Games with Incomplete Information on the Both Sides and with Public Signal on the State of the Game

Authors

  • Misha Gavrilovich National Research University Higher School of Economics
  • Victoria Kreps National Research University Higher School of Economics

Abstract

Supposing that Player 1's computational power is higher than that of Player 2, we give three examples of different kinds of public signal about the state of a two-person zero-sum game with symmetric incomplete information on both sides (both players do not know the state of the game) where Player 1 due to his computational power learns the state of the game meanwhile it is impossible for Player 2. That is, the game with incomplete information on both sides becomes a game with incomplete information on the side of Player 2. Thus we demonstrate that information about the state of a game may appear not only due to a private signal but as a result of a public signal and asymmetric computational resources of players.

Keywords:

zero-sum game, incomplete information, asymmetry, finite automata

Downloads

Download data is not yet available.

References

Neyman, A. (1997). Cooperation, repetition and automata. In: Hart, S., Mas-Colell, A. (Eds.), Cooperation: Game-Theoretic Approaches. In: NATO ASI Series F, vol.155. Springer-Verlag, 233–255.

Neyman, A. (1998). Finitely repeated games with finite automata. Math. Oper. Res., 23, 513–552.

Rubinstein, A. (1986). Finite automata play the repeated prisoners dilemma. J. Econ. Theory, 39, 83–96.

Abreu, D. and A. Rubinstein (1988). The structure of Nash equilibrium in repeated games with finite automata. Econometrica, 56, 1259–1281.

Hernández, P. and E. Solan (2016). Bounded computational capacity equilibrium. Journal of Economic Theory, 163, 342–364.

Harsanyi, J. (1967-68). Games with Incomplete Information Played by Bayesian Players. Parts I to III. Management Science, 14, 159–182, 320–334, and 486–502.

Aumann, R. and M. Maschler (1995). Repeated Games with Incomplete Information. The MIT Press: Cambridge, Massachusetts - London, England.

Gensbittel, F. (2016). Continuous-time limits of dynamic games with incomplete information and a more informed player. to appear in Int. J. of Game Theory.

Gensbittel, F., Oliu-Barton, M., H. Venel (2014). Existence of the uniform value in repeated games with a more informed controller. J. of Dynamics and Games, 1(3), 411–445.

Sakarovitch, J. (2009). Elements of Automata Theory. Cambridge University Press.

Kobrinskii, N. and B. Trakhtenbrot (1965). Introduction to the Theory of Finite Automata. Amsterdam, North-Holland.

Hagerup, T. (1990). A guided tour of Chernoff bounds. Information Processing Letters. 33 (6): 305. doi:10.1016/0020-0190(90)90214-I.

Borda, M. (2011). Fundamentals in Information Theory and Coding. Springer.

Mertens, J.-F. (1986). Repeated games. Proceedings of the International Congress of Mathematicians Berkeley, California, USA, 1528–1577.

Mertens, J.-F., Sorin, S., Zamir, S. (2015). Repeated games (Econometric Society Monographs). Cambridge Univ. Press

Shapley, L. (1953). Stochastic Games. Proc. Nat. Acad. Sci. U.S.A., 39, 1095–1100.

Downloads

Published

2022-04-17

How to Cite

Gavrilovich, M., & Kreps, V. (2022). Games with Incomplete Information on the Both Sides and with Public Signal on the State of the Game. Contributions to Game Theory and Management, 10. Retrieved from https://gametheory.spbu.ru/article/view/13252

Issue

Vol. 10 (2017)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.