{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:31:26Z","timestamp":1787322686884,"version":"build-2736575974"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>Aiming to provide a new class of game dynamics with good long-term convergence properties, we derive a second-order inertial system that builds on the widely studied \u201cheavy ball with friction\u201d optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framework where trajectories are accelerated by the players' unilateral payoff gradients and they slow down near Nash equilibria. Surprisingly (and in stark contrast to another second-order variant of the replicator dynamics), the inertial replicator dynamics are not well-posed; on the other hand, it is possible to obtain a well-posed system by endowing the mixed strategy space with a different Hessian--Riemannian (HR) metric structure, and we characterize those HR geometries that do so. In the single-agent version of the dynamics (corresponding to constrained optimization over simplex-like objects), we show that regular maximum points of smooth functions attract all nearby solution orbits with low initial speed. More generally, we establish an inertial variant of the so-called folk theorem of evolutionary game theory, and we show that strict equilibria are attracting in asymmetric (multipopulation) games, provided, of course, that the dynamics are well-posed. A similar asymptotic stability result is obtained for evolutionarily stable states in symmetric (single-population) games.<\/jats:p>","DOI":"10.1137\/130920253","type":"journal-article","created":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T12:48:35Z","timestamp":1444135715000},"page":"3141-3170","source":"Crossref","is-referenced-by-count":9,"title":["Inertial Game Dynamics and Applications to Constrained Optimization"],"prefix":"10.1137","volume":"53","author":[{"given":"Rida","family":"Laraki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Panayotis","family":"Mertikopoulos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,10,6]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"E. 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