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The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has…
We consider games in which players search for a hidden prize, and they have asymmetric information about the prize location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an…
The $(m,b)$ Maker-Breaker percolation game on $(\mathbb{Z}^2)_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{Z}^2$ is removed independently with probability $1-p$. After…
Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness…
We study an all-pay contest in which players with low abilities are filtered out before competing for prizes. We consider a setting where the designer admits a certain number of top players. The admitted players update their beliefs based…
We study a mathematical model of voting contest with $m$ voters and $n$ candidates, with each voter ranking the candidates in order of preference, without ties. A Condorcet winner is a candidate who gets more than $m/2$ votes in pairwise…
Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
The Adjusted Winner procedure is an important fair division mechanism proposed by Brams and Taylor for allocating goods between two parties. It has been used in practice for divorce settlements and analyzing political disputes. Assuming…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
Competition is a primary driver of player satisfaction and engagement in multiplayer online games. Traditional matchmaking systems aim at creating matches involving teams of similar aggregated individual skill levels, such as Elo score or…
Something is definitely wrong. If the game has a linear winning strategy, then it is tractable. What's going on? Well, we describe a two-person game which has a definite winner, that is, a player who can force a win in a finite number of…
Consider the following Maker-Breaker game. Fix a finite subset $S\subset\mathbb{N}$ of the naturals. The players Maker and Breaker take turns choosing previously unclaimed natural numbers. Maker wins by eventually building a homothetic copy…
Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…
We consider the manipulability of tournament rules which map the results of $\binom{n}{2}$ pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match…
This project explores adversarial training techniques to develop fairer Deep Neural Networks (DNNs) to mitigate the inherent bias they are known to exhibit. DNNs are susceptible to inheriting bias with respect to sensitive attributes such…
Automated systems built on artificial intelligence (AI) are increasingly deployed across high-stakes domains, raising critical concerns about fairness and the perpetuation of demographic disparities that exist in the world. In this context,…
Learning from human preference data is becoming a useful tool, from fine-tuning large language models to training reinforcement learning agents. However, in most scenarios, the model is trained on the average preference of all human…
The article explores the emerging domain of incentive-aware machine learning (ML), which focuses on algorithmic decision-making in contexts where individuals can strategically modify their inputs to influence outcomes. It categorizes the…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…