2 citations · 4 across the 9 of their papers we have counts for
10 papers
The Test and Find Model
Michael Grabchak, Xingjie Li, Isaac M. Sonin
We introduce the Test and Find (TF) problem, where a decision maker (DM) faces the following situation: identical objects are randomly allocated to distinct boxes (sites) a…
The Game of Marginal Utilities
Isaac M. Sonin, Georgy Gaitsgori, Yaakov Malinovsky
We study a noncooperative resource-allocation game in which players distribute fixed resources among projects and the payoff of player is given by \[ F^j(x) = \sum_{i=1…
The Water Puzzle and Marginal Utility Optimization
Yaakov Malinovsky, Isaac M. Sonin
We present a variation of the water puzzle, which is related to a simple model of marginal utility. The problem has an intriguing solution and can be extended in several directions…
Symmetric Case of Locks, Bombs and Testing Model
Isaac M. Sonin
We present a Defense/Attack resource allocation model, where Defender has some number of ``locks" to protect vulnerable boxes (sites), and Attacker is trying to destroy these b…
A Zero-One Law for Markov Chains
Michael Grabchak, Isaac Sonin
We prove an analog of the classical Zero-One Law for both homogeneous and nonhomogeneous Markov chains (MC). Its almost precise formulation is simple: given any event from the…
Bayesian Game of Locks, Bombs and Testing
Isaac M. Sonin
We consider the game with discrete units of resources for protection and destruction of some sites. In our model, Defender (DF) has locks and Attacker (AT) has bombs to allocate am…
Some Nontrivial Properties of a Formula for Compound Interest
Isaac M. Sonin, Mark Whitmeyer
We analyze the classical model of compound interest with a constant per-period payment and interest rate. We examine the outstanding balance function as well as the periodic paymen…
Banks as Tanks: A Continuous-Time Model of Financial Clearing
Isaac M. Sonin, Konstantin Sonin
We present a simple continuous-time model of clearing in financial networks. Financial firms are represented as "tanks" filled with fluid (money), flowing in and out. Once "pipes"…
Independent Events in a Simple Random Experiment and the Meaning of Independence
Isaac M. Sonin
We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first numb…
On some estimates for bounded submartingales and the shift inequality
Leonid Galtchouk, Isaac Sonin
It is well known that if a submartingale is bounded then the increasing predictable process and the martingale from the Doob decomposition can be unbounded. I…