customers. We devise both an optimal algorithm based on a stochastic dynamic programming formulation and two heuristics that trade-off optimality and computational complexity. Our evaluation, which relies on an adaptation of a large-scale real-world workload trace of Google, shows that our algorithms can significantly increase revenue compared to an allocation without capacity control given that sufficient resource contention is present in the system. In addition, we show that our heuristics effectively allow for online decision making and quantify the revenue loss caused by the assumptions made to render the optimization problem tractable.

Adam Smith on Justice, Rights, and Law

The British National Health Service has been a great inspiration for other countries during the past 50 years. A central theme has been the role that the state can play...

The COVID-19 pandemic has served as a revealing lens, bringing into sharper focus the societal fissures that were already present but less visible. This crisis has forced a critical examination of the ethical foundations that underpin our societies and economies, urging us to reflect on the principles of equity and justice that should permeate our communal existence. The Pandemic Divide: How COVID Increased Inequality in America offers a comprehensive exploration of the societal and economic impacts of COVID-19 in the United States, particularly highlighting the exacerbation of inequalities. Covering a broad spectrum of issues, including healthcare, employment, education and housing, the book provides a detailed overview of the pandemic's wide-ranging and intricate effects. Organised into four sections and 11 chapters, the book addresses various crucial topics, such as the impact of systemic racism on COVID-19 disparities, the historical context of labour and housing in pandemic responses and the complex interactions of race, religion and community during this crisis. A blend of secondary empirical data underpins this comprehensive exploration of inequalities intensified by the pandemic. The authors adeptly consolidate diverse data from established sources such as health statistics, economic reports and academic studies. However, readers seeking detailed discussions on specific facets of inequality might find the book's broad scope challenging due to its extensive coverage of various topics. The initial chapters establish a broad context, examining systemic racism's impact on healthcare disparities and economic challenges during the pandemic. As the book progresses, it shifts to more specific topics. Chapter 4, COVID-19, Race, and Mass Incarceration, for instance, offers an in-depth look at how the pandemic has exacerbated issues within the criminal justice system, specifically focusing on the experiences of incarcerated populations. This chapter's detailed examination of a singular aspect of inequality—combining historical analysis with contemporary trends—presents a shift from the more general discussions in earlier chapters. While such depth enriches the narrative, it may challenge thematic cohesion by moving away from the broader view of systemic inequalities. Furthermore, this transition could pose engagement challenges for readers who may find the abrupt deep dive into specialised topics a significant shift from the more overarching analyses presented earlier. This variation in focus and depth could require readers to adjust their engagement approach, impacting their ability to maintain a cohesive understanding of the book's central theme. The authors effectively balance scholarly depth with accessibility, engaging academic audiences and those interested in the societal impacts of the pandemic. The use of statistical evidence and historical context throughout the book bolsters its arguments and adds to its overall credibility and depth. The book's main strength is its comprehensive scope, covering many topics illuminating the pandemic's multifaceted impacts on society. It offers insightful observations, profoundly exploring the underlying causes and extensive consequences of these inequalities. However, this thorough approach could have been further enriched. For instance, while the book discusses the systemic impacts of COVID-19 on healthcare disparities, incorporating counterarguments about personal responsibility or healthcare policy alternatives could have provided a more nuanced view. Similarly, a discussion contrasting different economic theories or approaches to pandemic relief could have offered a broader perspective in analysing economic inequalities. The Pandemic Divide also contributes to our understanding of pre-existing inequalities, presenting a fresh and timely perspective that addresses a critical gap in the literature on pandemics. It is especially relevant to public health, sociology, medical humanities, racial studies, policymakers and health professionals. Despite its academic leaning, the book remains highly relevant to broader health equity and social justice discussions, serving as a crucial resource for activists and community leaders. Its structured format also assists in navigating complex topics despite its scholarly tone. Contrary to the book COVID-19 in Europe and North America: Policy Responses and Multi-Level Governance, which examines policy responses across two continents, The Pandemic Divide zeroes in on the socio-economic inequalities in the U.S. intensified by the pandemic. This juxtaposition enriches our understanding of the pandemic's diverse impacts, from Europe and North America's political and governance challenges to the U.S.'s specific socio-economic disparities. The book prompts reflection on the philosophical concept of the 'common good' and the balancing act between individual freedoms and collective welfare, providing a critical viewpoint on our shared human experiences and ethical responsibilities towards each other (Molinari and Beylier, 2022). The Pandemic Divide presents a thorough analysis of the inequalities deepened by the COVID-19 pandemic, though it could have further explored intersectionality, examining how gender, age and disability intersect with racial and socio-economic disparities. While its broad scope brings intellectual richness, it sometimes detracts from the thematic unity and accessibility of the discussion. Nevertheless, the insights it offers into the complex dynamics of inequality amid a global health crisis are profoundly valuable, affirming the book's significance within academic and policy-making circles.