Percolation Games

References

• [1] Alon N, Rudov K, Yariv L (2021) Dominance solvability in random games. Preprint, submitted May 22, https://arxiv.org/abs/2105.10743.Google Scholar
• [2] Amiet B, Collevecchio A, Scarsini M, Zhong Z (2021) Pure Nash equilibria and best-response dynamics in random games. Math. Oper. Res. 46(4):1552–1572.Link, Google Scholar
• [3] Armstrong S, Cardaliaguet P (2015) Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations. Comm. Partial Differential Equations 40(3):540–600.Crossref, Google Scholar
• [4] Armstrong S, Cardaliaguet P (2018) Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc. 20(4):797–864.Crossref, Google Scholar
• [5] Armstrong S, Smart C (2012) A finite difference approach to the infinity Laplace equation and tug-of-war games. Trans. Amer. Math. Soc. 364(2):595–636.Crossref, Google Scholar
• [6] Armstrong S, Souganidis P (2012) Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments. J. Math. Pures Appl. 97(5):460–504.Crossref, Google Scholar
• [7] Armstrong S, Souganidis P (2013) Stochastic homogenization of level-set convex Hamilton-Jacobi equations. Internat. Math. Res. Notices 2013(15):3420–3449.Crossref, Google Scholar
• [8] Armstrong S, Tran H (2014) Stochastic homogenization of viscous Hamilton-Jacobi equations and applications. Anal. PDE 7(8):1969–2007.Crossref, Google Scholar
• [9] Armstrong S, Cardaliaguet P, Souganidis PE (2014) Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations. J. Amer. Math. Soc., 27(2):479–540.Crossref, Google Scholar
• [10] Armstrong S, Tran H, Yu Y (2015) Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Calculus Variations Partial Differential Equations 54(2):1507–1524.Crossref, Google Scholar
• [11] Attia L, Oliu-Barton M (2019) A formula for the value of a stochastic game. Proc. Natl. Acad. Sci. USA 116(52):26435–26443.Crossref, Google Scholar
• [12] Bewley T, Kohlberg E (1976) The asymptotic theory of stochastic games. Math. Oper. Res. 1(3):197–208.Link, Google Scholar
• [13] Cardaliaguet P (2010) Ergodicity of Hamilton–Jacobi equations with a noncoercive nonconvex Hamiltonian. Annales de l’IHP Analyse non linéaire 27:837–856.Google Scholar
• [14] Davini A, Kosygina E (2020) Stochastic homogenization of a class of nonconvex viscous Hamilton-Jacobi equations in one space dimension. Preprint, submitted February 6, https://arxiv.org/abs/2002.02263.Google Scholar
• [15] de Bruijn N, Erdös P (1952) Some linear and some quadratic recursion formulas. II. Proc. Koninklijke Nederlandse Akademie van Wetenschappen Ser. A Math. Sci. 14:152–163.Google Scholar
• [16] Evans L (2014) Envelopes and nonconvex Hamilton–Jacobi equations. Calculus Variations Partial Differential Equations 50(1–2):257–282.Crossref, Google Scholar
• [17] Evans L, Souganidis P (1984) Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations. Indiana Univ. Math. J. 33(5):773–797.Crossref, Google Scholar
• [18] Fehrman B (2014) A partial homogenization result for nonconvex viscous Hamilton-Jacobi equations. Preprint, submitted February 21, https://arxiv.org/abs/1402.5191.Google Scholar
• [19] Feldman W, Souganidis P (2017) Homogenization and non-homogenization of certain non-convex Hamilton–Jacobi equations. J. Math. Pures Appl. 108(5):751–782.Crossref, Google Scholar
• [20] Feldman W, Fermanian J-B, Ziliotto B (2021) An example of failure of stochastic homogenization for viscous Hamilton-Jacobi equations without convexity. J. Differential Equations 280:464–476.Crossref, Google Scholar
• [21] Gao H (2016) Random homogenization of coercive Hamilton–Jacobi equations in 1d. Calculus Variations Partial Differential Equations 55(2):30.Crossref, Google Scholar
• [22] Hansen K, Koucky M, Lauritzen N, Miltersen P, Tsigaridas E (2011) Exact algorithms for solving stochastic games. Proc. 43rd Annual ACM Sympos. Theory Comput., 205–214.Google Scholar
• [23] Heinrich T, Jang Y, Mungo L, Pangallo M, Scott A, Tarbush B, Wiese S (2021) Best-response dynamics, playing sequences, and convergence to equilibrium in random games. Preprint, submitted January 11, https://arxiv.org/abs/2101.04222.Google Scholar
