Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums

References

• [1] Abreu D, Pearce D, Stacchetti E (1990) Toward a theory of discounted repeated games with imperfect monitoring. Econometrica 58(5):1041–1063.Crossref, Google Scholar
• [2] Aubin JP, Frankowska H (2009) Set-Valued Analysis (Springer Science & Business Media, Berlin).Crossref, Google Scholar
• [3] Barles G, Soner H, Souganidis P (1993) Front propagation and phase field theory. SIAM J. Control Optim. 31(2):439–469.Crossref, Google Scholar
• [4] Bensoussan A, Frehse J (2000) Stochastic games for n players. J. Optim. Theory Appl. 105:543–565.Crossref, Google Scholar
• [5] Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (Wiley, New York).Crossref, Google Scholar
• [6] Buckdahn R, Cardaliaguet P, Rainer C (2004) Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Control Optim. 43(2):624–642.Crossref, Google Scholar
• [7] Buckdahn R, Li J, Quincampoix M (2014) Value in mixed strategies for zero-sum stochastic differential games without isaacs condition. Ann. Probab. 42(4):1724–1768.Crossref, Google Scholar
• [8] Cardaliaguet P, Plaskacz S (2003) Existence and uniqueness of a nash equilibrium feedback for a simple nonzero-sum differential game. Internat. J. Game Theory. 32:33–71.Crossref, Google Scholar
• [9] Cardaliaguet P, Quincampoix M, Saint-Pierre P (1999) Set-Valued Numerical Analysis for Optimal Control and Differential Games (Birkhäuser, Boston), 177–247.Crossref, Google Scholar
• [10] Dupire B (2019) Functional itô calculus. Quant. Finance 19(5):721–729.Crossref, Google Scholar
• [11] Ekren I, Touzi N, Zhang J (2016) Viscosity solutions of fully nonlinear parabolic path dependent pdes: Part i. Ann. Probab. 44(2):1212–1253.Crossref, Google Scholar
• [12] Ekren I, Touzi N, Zhang J (2016) Viscosity solutions of fully nonlinear parabolic path dependent pdes: Part ii. Ann. Probab. 44(4):2507–2553.Crossref, Google Scholar
• [13] El-Karoui N, Hamadene S (2003) Bsdes and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations. Stochastic Process. Appl. 107(1):145–169.Crossref, Google Scholar
• [14] Espinosa GE, Touzi N (2015) Optimal investment under relative performance concerns. Math. Finance 25(2):221–257.Crossref, Google Scholar
• [15] Feinstein Z (2020) Continuity and sensitivity analysis of parameterized nash games. Preprint, submitted July 10, https://arxiv.org/pdf/200704388.pdf.Google Scholar
• [16] Feinstein Z, Rudloff B (2019) Time consistency for scalar multivariate risk measures Preprint, submitted January 8, https://arxiv.org/pdf/1810.04978.pdf.Google Scholar
• [17] Frei C, dos Reis G (2011) A financial market with interacting investors: Does an equilibrium exist? Math. Financial Econom. 4:161–182.Crossref, Google Scholar
• [18] Friedman A (1972) Stochastic differential games. J. Differential Equations 11:79–108.Crossref, Google Scholar
• [19] Hamadene S (1999) Nonzero sum linear-quadratic stochastic differential games and backward-forward equations. Stoch. Anal. Appl. 17:117–130.Crossref, Google Scholar
• [20] Hamadene S, Mannucci P (2019) Regularity of Nash payoffs of Markovian nonzero-sum stochastic differential games. Stochastics 91(5):695–715.Crossref, Google Scholar
• [21] Hamadene S, Mu R (2014) Bangbang-type nash equilibrium point for markovian nonzero-sum stochastic differential game. C. R. Math. Acad. Sci. Paris 352(9):699–706.Crossref, Google Scholar
• [22] Hamadene S, Mu R (2015) Existence of nash equilibrium points for markovian non-zero-sum stochastic differential games with unbounded coefficients. Stochastics 87(1):85–111.Crossref, Google Scholar
• [23] Hamadene S, Lepeltier JP, Peng S (1997) BSDEs with continuous coefficients and stochastic differential games. El Karoui N, Mazliak L, eds. Pittman Research Notes in Mathematics Series (Longman, UK) 115–128.Google Scholar
• [24] Ho K, Rosen AM (2017) Partial Identification in Applied Research: Benefits and Challenges, Economic Society of Monographs, vol. 2 (Cambridge University Press, Cambridge, UK), 307–359.Google Scholar
• [25] Karnam C, Ma J, Zhang J (2017) Dynamic approaches for some time inconsistent problems. Ann. Appl. Probab. 27(6):3435–3477.Crossref, Google Scholar
• [26] Lin Q (2012) A BSDE approach to nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. Stochastic Process. Appl. 122(1):357–385.Crossref, Google Scholar
• [27] Ma J, Yong J (1995) Solvability of forward-backward SDEs and the nodal set of hamilton-jacobi-bellman equations. Chin. Ann. Math. Ser. B. 16:279–298.Google Scholar
• [28] Mannucci P (2004) Nonzero-sum stochastic differential games with discontinuous feedback. SIAM J. Control Optim. 43(4):1222–1233.Crossref, Google Scholar
• [29] Mannucci P (2014) Nash points for nonzero-sum stochastic differential games with separate hamiltonians. Dyn. Games Appl. 4:329–344.Crossref, Google Scholar
• [30] Mertens J, Sorin S, Zamir S (2015) Repeated Games (Econometric Society Monographs). (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• [31] Olsder GJ (2001) On open- and closed-loop bang-bang control in nonzero-sum differential games. SIAM J. Control Optim. 40(4):1087–1106.Crossref, Google Scholar
• [32] Pham T, Zhang J (2004) Two person zero–sum game in weak formulation and path dependent bellman-isaacs equation. SIAM J. Control Optim. 52(4):2090–2121.Crossref, Google Scholar
• [33] Possamai D, Touzi N, Zhang J (2020) Zero-sum path-dependent stochastic differential games in weak formulation. Ann. Appl. Probab. 30(4):1415–1457.Google Scholar
• [34] Rainer C (2007) Two different approaches to nonzero-sum stochastic differential games. Appl. Math. Optim. 56:131–144.Crossref, Google Scholar
• [35] Ren Z, Touzi N, Zhang J (2017) Comparison of viscosity solutions of fully nonlinear degenerate parabolic path-dependent PDEs. SIAM J. Math. Anal. 49(5):4093–4116.Crossref, Google Scholar
• [36] Sannikov Y (2007) Games with imperfectly observable actions in continuous time. Econometrica 75(5):1285–1329.Crossref, Google Scholar
• [37] Sun J, Yong J (2019) Linear-quadratic stochastic two-person nonzero-sum differential games: open-loop and closed-loop nash equilibria. Stochastic Process. Appl. 129(2):381–418.Crossref, Google Scholar
• [38] Uchida K (1978) On existence of a nash equilibrium point in n-person nonzero sum stochastic differential games. SIAM J. Control Optim. 16(1):142–149.Crossref, Google Scholar
• [39] Wu Z (2005) Forward-backward stochastic differential equations, linear quadratic stochastic optimal control and nonzero sum differential games. J. Systems Sci. Complexity 18(2):179–192.Google Scholar
• [40] Zhang J (2017) Backward Stochastic Differential Equations — From Linear to Fully Nonlinear Theory (Springer, New York).Crossref, Google Scholar