Quick or cheap? Breaking points in dynamic markets

We examine two-sided markets where players arrive stochastically over time. The cost of matching a client and provider is heterogeneous, and the distribution of costs – but not their realization – is known. In this way, a social planner is faced with two contending objectives:(a) to reduce the players’ waiting time before getting matched; and (b) to reduce matching costs. In this paper, we aim to understand when and how these objectives are incompatible. We identify two regimes dependent on the ‘speed of improvement’ of the cost of matching with respect to market size. One regime results in a quick or cheap dilemma without ‘free lunch’: there exists no clearing schedule that is simultaneously optimal along both objectives. In that regime, we identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. The other regime features a window of opportunity in which free lunch can be achieved. Which scheduling policy is optimal depends on the heterogeneity of match costs. Under limited heterogeneity, e.g., when there is a finite number of possible match costs, greedy scheduling is approximately optimal, in line with the related literature. However, with more heterogeneity greedy scheduling is never optimal. Finally, we analyze a particular model where match costs are exponentially distributed and show that it is at the boundary of the no-free-lunch regime We then characterize the optimal clearing schedule for varying social planner desiderata

Collaborative Coalitions in Multi-Agent Systems: Quantifying the Strong Price of Anarchy for Resource Allocation Games

The emergence of new communication technologies allows us to expand our understanding of distributed control and consider collaborative decision-making paradigms. With collaborative algorithms, certain local decision-making entities (or agents) are enabled to communicate and collaborate on their actions with one another to attain better system behavior. By limiting the amount of communication, these algorithms exist somewhere between centralized and fully distributed approaches. To understand the possible benefits of this inter-agent collaboration, we model a multi-agent system as a common-interest game in which groups of agents can collaborate on their actions to jointly increase the system welfare. We specifically consider $k$-strong Nash equilibria as the emergent behavior of these systems and address how well these states approximate the system optimal, formalized by the $k$-strong price of anarchy ratio. Our main contributions are in generating tight bounds on the $k$-strong price of anarchy in finite resource allocation games as the solution to a tractable linear program. By varying $k$ --the maximum size of a collaborative coalition--we observe exactly how much performance is gained from inter-agent collaboration. To investigate further opportunities for improvement, we generate upper bounds on the maximum attainable $k$-strong price of anarchy when the agents' utility function can be designed

Nichtkooperative Spieltheorie

Die Spieltheorie ist eine mathematische Sprache zur Formalisierung von interaktiven Entscheidungssituationen. Im Unterschied zur (herkömmlichen) Entscheidungstheorie, die Situationen beschreibt, in denen ein einzelnes Individuum sich zwischen verschiedenen Lotterien entscheidet, gibt es in der Spieltheorie in der Regel Interaktionen zwischen den Entscheidungen mehrerer Entscheidungsträger, so dass der Nutzen des Einzelnen (im Sinne des individuellen „von Neumann-Morgenstern-Nutzens“ – vgl. Kapitel II.1 zur Entscheidungstheorie) nicht nur von den Lotterien und den eigenen Entscheidungen, sondern auch von den Entscheidungen der anderen Entscheidungsträger abhängt. Der spieltheoretische Ansatz hat revolutionären Einfluss auf die Entwicklung der Biologie und Sozialwissenschaften genommen, insbesondere in der Wirtschaftsforschung, was dadurch belegt ist, dass bis heute 13 Spieltheoretiker den Wirtschaftsnobelpreis gewonnen haben, unter ihnen auch der in Deutschland geborene Robert Aumann und der bisher einzige deutsche Preisträger Reinhard Selten

Collaborative Decision-Making and the k-Strong Price of Anarchy in Common Interest Games

The control of large-scale, multi-agent systems often entails distributing decision-making across the system components. However, with advances in communication and computation technologies, we can consider new collaborative decision-making paradigms that exist somewhere between centralized and distributed control. In this work, we seek to understand the benefits and costs of increased collaborative communication in multi-agent systems. We specifically study this in the context of common interest games in which groups of up to k agents can coordinate their actions in maximizing the common objective function. The equilibria that emerge in these systems are the k-strong Nash equilibria of the common interest game; studying the properties of these states can provide relevant insights into the efficacy of inter-agent collaboration. Our contributions come threefold: 1) provide bounds on how well k-strong Nash equilibria approximate the optimal system welfare, formalized by the k-strong price of anarchy, 2) study the run-time and transient performance of collaborative agent-based dynamics, and 3) consider the task of redesigning objectives for groups of agents which improve system performance. We study these three facets generally as well as in the context of resource allocation problems, in which we provide tractable linear programs that give tight bounds on the k-strong price of anarchy.Comment: arXiv admin note: text overlap with arXiv:2308.0804

