Optimality and Complexity of Pure Nash Equilibria in the Coverage Game
In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense t...
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Veröffentlicht in: | IEEE journal on selected areas in communications 2008-09, Vol.26 (7), p.1170-1182 |
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creator | Xin Ai Srinivasan, V. Chen-khong Tham |
description | In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense the field. A key challenge is to achieve this partition in a distributed manner with purely local information and yet provide near optimal coverage. We appropriately formulate this coverage problem as a coverage game and prove that the optimal solution is a pure Nash equilibrium. Then, we design synchronous and asynchronous algorithms, which converge to pure Nash equilibria. Moreover, we analyze the optimality and complexity of pure Nash equilibria in the coverage game. We prove that, the ratio between the optimal coverage and the worst case Nash equilibrium coverage, is upper bounded by 2 - 1/m+1 (m is the maximum number of nodes, which cover any point, in the Nash equilibrium solution s*). We prove that finding pure Nash equilibria in the general coverage game is PLS-complete, i.e. "as hard as that of finding a local optimum in any local search problem with efficient computable neighbors". Finally, via extensive simulations, we show that, the Nash equilibria coverage performance is very close to the optimal coverage and the convergence speed is sublinear. Even under the noisy environment, our algorithms can still converge to the pure Nash equilibria. |
doi_str_mv | 10.1109/JSAC.2008.080914 |
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We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense the field. A key challenge is to achieve this partition in a distributed manner with purely local information and yet provide near optimal coverage. We appropriately formulate this coverage problem as a coverage game and prove that the optimal solution is a pure Nash equilibrium. Then, we design synchronous and asynchronous algorithms, which converge to pure Nash equilibria. Moreover, we analyze the optimality and complexity of pure Nash equilibria in the coverage game. We prove that, the ratio between the optimal coverage and the worst case Nash equilibrium coverage, is upper bounded by 2 - 1/m+1 (m is the maximum number of nodes, which cover any point, in the Nash equilibrium solution s*). We prove that finding pure Nash equilibria in the general coverage game is PLS-complete, i.e. "as hard as that of finding a local optimum in any local search problem with efficient computable neighbors". Finally, via extensive simulations, we show that, the Nash equilibria coverage performance is very close to the optimal coverage and the convergence speed is sublinear. Even under the noisy environment, our algorithms can still converge to the pure Nash equilibria.</description><identifier>ISSN: 0733-8716</identifier><identifier>EISSN: 1558-0008</identifier><identifier>DOI: 10.1109/JSAC.2008.080914</identifier><identifier>CODEN: ISACEM</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithm design and analysis ; Computational modeling ; Convergence ; coverage ; Game theory ; Nash equilibrium ; Partitioning algorithms ; Scattering ; Search problems ; Studies ; Wireless sensor networks ; Working environment noise</subject><ispartof>IEEE journal on selected areas in communications, 2008-09, Vol.26 (7), p.1170-1182</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c450t-aafda99a09ac3570ee96ed8004db7bfda301f879b57c55e6501168477db1eecd3</citedby><cites>FETCH-LOGICAL-c450t-aafda99a09ac3570ee96ed8004db7bfda301f879b57c55e6501168477db1eecd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4604742$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4604742$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Xin Ai</creatorcontrib><creatorcontrib>Srinivasan, V.</creatorcontrib><creatorcontrib>Chen-khong Tham</creatorcontrib><title>Optimality and Complexity of Pure Nash Equilibria in the Coverage Game</title><title>IEEE journal on selected areas in communications</title><addtitle>J-SAC</addtitle><description>In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense the field. A key challenge is to achieve this partition in a distributed manner with purely local information and yet provide near optimal coverage. We appropriately formulate this coverage problem as a coverage game and prove that the optimal solution is a pure Nash equilibrium. Then, we design synchronous and asynchronous algorithms, which converge to pure Nash equilibria. Moreover, we analyze the optimality and complexity of pure Nash equilibria in the coverage game. We prove that, the ratio between the optimal coverage and the worst case Nash equilibrium coverage, is upper bounded by 2 - 1/m+1 (m is the maximum number of nodes, which cover any point, in the Nash equilibrium solution s*). We prove that finding pure Nash equilibria in the general coverage game is PLS-complete, i.e. "as hard as that of finding a local optimum in any local search problem with efficient computable neighbors". Finally, via extensive simulations, we show that, the Nash equilibria coverage performance is very close to the optimal coverage and the convergence speed is sublinear. Even under the noisy environment, our algorithms can still converge to the pure Nash equilibria.