Researchers strategically choose where to submit their work in order to maximize its impact, and these publication decisions in turn determine venues' impact factors. To analyze how individual publication choices both respond to and shape venue impact, we introduce a game-theoretic framework - coined the Publication Choice Problem - that captures this two‐way interplay. We show the existence of a pure-strategy equilibrium in the Publication Choice Problem and its uniqueness under binary researcher types. Our characterizations of the equilibrium properties offer insights about what publication behaviors better indicate a researcher's impact level. Through equilibrium analysis, we further investigate how labeling papers with ``spotlight'' affects the impact factor of venues in the research community. Our analysis shows that competitive venue labeling top papers with ``spotlight'' may decrease the overall impact of other venues in the community, while less competitive venues with ``spotlight'' labeling have an opposite impact.
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Recent research on instant runoff voting (IRV) shows that it exhibits a striking property over unimodal one-dimensional preferences: there is an exclusion zone around the median voter such that the winner must come from the exclusion zone, unless no such candidate exists. Thus, IRV cannot elect an extreme candidate in this setting as long as a sufficiently moderate candidate runs. In this work, we examine the mathematical structure of exclusion zones as a broad phenomenon in more general preference spaces. We prove that with voters uniformly distributed over any d-dimensional hyperrectangle (for d > 1), IRV has no such exclusion zone. However, we also show that IRV exclusion zones are not solely a one-dimensional phenomenon. For irregular higher-dimensional preference spaces with fewer symmetries than hyperrectangles, IRV can have nontrivial exclusion zones. As a further exploration, we study IRV exclusion zones with graph-based preferences, where nodes represent voters who prefer candidates closer to them in the graph. Here, we show that IRV exclusion zones present a surprising computational challenge: even checking whether a given set of positions is an IRV exclusion zone is NP-hard. We develop an efficient randomized approximation algorithm for checking and finding exclusion zones in graphs. Finally, we report on computational experiments with exclusion zones: (i) performing an exhaustive computer search of small graphs and trees, we find nontrivial IRV exclusion zones in most small graphs; and (ii) applying our approximation algorithm to a collection of larger real-world school friendship networks, we find that about 60% of these networks have probable nontrivial IRV exclusion zones. While our focus is on IRV, the properties of exclusion zones we establish provide new methods for analyzing voting systems in metric spaces more generally.
A safe Pareto improvement (SPI) is a modification of a game that leaves all players better off with certainty. SPIs are typically proven under qualitative assumptions about the way different games are played. For example, we assume that strictly dominated strategies can be iteratively removed and that isomorphic games are played isomorphically. In this work, we study SPIs achieved through three types of \textit{ex post} verifiable commitments -- promises about player behavior from which deviations can be detected by observing the game. First, we consider disarmament -- commitments not to play certain actions. Next, we consider SPIs based on \textit{token games}. A token game is a game played by simply announcing an action (via cheap talk). As such, its outcome is intrinsically meaningless. However, we assume the players commit in advance to play specific (pure or correlated) strategy profiles in the original game as a function of the token game outcome. Under such commitments, the token game becomes a new, meaningful normal-form game. Finally, we consider default-conditional commitment: SPIs in settings where the players' default ways of playing the original game can be credibly revealed and hence the players can commit to act as a function of this default. We characterize the complexity of deciding whether SPIs exist in all three settings, giving a mixture of characterizations and efficient algorithms and \NP- and \textsc{Graph Isomorphism}-hardness
Cake-cutting algorithms, which aim to fairly allocate a continuous resource based on individual agent preferences, have seen significant progress over the past two decades. Much of the research has concentrated on fairness, with comparatively less attention given to other important aspects. In 2010, Chen et al. introduced an algorithm that, in addition to ensuring fairness, was strategyproof---meaning agents had no incentive to misreport their valuations. However, even in the absence of strategic incentives to misreport, agents may still hesitate to reveal their true preferences due to privacy concerns (e.g., when allocating advertising time between firms, revealing preferences could inadvertently expose planned marketing strategies or product launch timelines). In this work, we extend the strategyproof algorithm of Chen et al. by introducing a privacy-preserving dimension. To the best of our knowledge, we present the first private cake-cutting protocol, and, in addition, this protocol is also envy-free and strategyproof. Our approach replaces the algorithm’s centralized computation with a novel adaptation of cryptographic techniques, enabling privacy without compromising fairness or strategyproofness. Thus, our protocol encourages agents to report their true preferences not only because they are not incentivized to lie, but also because they are protected from having their preferences exposed.