On market prices in double auctions

We address some open issues regarding the characterization of double auctions. Our model is a two-sided commodity market with either finitely or infinitely many traders. We first unify existing formulations for both finite and infinite markets and generalize the characterization of market clearing in the presence of ties. Second, we define a mechanism that achieves market clearing in any, finite or infinite, market instance and show that it coincides with the k-double auction by Rustichini et al. (1994) in the former case. In particular, it clarifies the consequences of ties in submissions and makes common regularity assumptions obsolete. Finally, we show that the resulting generalized mechanism implements Walrasian competitive equilibrium

Markets and transaction costs

Transaction costs are omnipresent in markets yet are often omitted in economic models. We show that their presence can fundamentally alter incentives and welfare in markets in which the price equates supply and demand. We categorize transaction costs into two types. Asymptotically uninfluenceable transaction costs—such as fixed and price fees—preserve the key asymptotic properties of markets without transaction costs, namely strategyproofness, efficiency, and robustness to misspecified beliefs and to aggregate uncertainty. In contrast, influenceable transaction costs—such as spread fees—lead to complex strategic behavior (which we call price guessing) and may result in severe market failure. In our analysis of optimal design we focus on transaction costs that are fees collected by a platform as revenue. We show how optimal design depends on the traders’ beliefs. In particular, with common prior beliefs, any asymptotically uninfluenceable fee schedule can be scaled to be optimal, while purely influenceable fee schedules lead to zero revenue. Our insights extend beyond markets equalizing demand and supply

Double auctions and transaction costs

Transaction costs are omnipresent in markets but are often omitted in economic models. We show that the presence of transaction costs can fundamentally alter incentive and welfare properties of Double Auctions, a canonical market organization. We further show that transaction costs can be categorized into two types. Double Auctions with homogeneous transaction costs—a category that includes fixed fees and price based fees—preserve the key advantages of Double Auctions without transaction costs: markets with homogeneous transaction costs are asymptotically strategyproof, and there is no efficiency-loss due to strategic behavior. In contrast, double auctions with heterogeneous transaction costs—such as spread fees—lead to complex strategic behavior (price guessing) and may result in severe market failures. Allowing for aggregate uncertainty, we extend these insights to market organizations other than Double Auctions

Competitive Market Behavior: Convergence and asymmetry in the experimental double auction

We conducted a large number of controlled continuous double auction experiments to reproduce and stress‐test the phenomenon of convergence to competitive equilibrium under private information with decentralized trading feedback. Our main finding is that across a total of 104 markets (involving over 1,700 subjects), convergence occurs after a handful of trading periods. Initially, however, there is an inherent asymmetry that favors buyers, typically resulting in prices below equilibrium levels. Analysis of over 80,000 observations of individual bids and asks helps identify empirical ingredients contributing to the observed phenomena including higher levels of aggressiveness initially among buyers than sellers

Endogenous social distancing and its underappreciated impact on the epidemic curve

Social distancing is an effective strategy to mitigate the impact of infectious diseases. If sick or healthy, or both, predominantly socially distance, the epidemic curve flattens. Contact reductions may occur for different reasons during a pandemic including health-related mobility loss (severity of symptoms), duty of care for a member of a high-risk group, and forced quarantine. Other decisions to reduce contacts are of a more voluntary nature. In particular, sick people reduce contacts consciously to avoid infecting others, and healthy individuals reduce contacts in order to stay healthy. We use game theory to formalize the interaction of voluntary social distancing in a partially infected population. This improves the behavioral micro-foundations of epidemiological models, and predicts differential social distancing rates dependent on health status. The model’s key predictions in terms of comparative statics are derived, which concern changes and interactions between social distancing behaviors of sick and healthy. We fit the relevant parameters for endogenous social distancing to an epidemiological model with evidence from influenza waves to provide a benchmark for an epidemic curve with endogenous social distancing. Our results suggest that spreading similar in peak and case numbers to what partial immobilization of the population produces, yet quicker to pass, could occur endogenously. Going forward, eventual social distancing orders and lockdown policies should be benchmarked against more realistic epidemic models that take endogenous social distancing into account, rather than be driven by static, and therefore unrealistic, estimates for social mixing that intrinsically overestimate spreading