{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:55Z","timestamp":1787321275409,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are \u201cpayoff-based\u201d processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network.<\/jats:p>","DOI":"10.1137\/070680199","type":"journal-article","created":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T23:04:59Z","timestamp":1234393499000},"page":"373-396","source":"Crossref","is-referenced-by-count":191,"title":["Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games"],"prefix":"10.1137","volume":"48","author":[{"given":"Jason R.","family":"Marden","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H. Peyton","family":"Young","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G\u00fcrdal","family":"Arslan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff S.","family":"Shamma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1115\/1.2766722"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.809145"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01918335"},{"key":"R4","first-page":"341","volume":"1","author":"Foster D. P.","year":"2006","journal-title":"Theoret. Econom."},{"key":"R5","unstructured":"D. Fudenberg and D. K. Levine,\n                      The Theory of Learning in Games\n                      , MIT Press, Cambridge, MA, 1998."},{"key":"R6","unstructured":"D. Fudenberg and J. Tirole,\n                      Game Theory\n                      , MIT Press, Cambridge, MA, 1991."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. Ganguli, S. Susca, S. Martinez, F. Bullo, and J. Cortes,\n                      On collective motion in sensor networks: Sample problems and distributed algorithms\n                      , in Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005, pp. 4239\u20134244.","DOI":"10.1109\/CDC.2005.1582828"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2006.06.001"},{"key":"R9","unstructured":"S. B. Gershwin,\n                      Manufacturing Systems Engineering\n                      , Prentice-Hall, Englewood Cliffs, NJ, 1994."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00625.x"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"J. Hofbauer and K. 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Shamma,\n                      Regret based dynamics: Convergence in weakly acyclic games\n                      , in Proceedings of the 6th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), Honolulu, HI, 2007, article 42.","DOI":"10.1145\/1329125.1329175"},{"key":"R15","unstructured":"J. R. Marden, G. Arslan, and J. S. Shamma,\n                      Joint strategy fictitious play with inertia for potential games\n                      , IEEE Trans. Automat. Control, to appear."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.1996.0014"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"R. Montenegro and P. 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