Physical search problems applying economic search models

This paper considers the problem of an agent searching for a resource or a tangible good in a physical environment, where at each stage of its search it observes one source where this good can be found. The cost of acquiring the resource or good at a given source is uncertain (a-priori), and the agent can observe its true value only when physically arriving at the source. Sample applications involving this type of search include agents in exploration and patrol missions (e.g., an agent seeking to find the best location to deploy sensing equipment along its path). The uniqueness of these settings is that the expense of observing the source on each step of the process derives from the last source the agent explored. We analyze three variants of the problem, differing in their objective: minimizing the total expected cost, maximizing the success probability given an initial budget, and minimizing the budget necessary to obtain a given success probability. For each variant, we first introduce and analyze the problem with a single agent, either providing a polynomial solution to the problem or proving it is NP-Complete. We also introduce an innovative fully polynomial time approximation scheme algorithm for the minimum budget variant. Finally, the results for the single agent case are generalized to multi-agent settings.