{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:23:13Z","timestamp":1753881793599,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p> The matrix [Formula: see text] of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemke\u2019s algorithm can be successfully applied to reach a complementary solution or infeasibility when the game satisfies the following conditions: (i) Value of [Formula: see text] is equal to zero. (ii) For all principal minors of [Formula: see text] (transpose of [Formula: see text]) value is non-negative. (iii) For any optimal mixed strategy [Formula: see text] of the maximizer either [Formula: see text] or [Formula: see text] for each coordinate [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219198922500190","type":"journal-article","created":{"date-parts":[[2022,7,16]],"date-time":"2022-07-16T04:00:01Z","timestamp":1657944001000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on Linear Complementarity via Two-Person Zero-Sum Games"],"prefix":"10.1142","volume":"25","author":[{"given":"Dipti","family":"Dubey","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shiv Nadar University, Dadri, UP 201314, India"}]},{"given":"S. K.","family":"Neogy","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi 110016, India"}]},{"given":"T. E. 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