Abstract
We study search games in which the hider may hide in a finite number of locations. We assume that the cost of searching these locations does not depend on the order in which the locations are searched. From these assumptions we derive that the cost function is submodular, thus placing search games with an immobile hider in the context of coalitional games.
Highlights
Alpern and Asic (1985) defined the search value of a network by means of a search game that takes place on the network
The payoff of the search game is given by a submodular cost function f : 2X
Hider chooses a place to hide from a finite number of locations. Searcher goes through these locations one by one, and the game ends as soon as Searcher selects Hider’s location. This game is known as a search game on discrete locations with an immobile hider
Summary
Alpern and Asic (1985) defined the search value of a network by means of a search game that takes place on the network. Hider chooses a place to hide from a finite number of locations. Searcher goes through these locations one by one, and the game ends as soon as Searcher selects Hider’s location This game is known as a search game on discrete locations with an immobile hider. In this paper we want to study search games that are not necessarily placed on a network, and we follow an axiomatic approach, imposing general conditions only. In this game, Hider wants to maximize and Searcher wants to minimize the total cost of the search operation. We will often omit brackets for singletons and write f (x) instead of the more accurate f ({x})
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