Optimal search for a moving target with the option to wait

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

A continuous game of ambush

The article considers a two-person competitive problem in which a traveller wishes to choose a path across a rectangle from left to right in such a way as to avoid being ambushed by his adversary who has placed obstacles within the rectangle. Our results supplement those that have already been obtained by Ruckle and they indicate that, under certain conditions, the players need to adopt rather sophisticated strategies if they are to act optimally. This suggests that a complete solution to the problem could be difficult.     

On estimating population characteristics from record-breaking observations II. Nonparametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. Such data arise in life testing and stress testing and in industrial quality-control experiments. When only a single sequence of random records are available, efficient estimation of the underlying distribution F is possible only in a parametric framework (see Samaniego and Whitaker [9]). In the present article we study the problem of estimating certain population quantiles nonparametrically from such data. Furthermore, under the assumption that the process of observing random records can be replicated, we derive and study the nonparametric maximum-likelihood estimator F̂ of F. We establish the strong uniform consistency of this estimator as the number of replications grows large, and identify its asymptotic distribution theory. The performance of F̂ is compared to that of two possible competing estimators.     

Unblocking inertia: US-Russian nuclear arms control and missile defenses

The United States and Russia, in the aftermath of Russia’s annexation of Crimea and destabilization of Ukraine, seem to have ditched entirely the “reset” in their political relations. Despite this odor of Cold War redux, there remain the opportunities and necessities for renewed attention to strategic nuclear arms control as between the two governments. US and NATO missile defenses as planned for European deployment figure into this equation, although in somewhat unpredictable ways, given technological uncertainties in existing and foreseeable defenses, as well as the possibility of improved delivery systems for offensive conventional or nuclear weapons.