We study how the design of testing institutions, encompassing both the tests themselves and the procedures used to administer them, shapes selection outcomes in environments with multiple criteria and strategic agents. We model the testing agency as either a set of independent bureaucracies (each test administered separately) or a joint bureaucracy (where test order and personalization can be coordinated). Our mechanism design analysis shows that under a joint bureaucracy, fixed-order sequential mechanisms with stringent tests are optimal for maximizing the probability mass of qualified candidates selected. Furthermore, we demonstrate that personalizing tests through upfront communication, now increasingly feasible via AI and automation, can select all qualified candidates. Finally, we compare institutional settings and quantify the value of controlling test order, showing that the benefit depends critically on the distribution of testees and the stringency of optimal tests. Our results contribute to the design of robust, efficient, and fair testing systems in both human and AI-mediated environments.
Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders---with the seller---to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders---these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques---and build upon existing quadratic programming techniques---to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.
The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model.Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVAkADD, a novel approximation method that fits a k-additive surrogate game. By taking advantage of k-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.
This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice---such as the Method of Equal Shares and the Nash Rule---and supports them through both theoretical analysis and extensive experimental evaluation.
We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled via a convex cost function. Additionally, items are partitioned into groups, and each platform also incurs group-specific convex cost over the number of items from each group that can be assigned to the platform. These costs promote group fairness by penalizing imbalances, yielding a soft variation of fairness notions introduced in prior work, such as Restricted Dominance and Minority protection. Restricted Dominance enforces upper bounds on group representation, while Minority protection enforces lower bounds. Our approach replaces such hard constraints with cost-based penalties, allowing more flexible trade-offs. Our model also captures Nash Social Welfare kind of objective. The cost of an assignment is the sum of the values of all the cost functions across all the groups and platforms. The objective is to find an assignment that minimizes the cost while achieving a total utility that is at least a user-specified threshold. The main challenge lies in balancing the overall platform cost with group-specific costs, both governed by convex functions, while meeting the utility constraint. We present an efficient polynomial-time approximation algorithm, supported by theoretical guarantees and experimental evaluation. Our algorithm is based on techniques involving linear programming and network flows. We also provide an exact algorithm for a special case with uniform utilities and establish the hardness of the general problem when the groups can intersect arbitrarily. This work has applications in cloud computing, logistics, resource-constrained machine learning deployment, federated learning, and network design, where resources must be allocated across platforms with diverse cost structures and diminishing returns.
We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions, nor sharing information. Prior works established polynomial-time convergence to an approximate Nash equilibrium under strong reachability and mixing time assumptions. We propose a convergent algorithm that significantly relaxes these assumptions, requiring only the existence of a single policy with bounded reachability and mixing time. Our key algorithmic novelty is introducing Tsallis entropy regularization to smooth the best-response policy updates. By suitably tuning this regularization, we ensure sufficient exploration, thus bypassing previous stringent assumptions on the MDP. We prove a polynomial-time convergence to an approximate Nash equilibrium by establishing novel properties of the value and policy updates induced by the Tsallis entropy regularizer.
