Abstract
An introduction to stochastic game theory with static information, as included in this chapter, follows the basic lines of the first two sections of Chap. 2, which were devoted to stochastic teams, with however some rather subtle differences in the setup and solution concepts. Accordingly, in the following, we introduce the game setup, paralleling the flow of Chap. 2 for teams, intentionally allowing for redundancies or repetitions, so that the coverage is self-contained while also bringing forth connections to the team formulation.
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Notes
- 1.
The best security strategy safeguards the leader against the uncertainty brought about by the non-uniqueness of the rational reaction function. The best cooperative strategy, on the other hand, uses this uncertainty to the leader’s advantage as though the follower were cooperating with him on his indifference curve; for further discussion and results on this extended Stackelberg solution, see Başar and Olsder [97].
- 2.
This property will formally be established in Sect. 11.2: In a zero-sum game one can obtain a Blackwell order on information structures, a corollary of which is that more information does not hurt the player receiving it while the other’s information is unaltered. This may seem immediate first; however one should be cautious that, unlike in team theory, here equilibrium does not allow an argument of the type one can choose to ignore the additional information and thus no information cannot hurt. The discussions in the next two chapters will present further insight and mathematical reasoning.
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Yüksel, S., Başar, T. (2024). An Introduction to Stochastic Game Theory. In: Stochastic Teams, Games, and Control under Information Constraints. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-54071-4_9
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