A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial (PS) mechanism that is an anonymous, neutral, Pareto optimal, and weak strategyproof mechanism when the preferences are considered with respect to stochastic ...

Traditional accounts of quantifier scope employ qualitative constraints or rules to account for scoping preferences. This paper outlines a feature-based parsing algorithm for a grammar with multiple simultaneous levels of representation, one of which corresponds to a partial ordering among quantifiers according to scope. The optimal such ordering (as well as the ranking of other orderings) is d...

In this paper we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental ”ergodicity” property for a class of ”infinitesimal control systems” associated with the fast mode, we show that th...

Abstract: Each period, a player must choose an action without knowing the outcome that will be chosen by “Nature,” according to an unknown and possibly history-dependent stochastic rule. We discuss have a class of procedures that assign observations to categories, and prescribe a simple randomized variation of fictitious play within each category. These procedures are “conditionally consistent,...

In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, som...

This paper introduces the concept of random context representations for the transition probabilities of a finitealphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length Markov chains), and are proven to coincide with processes whose transition probabilities are almost surely continuous functions of the (infinite) past. This is s...

Abstract. We consider a linear-quadratic-Gaussian (LQG) optimal control problem where the generalized state space is the product of an Euclidian space and an infinite dimensional function space. This model originates from a mean field LQG game with a major player and a large number of minor players, and has importance in designing decentralized strategies in the game. We show that the underlyin...

We consider the problem of repeatedly matching a set of alternatives to a set of agents with dynamic ordinal preferences. Despite a recent focus on designing one-shot matching mechanisms in the absence of monetary transfers, little study has been done on strategic behavior of agents in sequential assignment problems. We formulate a generic dynamic matching problem via a sequential stochastic ma...

We consider the problem of finding a stopping time that minimises the L1distance to θ, the time at which a Lévy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a finite time horizon. We consider a general Lévy process and an infinite time horizon (only compound Poisson processes are excluded, furthermore due to the infinite horizon th...

Quantification of demand flexibility is key importance to decision makers at the planning level, when designing response programs and determining capacity requirements for new battery storage installations, and, operation assessing demand-side potential providing grid services. While different frameworks have been proposed quantification, literature still lacks a framework that considers uncert...