Counterfactual Regret Minimization (CFR) algorithms are widely used to compute a Nash equilibrium (NE) in two-player zero-sum imperfect-information extensive-form games (IIGs). Among them, Predictive CFR+ (PCFR+) is particularly powerful, achieving an exceptionally fast empirical convergence rate via the prediction in many games. However, the empirical convergence rate of PCFR+ would significantly degrade if the prediction is inaccurate, leading to unstable performance on certain IIGs. To enhance the robustness of PCFR+, we propose Asymmetric PCFR+ (APCFR+), which employs an adaptive asymmetry of step sizes between the updates of implicit and explicit accumulated counterfactual regrets to mitigate the impact of the prediction inaccuracy on convergence. We present a theoretical analysis demonstrating why APCFR+ can enhance the robustness. To the best of our knowledge, we are the first to propose the asymmetry of step sizes, a simple yet novel technique that effectively improves the robustness of PCFR+. Then, to reduce the difficulty of implementing APCFR+ caused by the adaptive asymmetry, we propose a simplified version of APCFR+ called Simple APCFR+ (SAPCFR+), which uses a fixed asymmetry of step sizes to enable only a single-line modification compared to original PCFR+. Experimental results on five standard IIG benchmarks and two heads-up no-limit Texas Hold’em (HUNL) Subagems show that (i) both APCFR+ and SAPCFR+ outperform PCFR+ in most of the tested games, (ii) SAPCFR+ achieves a comparable empirical convergence rate with APCFR+, and (iii) our approach can be generalized to improve other CFR algorithms, e.g., Discount CFR (DCFR).
The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying participation costs and share a possibly heuristic belief about their pivotality (ability to influence the outcome). In a costly voting setup where voters abstain if their participation cost is greater than their pivotality estimate, we identify a single property of the heuristic belief---weakly vanishing pivotality---that gives rise to multiple stable equilibria in which elections are nearly tied. In contrast, strongly vanishing pivotality (as in the standard Calculus of Voting model) yields a unique, trivial equilibrium where only zero-cost voters participate as the population grows. We then characterize when nontrivial equilibria satisfy a version of the Jury Theorem: below a sharp threshold, the majority-preferred candidate wins with probability approaching one; above it, both candidates either win with equal probability.
This paper presents a novel strategy for a multi-agent pursuit-evasion game involving multiple faster pursuers with heterogenous speeds and a single slower evader. We define a geometric region, the evader's safe-reachable set, as the intersection of Apollonius circles derived from each pursuer-evader pair. The capture strategy is formulated as a zero-sum game where the pursuers cooperatively minimize the area of this set, while the evader seeks to maximize it, effectively playing a game of spatial containment. By deriving the analytical gradients of the safe-reachable set's area with respect to agent positions, we obtain closed-form, instantaneous optimal control laws for the heading of each agent. These strategies are computationally efficient, allowing for real-time implementation. Simulations demonstrate that the gradient-based controls effectively steer the pursuers to systematically shrink the evader’s safe region, leading to guaranteed capture. This area-minimization approach provides a clear geometric objective for cooperative capture.
Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for mechanisms: a mechanism is said to satisfy PEF1 if for any pair of agent orderings, no agent prefers their bundle determined under one ordering to that under another ordering by more than the utility of a single good. First, we propose a scale-invariant, polynomial-time mechanism that satisfies PEF1 and yields an envy-freeness up to one good (EF1) allocation. For the case of two agents, we establish that any mechanism producing a maximum Nash welfare allocation eliminates envy based on positions by removing one good, provided that utilities are positive. Additionally, we present a polynomial-time mechanism based on the adjusted winner procedure, which satisfies PEF1 and produces an EF1 and Pareto optimal allocation for two agents. In contrast, we demonstrate that well-known mechanisms such as round-robin and envy-cycle elimination do not generally satisfy PEF1.