</description><subject>Algorithm design and analysis</subject><subject>Computational modeling</subject><subject>Convergence</subject><subject>coverage</subject><subject>Game theory</subject><subject>Nash equilibrium</subject><subject>Partitioning algorithms</subject><subject>Scattering</subject><subject>Search problems</subject><subject>Studies</subject><subject>Wireless sensor networks</subject><subject>Working environment noise</subject><issn>0733-8716</issn><issn>1558-0008</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkb1PwzAQxS0EEqWwI7FEDDClnGM7dsaqaguookjAHDnJhabKR2sniP73OApiYIDJsv1773TvEXJJYUIpRHePL9PZJABQE1AQUX5ERlQI5YN7OiYjkIz5StLwlJxZuwWgnKtgRBbrXVtUuizag6frzJs11a7Ez_7a5N5zZ9B70nbjzfddURaJKbRX1F67QUd-oNHv6C11hefkJNelxYvvc0zeFvPX2b2_Wi8fZtOVn3IBra91nuko0hDplAkJiFGImQLgWSIT98eA5kpGiZCpEBgKoDRUXMosoYhpxsbkdvDdmWbfoW3jqrAplqWuselsrGRAORUhd-TNnyTjIpBMsX9Bl2moXHIOvP4FbpvO1G7dWIWBdFNl7wYDlJrGWoN5vDMuX3OIKcR9UXFfVG-q4qEoJ7kaJAUi_uA8BC55wL4AS7uNPA</recordid><startdate>20080901</startdate><enddate>20080901</enddate><creator>Xin Ai</creator><creator>Srinivasan, V.</creator><creator>Chen-khong Tham</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><scope>7U1</scope><scope>7U2</scope><scope>C1K</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20080901</creationdate><title>Optimality and Complexity of Pure Nash Equilibria in the Coverage Game</title><author>Xin Ai ; Srinivasan, V. ; Chen-khong Tham</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c450t-aafda99a09ac3570ee96ed8004db7bfda301f879b57c55e6501168477db1eecd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Algorithm design and analysis</topic><topic>Computational modeling</topic><topic>Convergence</topic><topic>coverage</topic><topic>Game theory</topic><topic>Nash equilibrium</topic><topic>Partitioning algorithms</topic><topic>Scattering</topic><topic>Search problems</topic><topic>Studies</topic><topic>Wireless sensor networks</topic><topic>Working environment noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xin Ai</creatorcontrib><creatorcontrib>Srinivasan, V.</creatorcontrib><creatorcontrib>Chen-khong Tham</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Risk Abstracts</collection><collection>Safety Science and Risk</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE journal on selected areas in communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Xin Ai</au><au>Srinivasan, V.</au><au>Chen-khong Tham</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimality and Complexity of Pure Nash Equilibria in the Coverage Game</atitle><jtitle>IEEE journal on selected areas in communications</jtitle><stitle>J-SAC</stitle><date>2008-09-01</date><risdate>2008</risdate><volume>26</volume><issue>7</issue><spage>1170</spage><epage>1182</epage><pages>1170-1182</pages><issn>0733-8716</issn><eissn>1558-0008</eissn><coden>ISACEM</coden><abstract>In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense the field. A key challenge is to achieve this partition in a distributed manner with purely local information and yet provide near optimal coverage. We appropriately formulate this coverage problem as a coverage game and prove that the optimal solution is a pure Nash equilibrium. Then, we design synchronous and asynchronous algorithms, which converge to pure Nash equilibria. Moreover, we analyze the optimality and complexity of pure Nash equilibria in the coverage game. We prove that, the ratio between the optimal coverage and the worst case Nash equilibrium coverage, is upper bounded by 2 - 1/m+1 (m is the maximum number of nodes, which cover any point, in the Nash equilibrium solution s*). We prove that finding pure Nash equilibria in the general coverage game is PLS-complete, i.e. "as hard as that of finding a local optimum in any local search problem with efficient computable neighbors". Finally, via extensive simulations, we show that, the Nash equilibria coverage performance is very close to the optimal coverage and the convergence speed is sublinear. Even under the noisy environment, our algorithms can still converge to the pure Nash equilibria.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/JSAC.2008.080914</doi><tpages>13</tpages></addata></record> |
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subjects | Algorithm design and analysis Computational modeling Convergence coverage Game theory Nash equilibrium Partitioning algorithms Scattering Search problems Studies Wireless sensor networks Working environment noise |
title | Optimality and Complexity of Pure Nash Equilibria in the Coverage Game |
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