In the contest design problem, there are $n$ strategic contestants, each of whom decides an effort level. A contest designer with a fixed budget must then design a mechanism that allocates a prize $p_i$ to the $i$-th rank based on the outcome, to incentivize contestants to exert higher costly efforts and induce high-quality outcomes. In this paper, we significantly deepen our understanding of optimal mechanisms under general settings by considering nonconvex objectives in contestants' qualities. Notably, our results accommodate the following objectives: (i) any convex combination of user welfare (motivated by recommender systems) and the average quality of contestants, and (ii) arbitrary posynomials over quality, both of which may neither be convex nor concave. In particular, these subsume classic measures such as social welfare, order statistics, and (inverse) S-shaped functions, which have received little or no attention in the contest literature to the best of our knowledge. Surprisingly, across all these regimes, we show that the optimal mechanism is highly structured: it allocates potentially higher prize to the first-ranked contestant, zero to the last-ranked one, and equal p
This paper investigates a two-stage game-theoretical model with multiple parallel rank-order contests. In this model, each contest designer sets up a contest and determines the prize structure within a fixed budget in the first stage. Contestants choose which contest to participate in and exert costly effort to compete against other participants in the second stage. First, we fully characterize the symmetric Bayesian Nash equilibrium in the subgame of contestants, accounting for both contest selection and effort exertion, under any given prize structures. Notably, we find that, regardless of whether contestants know the number of participants in their chosen contest, the equilibrium remains unchanged in expectation. Next, we analyze the designers' strategies under two types of objective functions based on effort and participation, respectively. For a broad range of effort-based objectives, we demonstrate that the winner-takes-all prize structure-optimal in the single-contest setting-remains a dominant strategy for all designers. For the participation objective, which maximizes the number of participants surpassing a skill threshold, we show that the optimal prize structure is alway
Benchmark hacking refers to tuning a machine learning model to score highly on certain evaluation criteria without improving true generalization or faithfully solving the intended problem. We study this phenomenon in a generic machine learning contest, where each contestant chooses two types of effort: creative effort that improves model capability as desired by the contest host, and mechanistic effort that only improves the model's fitness to the particular task in contest without contributing to true generalization. We establish the existence of a symmetric monotone pure strategy equilibrium in this competition game. It also provides a natural definition of benchmark hacking in this strategic context by comparing a player's equilibrium effort allocation to that of a single-agent baseline scenario. Under our definition, contestants with types below certain threshold (low types) always engage in benchmark hacking, whereas those above the threshold do not. Furthermore, we show that more skewed reward structures (favoring top-ranked contestants) can elicit more desirable contest outcomes. We also provide empirical evidence to support our theoretical predictions.
We study a tractable two-player contest built on a truncated cubic contest success function. Its defining feature is a strategic-feedback parameter whose sign determines whether a leading player's effort lowers (suppression) or raises (empowerment) the marginal effectiveness of the trailing player's effort; standard lottery contests impose suppression by construction. The benchmark yields closed-form mixed equilibria under complete information and a unique affine Bayesian Nash equilibrium under IID private information. Expected effort is typically single-peaked in the feedback parameter. Uncertainty lowers effort under suppression but raises it under empowerment, and the same asymmetry governs information disclosure: an effort-maximizing designer withholds information under suppression and discloses fully under empowerment. Several familiar conclusions of contest theory turn out to reflect suppressive benchmarks rather than contests as such.
Shortlisting is a common and effective method for pre-selecting participants in competitive settings. To ensure fairness, a cut-off score is typically announced, allowing only contestants who exceed it to enter the contest, while others are eliminated. In this paper, we study rank-order contests with shortlisting and cut-off score disclosure. We fully characterize the equilibrium behavior of shortlisted contestants for any given prize structure and shortlist size. We examine two objective functions: the highest individual performance and total performance. For both objectives, the optimal contest is in a winner-take-all format. For the highest individual performance, the optimal shortlist size is exactly two contestants, but, in contrast, for total performance, the shortlist size does not affect the outcome, i.e., any size yields the same total performance. Furthermore, we compare the highest individual performance achieved with and without shortlisting, and show that the former is 4/3 times greater than the latter.