Audit games are an important variant of the Stackelberg security game, a widely studied game-theoretic model over the past years. It has been acknowledged that a pre-audit phase can notably enhance the audit's efficiency by informing and directing the following audit procedures. In this paper, we model the above process with a two-stage audit game. The game encompasses two stages: an investigation stage where the auditor gathers information about potential policy breaches, and an audit stage where the auditor allocates the audit resources based on the investigation results. We formulate the problem as a set of mathematical programs. Due to the non-convexity of the programs, we consider a restricted strategy space and show that the optimal strategy in the restricted space can be determined by solving a polynomial number of convex optimization problems. Finally, we conduct extensive experiments to evaluate the effect of introducing the initial investigation stage and our algorithm. Our experiments show that even a small budget for the initial investigations can significantly enhance the defender's utility.
Real-world security applications (e.g., cybersecurity) often involve multiple attack paths, each with layers of defenses that an attacker needs to sequentially overcome before a successful attack on the entire system. Each defensive resource changes dynamically in efficacy as the attack unfolds. In this paper, we study the case where attackers are adaptive, potentially switching paths over time in response to these changes with the goal to minimize the expected time until a successful attack. We formalize this as a min-max game and give examples where adaptive attackers are more powerful than non-adaptive ones. We show that defenses that do not account for adaptivity can perform arbitrarily worse. A connection between the attacker's optimal strategy with the classical theory of multi-armed bandits and the Gittins index is made, yielding a simple gradient based algorithm to solve our proposed min-max game. Experiments on synthetic settings validate our approach.
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.
We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations. As fair we consider the allocations that are envy-free-up-to-any-good (EFX). Finding if EFX allocations always exist, even for agents with additive valuations, is a major open problem in Fair Division. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph, respectively, and only the endpoints of an edge may have non-zero marginal value for it. We show that for hypergraphs with girth at least 4 and agents with general monotone valuations there always exists an EFX allocation and can be constructed in polynomial time. We generalize our approach to also show that multi-hypergraphs with girth (on the simple hypergraph) at least 4 always admit an EFX allocation, as long as there exists a single vertex whose adjacent edges have multiplicity at most the size of that edge minus 2; our construction in this case needs pseudo-polynomial time.
In Facility Location problems there are agents that should be connected to facilities and locations where facilities may be opened so that agents can connect to them. We depart from Uncapacitated Facility Location and by assuming that the connection costs of agents to facilities are congestion dependent, we define a novel problem, namely, Facility Location for Congesting (Selfish) Commuters. The connection costs of agents to facilities come as a result of how the agents commute to reach the facilities in an underlying network with cost functions on the edges. Inapproximability results follow from the related literature and thus approximate solutions is all we can hope for. For when the cost functions are nondecreasing we employ in a novel way an approximate version of Caratheodory’s Theorem to show how approximate solutions for different versions of the problem can be derived. For when the cost functions are nonincreasing we show how this problem generalizes the Cost-Distance problem and provide an algorithm that for this more general case achieves the same approximation guarantees.
We study the computational complexity of winner determination problems in approval-based committee elections under Thiele voting rules. These form a class of rules parameterized by a fixed weight vector that specifies how a voter's satisfaction depends on the number of approved candidates elected. We first analyze the structure of optimal solutions based on the sets of voters who approve each candidate---that is, how voters' approval ballots induce dependencies between candidates---revealing constraints on a winning committee under any fixed Thiele voting rule. Using this, we design FPT algorithms for Proportional Approval Voting (PAV) and other Thiele rules on a natural restricted domain known as the Voter Interval domain---that is, after a suitable ordering of voters, each candidate is approved by a consecutive interval of voters. In particular, we show that every Thiele rule on Voter Interval is FPT with respect to a parameter for which the problem is NP-hard on general instances, even when the parameter takes constant values. Our results advance the understanding of the computational complexity of PAV on Voter Interval instances, which remains one of the central open questions in this area. We further resolve two open questions from the literature on PAV (and other Thiele voting rules) by providing a polynomial-time algorithm for instances where each candidate is approved by at most two voters, and an FPT algorithm parameterized by the total score of a winning committee.