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In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
Oversubscribed treatments are often allocated using randomized waiting lists. Applicants are ranked randomly, and treatment offers are made following that ranking until all seats are filled. To estimate causal effects, researchers often…
Machine learning actively impacts our everyday life in almost all endeavors and domains such as healthcare, finance, and energy. As our dependence on the machine learning increases, it is inevitable that these algorithms will be used to…
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…
Sortition is based on the idea of choosing randomly selected representatives for decision making. The main properties that make sortition particularly appealing are fairness -- all the citizens can be selected with the same probability --…
We study the dynamics of repeated fair division between two players, Alice and Bob, where Alice partitions a cake into two subsets and Bob chooses his preferred one over $T$ rounds. Alice aims to minimize her regret relative to the…
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or…
In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from…
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires…
We construct irreducible balanced non-transitive sets of $n$-sided dice for any positive integer $n$, which was raised in \cite[Question 5.2]{SS17}. One main tool of the construction is to study so-called fair sets of dice. Furthermore, we…
Election systems based on scores generally determine the winner by computing the score of each candidate and the winner is the candidate with the best score. It would be natural to expect that computing the winner of an election is at least…
The study of proportionality in multiwinner voting with approval ballots has received much attention in recent years. Typically, proportionality is captured by variants of the Justified Representation axiom, which say that cohesive groups…
In forecasting competitions, the traditional mechanism scores the predictions of each contestant against the outcome of each event, and the contestant with the highest total score wins. While it is well-known that this traditional mechanism…
When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism…
This paper analyzes the question of where one should stand when playing darts. If one stands at distance $d>0$ and aims at $a\in \mathbb{R}^n$, then the dart (modelled by a random vector $X$ in $\mathbb{R}^n$) hits a random point given by…
We present some new analytical expressions for the so-called Parrondo effect, where simple coin-flipping games with negative expected value are combined into a winning game. Parrondo games are state-dependent. By identifying the game state…
We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score…