On the Characterization of Local Nash Equilibria in Continuous Games
We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equi...
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| Veröffentlicht in: | IEEE transactions on automatic control 2016-08, Vol.61 (8), p.2301-2307 |
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| container_title | IEEE transactions on automatic control |
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| creator | Ratliff, Lillian J. Burden, Samuel A. Sastry, S. Shankar |
| description | We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria. Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games. |
| doi_str_mv | 10.1109/TAC.2016.2583518 |
| format | Article |
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We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.</description><subject>Automatic control</subject><subject>Cost function</subject><subject>Game theory</subject><subject>Games</subject><subject>Manganese</subject><subject>Manifolds</subject><subject>Nash equilibrium</subject><subject>optimization</subject><subject>Programming</subject><subject>Strategy</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkD1PwzAQhi0EEqWwI7FYYmFJ8fkjiccqlIJU0aXMluM4qqs0bu1kgF-PqyIGptNJz3t670HoHsgMgMjnzbyaUQL5jIqSCSgv0ASEKDMqKLtEE0KgzCQt82t0E-MurTnnMEEv6x4PW4urrQ7aDDa4bz0432Pf4pU3usMfOm7x4ji6ztXBaex6XPl-cP3ox4iXem_jLbpqdRft3e-cos_XxaZ6y1br5Xs1X2WGST5kudQaDNFaiEZYZg1rc9bIQoLkBhpopOHAm5blstGGS9lqagTUtqY1gBVsip7Odw_BH0cbB7V30diu071NZRSkz9NbFFhCH_-hOz-GPrVLFCkkJTmniSJnygQfY7CtOgS31-FLAVEnrSppVSet6ldrijycI85a-4cXXBaCUfYD5w9yPg</recordid><startdate>201608</startdate><enddate>201608</enddate><creator>Ratliff, Lillian J.</creator><creator>Burden, Samuel A.</creator><creator>Sastry, S. 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| subjects | Automatic control Cost function Game theory Games Manganese Manifolds Nash equilibrium optimization Programming Strategy |
| title | On the Characterization of Local Nash Equilibria in Continuous Games |
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