AI-assisted gait analysis holds promise for improving Parkinson's Disease (PD) care, but current clinical dashboards lack transparency and offer no meaningful way for clinicians to interrogate or contest AI decisions. We present Con-GaIT (Contestable Gait Interpretation & Tracking), a clinician-centered system that advances Contestable AI through a tightly integrated interface designed for interpretability, oversight, and procedural recourse. Grounded in HCI principles, ConGaIT enables structured disagreement via a novel Contest & Justify interaction pattern, supported by visual explanations, role-based feedback, and traceable justification logs. Evaluated using the Contestability Assessment Score (CAS), the framework achieves a score of 0.970, demonstrating that contestability can be operationalized through human-centered design in compliance with emerging regulatory standards. A demonstration of the framework is available at https://github.com/hungdothanh/Con-GaIT.
Selective contests can impair participants' overall welfare in overcompetitive environments, such as school admissions. This paper models the situation as an optimal contest design problem with binary actions, treating effort costs as societal costs incurred to achieve a desired level of selectivity. We provide a characterization for the feasible set of selection efficiency and societal cost in selective contests by establishing their relationship with feasible equilibrium strategies. We find that selection efficiency and contestants' welfare are complementary, i.e. it is almost impossible to improve one without sacrificing the other. We derive the optimal equilibrium outcome given the feasible set and characterize the corresponding optimal contest design. Our analysis demonstrates that it is always optimal for a contest designer who is sufficiently concerned with societal cost to intentionally introduce randomness into the contest. Furthermore, we show that the designer can optimize any linear payoff function by adjusting a single parameter related to the intensity of randomness, without altering the specific structure of the contest.
There has been much discourse on the ethics of AI, to the extent that there are now systems that possess inherent moral reasoning. Such machines are now formally known as Artificial Moral Agents or AMAs. However, there is a requirement for a dedicated framework that can contest the morality of these systems. This paper proposes a 5E framework for contesting AMAs based on five grounds: ethical, epistemological, explainable, empirical, and evaluative. It further includes the spheres of ethical influences at individual, local, societal, and global levels. Lastly, the framework contributes a provisional timeline that indicates where developers of AMA technologies may anticipate contestation, or may self-contest in order to adhere to value-aligned development of truly moral AI systems.
In daily fantasy sports, players enter into "contests" where they compete against each other by building teams of athletes that score fantasy points based on what actually occurs in a real-life sports match. For any given sports match, there are a multitude of contests available to players, with substantial variation across 3 main dimensions: entry fee, number of spots, and the prize pool distribution. As player preferences are also quite heterogeneous, contest personalization is an important tool to match players with contests. This paper presents a scalable contest recommendation system, powered by a Wide and Deep Interaction Ranker (WiDIR) at its core. We productionized this system at our company, one of the large fantasy sports platforms with millions of daily contests and millions of players, where online experiments show a marked improvement over other candidate models in terms of recall and other critical business metrics.
We study dynamic multi-battle contests and examine how the contest structure shapes dynamic incentives and determines the extent of rent dissipation. A discouragement effect often arises -- such as in tug-of-war and best-of-$K$ contests -- preventing full rent dissipation even when the series can extend infinitely. We identify a structural property, exchangeability, that contributes to the effect. Leveraging this insight, we establish a necessary and sufficient condition for almost-full rent dissipation. As an application, we introduce the iterated incumbency contest, which illustrates how volatility in the surrounding environment sustains dynamic incentives and generates almost-full rent dissipation, and thus offers insights into various competitive phenomena.
This paper proposes a dynamic research contest, namely chasing contest, in which two asymmetric contestants exert costly effort to accomplish two breakthroughs. The contestants are asymmetric in that one of them is present-biased and has already achieved one breakthrough (the leader), whereas the other is time-consistent and needs to achieve two breakthroughs to win (the chaser). The principal can choose between two disclosure policies: immediately announcing the chaser's first breakthrough (public chasing contest) or announcing only the final result (hidden chasing contest). We characterize the unique x-start and y-stop equilibrium under both disclosure policies, in which the leader starts working from an instant x to the end while the chaser stops exerting effort by the instant y. In addition, the chaser will never stop earlier in the hidden chasing contest, whereas a late deadline extends the leader's effort in the public contest.
In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of distributional preferences of the contest designer. In contests with complete information, the representation significantly simplifies the characterization of the equilibria.
This paper explores the design of contests involving $n$ contestants, focusing on how the designer decides on the number of contestants allowed and the prize structure with a fixed budget. We characterize the unique symmetric Bayesian Nash equilibrium of contestants and find the optimal contests design for the maximum individual effort objective and the total effort objective.
