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A probabilistic approach to compute strategies for players of a search game in a bounded space

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Abstract

In this article, we present a unique search game model to search/hide an immobile object by/from a mobile sensor in a two-dimensional bounded space. In the proposed model, the mobile sensor is a searcher, the immobile object is a target and the search space is a square/rectangular region. The proposed model is suitable for the case where the searcher has no prior knowledge about the probability distribution of the target location in the region. The game model helps the players (searcher and target) to choose their best response strategies considering all possible strategies of their respective opponents and computes the expected payoffs and Nash Equilibrium of the game. The novelty of the proposed model is to guide both the players to choose their best response strategies. The proposed model is set up as follows: Initially, the search space which is a square/rectangular region is divided into square blocks of equal size to represent it as a grid and the distance is measured from the starting block of the searcher to all other blocks using shortest path followed by which the transition probabilities of each block is determined. Once the payoff matrix is obtained, we use lrslib tool to compute the mixed strategies, Nash equilibria and expected payoffs. The proposed model is applicable in real-time scenarios which involve large square/rectangular grids where the number of blocks is large.

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Acknowledgements

We are thankful to Dr. Debasish Pradhan, faculty member of Dept. of Applied Mathematics, DIAT and Ms. Monica Ravishankar, research scholar of Dept. of Computer Science And Engineering, DIAT for their valuable suggestions.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Defence Institute of Advanced Technology (DRDO), Pune, Maharashtra, India

    Tanmoy Hazra, Manisha Nene & C. R. S. Kumar

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  1. Tanmoy Hazra
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  2. Manisha Nene
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  3. C. R. S. Kumar
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Correspondence to Tanmoy Hazra.

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Hazra, T., Nene, M. & Kumar, C.R.S. A probabilistic approach to compute strategies for players of a search game in a bounded space. CSIT 5, 305–313 (2017). https://doi.org/10.1007/s40012-017-0175-7

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  • DOI: https://doi.org/10.1007/s40012-017-0175-7

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