Related papers: Competition between Discrete Random Variables, wit…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…
We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of union of edges. These polynomials arise naturally to model job-occupancy in…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…
We study a spatial two-strategy (cooperation and defection) Prisoner's Dilemma game with two types ($A$ and $B$) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy…
We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the…
This work focuses on Exchangeable Occupancy Models (EOM) and their relations with the Uniform Order Statistics Property (UOSP) for point processes in discrete time. As our main purpose, we show how definitions and results presented in…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies…
For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…
We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. Our focus is on picking…
In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…
In this paper, we study a variant of hedonic games, called \textsc{Seat Arrangement}. The model is defined by a bijection from agents with preferences for each other to vertices in a graph $G$. The utility of an agent depends on the…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…
Fairness and privacy are two important concerns in social decision-making processes such as resource allocation. We study privacy in the fair allocation of indivisible resources using the well-established framework of differential privacy.…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…