arXiv subjects

Bary S. R. Pradelski

Publications and source records attributed to Bary S. R. Pradelski.

10 recordsLinked to original sources

arXiv2026

On the existence of pure epsilon-equilibria

Departing from optimizing behavior by any $ε>0$ ensures the existence of stable outcomes in a broad class of many-agent games where utilities are drawn from a joint distribution. Specifically, in a game with iid drawn utilities from a continuous distribution and any $ε>0$, we show that as the number of agents gets large the probability that a pure $ε$-equilibrium exists converges to 1, while, by contrast, the probability that a pure Nash equilibrium exists is known to converge to $1-1/e\approx 0.63$. The asymptotic existence of pure $ε$-equilibrium extends to utilities that are negatively correlated across agents, and we identify a correlation threshold dependent on $ε$ that is tight for the zero-sum case. We also study the cases of correlation across action profiles and of utility ties and, in all cases, we also characterize the asymptotic distribution of pure $ε$-equilibria. Regarding pure Nash equilibrium---i.e., when $ε=0$---our results nest, organize, and extend the existing literature. All our results and those from the prior literature are applications of our ``master theorem'', which builds on the Chen--Stein method and Stein's method.

econ.TH↗

arXiv2026

Avoiding the Worst: The Computational Complexity of Not Worst-Responding

Finding, counting, or determining the existence of pure Nash equilibria, where players must play optimally given the others' actions, are known to be computationally intractable problems. We ask whether weakening optimality to the requirement that each player merely avoid worst responses yields tractable solution concepts. We show that it does not: any solution concept with this minimal guarantee is broadly "as intractable" as pure Nash equilibrium. In general games, determining the existence of no-worst response action profiles is NP-complete, and counting them is #P-complete. In potential games, where existence is guaranteed, the search problem is PLS-complete. However, a class of graphical games reveal a wedge in terms of complexity. Computational intractability therefore stems not only from the requirement of optimality, but from the interactivity of games that makes even a minimal rationality guarantee for each player intractable. Moreover, relaxing the latter requirement gives rise to a tractability trade off between the strength of individual rationality guarantees and the fraction of players satisfying them.

cs.GT↗

arXiv2026

Satisficing Equilibrium

In a satisficing equilibrium each agent $i$ plays one of her top $k_i$ actions in response to the actions of the other agents. Our concept unifies models of bounded rationality and yields predictions that differ from canonical solution concepts. We study its theoretical properties and show that it provides sharp predictions, exists in most games as well as in a broad new class of economic environments, admits standard epistemic and dynamic foundations, and is empirically falsifiable.

econ.TH↗

arXiv2026

Minimizing Volatility: Optimal Adjustment with Evolving Feasibility Constraints

Minimizing volatility and adjustment costs is of central importance in many economic environments, yet it is often complicated by evolving feasibility constraints. We study a decision maker who repeatedly selects an action from a stochastically evolving interval of feasible actions in order to minimize either average adjustment costs or variance. We show that for strictly convex adjustment costs (such as quadratic variation), the optimal decision rule is a reference rule in which the decision maker minimizes the distance to a target action. In general, the optimal target depends both on the previous action and the expectation of future constraints; but for the special case where the constraints follow a random walk, the optimal mechanism is to simply target the previous action. If the decision maker minimizes variance, the optimal policy is also a reference rule, but the target is a constant, which is not necessarily equal to the long-term average action. Compared to mid-point heuristics, these optimal rules may substantially reduce quadratic variation and variance, in natural environments by $50\%$ or more. Applied to stock market auctions, our results provide an explanation for the wide-spread use of reference price rules. We also apply our results to bilateral trade in over-the-counter markets, capacity planning in supply chains, and positioning in political agenda setting.

econ.TH↗

arXiv2025

Correlation of Rankings in Matching Markets

We study the role of correlation in matching markets, where multiple decision-makers simultaneously face selection problems from the same pool of candidates. We propose a model in which a candidate's priority scores across different decision-makers exhibit varying levels of correlation dependent on the candidate's sociodemographic group. Such differential correlation can arise in school choice due to the varying prevalence of selection criteria, in college admissions due to test-optional policies, or due to algorithmic monoculture, that is, when decision-makers rely on the same algorithms and data sets to evaluate candidates. We show that higher correlation for one of the groups generally improves the outcome for all groups, leading to higher efficiency. However, students from a given group are more likely to remain unmatched as their own correlation level increases. This implies that it is advantageous to belong to a low-correlation group. Finally, we extend the tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to differential correlation as a previously overlooked systemic source of group inequalities in school, university, and job admissions.

cs.GT↗

arXiv2024

No-regret learning in harmonic games: Extrapolation in the face of conflicting interests

The long-run behavior of multi-agent learning - and, in particular, no-regret learning - is relatively well-understood in potential games, where players have aligned interests. By contrast, in harmonic games - the strategic counterpart of potential games, where players have conflicting interests - very little is known outside the narrow subclass of 2-player zero-sum games with a fully-mixed equilibrium. Our paper seeks to partially fill this gap by focusing on the full class of (generalized) harmonic games and examining the convergence properties of follow-the-regularized-leader (FTRL), the most widely studied class of no-regret learning schemes. As a first result, we show that the continuous-time dynamics of FTRL are Poincaré recurrent, that is, they return arbitrarily close to their starting point infinitely often, and hence fail to converge. In discrete time, the standard, "vanilla" implementation of FTRL may lead to even worse outcomes, eventually trapping the players in a perpetual cycle of best-responses. However, if FTRL is augmented with a suitable extrapolation step - which includes as special cases the optimistic and mirror-prox variants of FTRL - we show that learning converges to a Nash equilibrium from any initial condition, and all players are guaranteed at most O(1) regret. These results provide an in-depth understanding of no-regret learning in harmonic games, nesting prior work on 2-player zero-sum games, and showing at a high level that harmonic games are the canonical complement of potential games, not only from a strategic, but also from a dynamic viewpoint.

cs.GT↗

arXiv2024

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.

cs.GT↗

arXiv2023

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.

cs.GT↗

arXiv2022

Selection in the Presence of Implicit Bias: The Advantage of Intersectional Constraints

In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation of candidates is known to produce persistent inequality and reduce aggregate utility for the decision maker. Interventions such as the Rooney Rule and its generalizations, which require the decision maker to select at least a specified number of individuals from each affected group, have been proposed to mitigate the adverse effects of implicit bias in selection. Recent works have established that such lower-bound constraints can be very effective in improving aggregate utility in the case when each individual belongs to at most one affected group. However, in several settings, individuals may belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, in the intersectional case, the aforementioned non-intersectional constraints can only recover part of the total utility achievable in the absence of implicit bias. On the other hand, we show that if one includes appropriate lower-bound constraints on the intersections, almost all the utility achievable in the absence of implicit bias can be recovered. Thus, intersectional constraints can offer a significant advantage over a reductionist dimension-by-dimension non-intersectional approach to reducing inequality.

cs.CY↗

arXiv2020

Quick or cheap? Breaking points in dynamic markets

We examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types. The cost of matching a client and provider varies, so a social planner is faced with two contending objectives: a) to reduce players' waiting time before getting matched; and b) to form efficient pairs in order to reduce matching costs. We show that such markets are characterized by a quick-or-cheap dilemma: Under a large class of distributional assumptions, there is no 'free lunch', i.e., there exists no clearing schedule that is simultaneously optimal along both objectives. We further identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. Generalizing this model, we identify two regimes: one, where no free lunch exists; the other, where a window of opportunity opens to achieve a free lunch. Remarkably, greedy scheduling is never optimal in this setting.

cs.GT↗