A search game taking account of attributes of searching resources

This article deals with a two‐person zero‐sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 2008     

An inspection game: Taking account of fulfillment probabilities of players' aims

This paper deals with an inspection game of customs and a smuggler. The customs can take two options of assigning a patrol or not. The smuggler has two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take actions during a limited number of days. When both players do, there are some possibilities that the customs captures the smuggler and, simultaneously, the smuggler possibly makes a success of the smuggling. If the smuggler is captured or there remain no days for playing the game, the game ends. In this paper, we formulate the problem into a multi‐stage two‐person zero‐sum stochastic game and investigate some characteristics of the equilibrium solution, some of which are given in a closed form in a special case. There have been some studies so far on the inspection game. However, some consider the case that the smuggler has only one opportunity of smuggling or the perfect‐capture case that the customs can certainly arrest the smuggler on patrol, and others think of a recursive game without the probabilities of fulfilling the players' purposes. In this paper, we consider the inspection game taking account of the fulfillment probabilities of the players' aims. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Discrete search allocation game with false contacts

This paper deals with a two‐person zero‐sum game called a search allocation game, where a searcher and a target participate, taking account of false contacts. The searcher distributes his search effort in a search space in order to detect the target. On the other hand, the target moves to avoid the searcher. As a payoff of the game, we take the cumulative amount of search effort weighted by the target distribution, which can be derived as an approximation of the detection probability of the target. The searcher's strategy is a plan of distributing search effort and the target's is a movement represented by a path or transition probability across the search space. In the search, there are false contacts caused by environmental noises, signal processing noises, or real objects resembling true targets. If they happen, the searcher must take some time for their investigation, which interrupts the search for a while. There have been few researches dealing with search games with false contacts. In this paper, we formulate the game into a mathematical programming problem to obtain its equilibrium point. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A cooperative game in search theory

Search theory originates from the military research efforts of WWII. Most researchers of that period modeled their search games in noncooperative games, where players are enemies or compete against each other. In this article, we deal with a cooperative search game, where multiple searchers behave cooperatively. First we describe several search problems and discuss the possibility of a coalition or cooperation among searchers. For the cooperative search game, we define a function named quasi‐characteristic function, which gives us a criterion similar to the so‐called characteristic function in the general coalition game with transferable utility. The search operation includes a kind of randomness with respect to whether the searchers can detect a target and get the value of the target. We also propose a methodology to divide the obtained target value among members of the coalition taking account of the randomness. As a concrete problem of the cooperative search game, we take the so‐called search allocation game, where searchers distribute their searching resources to detect a target in a cooperative way and the target moves in a search space to evade the searchers. Lastly, we discuss the core of the cooperative search allocation game. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009