Previous |  Up |  Next


incomplete information; sequential game; risk sensitive; turn selection process
The authors introduce risk sensitivity to a model of sequential games where players don't know beforehand which of them will make a choice at each stage of the game. It is shown that every sequential game without a predetermined order of turns with risk sensitivity has a Nash equilibrium, as well as in the case in which players have types that are chosen for them before the game starts and that are kept from the other players. There are also a couple of examples that show how the equilibria might change if the players are risk prone or risk adverse.
[1] Aliprantis, C. D., Border, K. C.: Infinite Dimensional Analysis. Springer, Berlin Heidelberg 2006. MR 2378491 | Zbl 1156.46001
[2] Arrow, K. J.: Aspects of the theory of risk-bearing. In: Essays in the Theory of Risk Bearing, Markham Publ. Co., Chicago 1971, pp. 90-109. MR 0363427
[3] Basu, A., Ghosh, M. K.: Nonzero-sum risk-sensitive stochastic games on a countable state space. Math. Oper. Res. 43 (2018), 516-532. DOI  | MR 3801104
[4] Bäuerle, N., Rieder, U.: Zero-sum risk-sensitive stochastic games. Stoch. Processes Appl. 12 (2017), 2, 622-642. DOI  | MR 3583765
[5] Becerril-Borja, R., Montes-de-Oca, R.: A family of models for finite sequential games without a predetermined order of turns. In: Operations Research and Enterprise Systems (B. Vitoriano, G. H. Parlier, eds.), Springer International Publishing, Cham 2017, 35-51. DOI 
[6] Border, K. C.: Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, Cambridge 1985. MR 0790845
[7] Eeckhoudt, L., Gollier, C., Schlesinger, H.: Economic and Financial Decisions under Risk. Princeton University Press, Princeton 2005. DOI 
[8] Fleming, W. H., McEneaney, W. M.: Risk sensitive optimal control and differential games. In: Stochastic Theory and Adaptive Control. Lecture Notes in Control and Information Sciences (T. E. Duncan and B. Pasik-Duncan, eds.), Springer, Berlin Heidelberg 1992, pp. 185-197. MR 1198930
[9] Howard, R. A., Matheson, J. E.: Risk sensitive Markov decision processes. Management Sci. 18 (1972), 356-369. DOI  | MR 0292497
[10] James, M. R., Baras, J., Elliott, R. J.: Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems. IEEE Trans. Automat. Control 39 (1994), 780-792. DOI  | MR 1276773
[11] Kakutani, S.: A generalization of Brouwer's fixed point theorem. Duke Math. J. 8 (1942), 457-459. DOI  | MR 0004776
[12] Klompstra, M. B.: Nash equilibria in risk-sensitive dynamic games. IEEE Trans. Automat. Control 45 (2000), 1397-1401. DOI  | MR 1780000
[13] Nowak, A. S.: Notes on risk-sensitive Nash equilibria. In: Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control (A. S. Nowak and K. Szajowski, eds.), Birkhäuser, Boston 2005, pp. 95-109. MR 2104370
[14] Pratt, J. W.: Risk aversion in the small and in the large. Econometrica 32 (1964), 122-136. DOI  | Zbl 0267.90010
[15] Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge 2008.
[16] Sladký, K.: Risk sensitive average optimality in Markov decision processes. Kybernetika 54 (2018), 1218-1230. DOI  | MR 3902630
[17] Tadelis, S.: Game Theory: An Introduction. Princeton University Press, Princeton 2013. MR 3235473
Partner of
EuDML logo