Contest success function (CSF) maps contestants' efforts to their winning probability. This paper provides axiomatizations of CSFs with headstarts. The results extend the classic axiomatization of the Tullock CSF and connect to CSFs that allow for draws. The central axiom is relative homogeneity of counterfactual deviation, which requires the pairwise influence of one contestant's effort on opponent's probabilistic allocation to be scale-invariant. Two fairness axioms and no advantageous reallocation further restrict the admissible functional forms with headstarts. We also introduce dummy consistency, requiring allocations to be consistent with and without inactive contestants, to clarify the relationship with earlier axiomatic work that rules out headstarts. Finally, we discuss an extension that drops the assumption of full allocation.
Organizations learn from the market, political, and societal responses to their actions. While in some cases both the actions and responses take place in an open manner, in many others, some aspects may be hidden from external observers. The Eurovision Song Contest offers an interesting example to study organizational level learning at two levels: organizers and participants. We find evidence for changes in the rules of the Contest in response to undesired outcomes such as runaway winners. We also find strong evidence of participant learning in the characteristics of competing songs over the 70-years of the Contest. English has been adopted as the lingua franca of the competing songs and pop has become the standard genre. Number of words of lyrics has also grown in response to this collective learning. Remarkably, we find evidence that four participating countries have chosen to ignore the "lesson" that English lyrics increase winning probability. This choice is consistent with utility functions that award greater value to featuring national language than to winning the Contest. Indeed, we find evidence that some countries -- but not Germany -- appear to be less susceptible to "pee
We investigate a two-stage competitive model involving multiple contests. In this model, each contest designer chooses two participants from a pool of candidate contestants and determines the biases. Contestants strategically distribute their efforts across various contests within their budget. We first show the existence of a pure strategy Nash equilibrium (PNE) for the contestants, and propose a polynomial-time algorithm to compute an $ε$-approximate PNE. In the scenario where designers simultaneously decide the participants and biases, the subgame perfect equilibrium (SPE) may not exist. Nonetheless, when designers' decisions are made in two substages, the existence of SPE is established. In the scenario where designers can hold multiple contests, we show that the SPE exists under mild conditions and can be computed efficiently.
We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2-approximations to conventional methods for a large family of "regular" distributions, and 4-approximations, otherwise.
We present a general theoretical model for the spatio-temporal dynamics of animal contests. Inspired by interactions between physical particles, the model is formulated in terms of effective interaction potentials, which map typical elements of contest behaviour into empirically verifiable rules of contestant motion. This allows us to simulate the observable dynamics of contests in various realistic scenarios, notably in dyadic contests over a localized resource. Assessment strategies previously formulated in game-theoretic models, as well as the effects of fighting costs, can be described as variations in our model's parameters. Furthermore, the trends of contest duration associated with these assessment strategies can be derived and understood within the model. Detailed description of the contestants' motion enables the exploration of spatio-temporal properties of asymmetric contests, such as the emergence of chase dynamics. Overall, our framework aims to bridge the growing gap between empirical capabilities and theory in this widespread aspect of animal behaviour.
This report presents solutions to three machine learning challenges developed as part of the Rayan AI Contest: compositional image retrieval, zero-shot anomaly detection, and backdoored model detection. In compositional image retrieval, we developed a system that processes visual and textual inputs to retrieve relevant images, achieving 95.38% accuracy and ranking first with a clear margin over the second team. For zero-shot anomaly detection, we designed a model that identifies and localizes anomalies in images without prior exposure to abnormal examples, securing second place with a 73.14% score. In the backdoored model detection task, we proposed a method to detect hidden backdoor triggers in neural networks, reaching an accuracy of 78%, which placed our approach in second place. These results demonstrate the effectiveness of our methods in addressing key challenges related to retrieval, anomaly detection, and model security, with implications for real-world applications in industries such as healthcare, manufacturing, and cybersecurity. Code for all solutions is available online (https://github.com/safinal/rayan-ai-contest-solutions).
We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a cutoff determined by a market clearing condition. A co-monotonicity property is essentially all that is needed for a representation in the general case, but significantly stronger conditions must hold to obtain an additive structure. We illustrate the usefulness of this framework by revisiting some of the classic questions in the contests literature.