Stochastic Approximations and Differential Inclusions, Part II: Applications

References

• Aubin J.-P.Viability Theory (1991) (Birkhäuser)Google Scholar
• Auer P., Cesa-Bianchi N., Freund Y., Schapire R. E. Gambling in a rigged casino: The adversarial multi-armed bandit problem. Proc. 36th Annual IEEE Sympos. Foundations Comput. Sci. (1995) 322–331Crossref, Google Scholar
• Auer P., Cesa-Bianchi N., Freund Y., Schapire R. E. The nonstochastic multiarmed bandit problem. SIAM J. Comput. (2002) 32:48–77Crossref, Google Scholar
• Banos A. On pseudo-games. Ann. Math. Statist. (1968) 39:1932–1945Crossref, Google Scholar
• Benaïm M. A dynamical system approach to stochastic approximation. SIAM J. Control Optim. (1996) 34:437–472Crossref, Google Scholar
• Benaïm M. Dynamics of stochastic approximation algorithms. Séminaire de Probabilités XXXIII, Lecture Notes in Mathematics (1999) 1709(Springer)1–68Crossref, Google Scholar
• Benaïm M., Arous G. Ben. A two armed bandit type problem. Internat. J. Game Theory (2003) 32:3–16Crossref, Google Scholar
• Benaïm M., Hirsch M. W. Asymptotic pseudotrajectories and chain recurrent flows, with applications. J. Dynam. Differential Equations (1996) 8:141–176Crossref, Google Scholar
• Benaïm M., Hirsch M. W. Mixed equilibria and dynamical systems arising from fictitious play in perturbed games. Games Econom. Behav. (1999) 29:36–72Crossref, Google Scholar
• Benaïm M., Hofbauer J., Sorin S. Stochastic approximations and differential inclusions. SIAM J. Control Optim. (2005) 44:328–348Crossref, Google Scholar
• Blackwell D. An analog of the minmax theorem for vector payoffs. Pacific J. Math. (1956) 6:1–8Crossref, Google Scholar
• Brown G., Koopmans T. C. Iterative solution of games by fictitious play. Activity Analysis of Production and Allocation (1951) (Wiley)374–376Google Scholar
• Cahn A. General procedures leading to correlated equilibria. Internat. J. Game Theory (2004) 33:21–40Crossref, Google Scholar
• Duflo M.Algorithmes Stochastiques (1996) (Springer)Google Scholar
• Foster D., Vohra R. Calibrated learning and correlated equilibria. Games Econom. Behav. (1997) 21:40–55Crossref, Google Scholar
• Foster D., Vohra R. Asymptotic calibration. Biometrika (1998) 85:379–390Crossref, Google Scholar
• Foster D., Vohra R. Regret in the on-line decision problem. Games Econom. Behav. (1999) 29:7–35Crossref, Google Scholar
• Freund Y., Schapire R. E. Adaptive game playing using multiplicative weights. Games Econom. Behav. (1999) 29:79–103Crossref, Google Scholar
• Fudenberg D., Levine D. K. Consistency and cautious fictitious play. J. Econom. Dynam. Control (1995) 19:1065–1089Crossref, Google Scholar
• Fudenberg D., Levine D. K.The Theory of Learning in Games (1998) (MIT Press)Google Scholar
• Fudenberg D., Levine D. K. Conditional universal consistency. Games Econom. Behav. (1999) 29:104–130Crossref, Google Scholar
• Hannan J., Dresher M., Tucker A. W., Wolfe P. Approximation to Bayes risk in repeated plays. Contributions to the Theory of Games (1957) III(Princeton University Press, Princeton, NJ) 97–139Google Scholar
• Hart S. Adaptive heuristics. Econometrica (2005) 73:1401–1430Crossref, Google Scholar
• Hart S., Mas-Colell A. A simple adaptive procedure leading to correlated equilibria. Econometrica (2000) 68:1127–1150Crossref, Google Scholar
• Hart S., Mas-Colell A. A general class of adaptive strategies. J. Econom. Theory (2001) 98:26–54Crossref, Google Scholar
• Hart S., Mas-Colell A., Debreu G., Neuefeind W., Trockel W. A reinforcement procedure leading to correlated equilibria. Economic Essays: A Festschrift for W. Hildenbrandt (2001) (Springer)181–200Crossref, Google Scholar
• Hart S., Mas-Colell A. Regret-based continuous time dynamics. Games Econom. Behav. (2003) 45:375–394Crossref, Google Scholar
• Hofbauer J., Sandholm W. H. On the global convergence of stochastic fictitious play. Econometrica (2002) 70:2265–2294Crossref, Google Scholar
• Hofbauer J., Sorin S. Best response dynamics for continuous zero-sum games. Discrete Contin. Dynamical Systems, Series B (2006) 6:215–224Google Scholar
• Megiddo N. On repeated games with incomplete information played by non-Bayesian players. Internat. J. Game Theory (1980) 9:157–167Crossref, Google Scholar
• Métivier M., Priouret P. Théorèmes de convergence presque-sûre pour une classe d’algorithmes stochastiques à pas décroissants. Probab. Theory Related Fields (1992) 74:403–438Crossref, Google Scholar
• Robinson J. An iterative method of solving a game. Ann. Math. (1951) 54:296–301Crossref, Google Scholar
• Sorin S.A First Course on Zero-Sum Repeated Games (2002) (Springer)Google Scholar