• [24] Imbert C, Serfaty S (2011) Repeated games for non-linear parabolic integro-differential equations and integral curvature flows. Discrete Continuous Dynamical Systems 29(4):1517–1552.Crossref, Google Scholar
• [25] Jaśkiewicz A, Nowak A (2016) Non-zero-sum stochastic games. Handbook of Dynamic Game Theory (Springer, New York), 1–64.Google Scholar
• [26] Kohn R, Serfaty S (2006) A deterministic-control-based approach motion by curvature. Comm. Pure Appl. Math. 59(3):344–407.Crossref, Google Scholar
• [27] Kohn R, Serfaty S (2010) A deterministic-control-based approach to fully nonlinear parabolic and elliptic equations. Comm. Pure Appl. Math. 63(10):1298–1350.Crossref, Google Scholar
• [28] Kosygina E, Rezakhanlou F, Varadhan SRS (2006) Stochastic homogenization of Hamilton-Jacobi-Bellman equations. Comm. Pure Appl. Math. 59(10):1489–1521.Crossref, Google Scholar
• [29] Lions PL, Souganidis P (2003) Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Comm. Pure Appl. Math. 56(10):1501–1524.Crossref, Google Scholar
• [30] Lions PL, Souganidis P (2005) Homogenization of “viscous” Hamilton-Jacobi equations in stationary ergodic media. Comm. Partial Differential Equations 30(1–3):335–375.Crossref, Google Scholar
• [31] Lions PL, Souganidis P (2010) Stochastic homogenization of Hamilton-Jacobi and “viscous”-Hamilton-Jacobi equations with convex nonlinearities—Revisited. Comm. Math. Sci. 8(2):627–637.Crossref, Google Scholar
• [32] Lions PL, Papanicolaou G, Varadhan S (1986) Homogenization of Hamilton-Jacobi equations. Preprint.Google Scholar
• [33] Luiro H, Parviainen M, Saksman E (2013) Harnack’s inequality for p-harmonic functions via stochastic games. Comm. Partial Differential Equations 38(11):1985–2003.Crossref, Google Scholar
• [34] Matic I, Nolen J (2012) A sublinear variance bound for solutions of a random Hamilton–Jacobi equation. J. Statist. Phys. 149(2):342–361.Crossref, Google Scholar
• [35] Mertens J-F, Neyman A (1981) Stochastic games. Internat. J. Game Theory 10(2):53–66.Crossref, Google Scholar
• [36] Oliu-Barton M (2021) New algorithms for solving zero-sum stochastic games. Math. Oper. Res. 46(1):255–267.Link, Google Scholar
• [37] Peres Y, Sheffield S (2008) Tug-of-war with noise: A game-theoretic view of the p-Laplacian. Duke Math. J. 145(1):91–120.Crossref, Google Scholar
• [38] Peres Y, Schramm O, Sheffield S, Wilson D (2009) Tug-of-war and the infinity Laplacian. J. Amer. Math. Soc. 22(1):167–210.Crossref, Google Scholar
• [39] Peters N (2001) Turbulent Combustion (Cambridge University Press, Cambridge, UK).Google Scholar
• [40] Rezakhanlou F, Tarver JE (2000) Homogenization for stochastic Hamilton-Jacobi equations. Arch. Rational Mech. Anal. 151(4):277–309.Crossref, Google Scholar
• [41] Schwab RW (2009) Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media. Indiana Univ. Math. J. 58(2):537–581.Crossref, Google Scholar
• [42] Shapley LS (1953) Stochastic games. Proc. Natl. Acad. Sci. USA 39(10):1095–1100.Crossref, Google Scholar
• [43] Solan E, Ziliotto B (2016) Stochastic games with signals. Advances in Dynamic and Evolutionary Games (Springer), 77–94.Crossref, Google Scholar
• [44] Souganidis P (1999) Stochastic homogenization of Hamilton-Jacobi equations and some applications. Asymptotic Anal. 20(1):1–11.Google Scholar
• [45] Vigeral G (2013) A zero-sum stochastic game with compact action sets and no asymptotic value. Dynamic Games Appl. 3(2):172–186.Crossref, Google Scholar
• [46] Williams F (1985) Turbulent combustion. The Mathematics of Combustion (SIAM, Philadelphia), 97–131.Crossref, Google Scholar
• [47] Yilmaz A (2020) Stochastic homogenization and effective Hamiltonians of HJ equations in one space dimension: The double-well case. Preprint, submitted July 15, https://arxiv.org/abs/2007.07854.Google Scholar
• [48] Ziliotto B (2016) A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games. Math. Oper. Res. 41(4):1522–1534.Link, Google Scholar
• [49] Ziliotto B (2016) Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture maxmin=limvn. Ann. Probab. 44(2):1107–1133.Crossref, Google Scholar
• [50] Ziliotto B (2017) Stochastic homogenization of nonconvex Hamilton-Jacobi equations: A counterexample. Comm. Pure Appl. Math. 70(9):1798–1809.Crossref, Google Scholar