By Adam Brandenburger
This quantity includes 8 papers written through Adam Brandenburger and his co-authors over a interval of 25 years. those papers are a part of a application to reconstruct video game conception so that it will make how gamers cause a few online game a valuable characteristic of the speculation. this system — now known as epistemic video game concept — extends the classical definition of a video game version to incorporate not just the sport matrix or online game tree, but in addition an outline of the way the avid gamers cause approximately each other (including their reasoning approximately different avid gamers' reasoning). With this richer mathematical framework, it turns into attainable to figure out the results of ways avid gamers explanation for how a online game is performed. Epistemic online game conception comprises conventional equilibrium-based thought as a different case, yet allows a variety of non-equilibrium behavior.
Readership: Graduate scholars and researchers within the fields of video game conception, theoretical computing device technological know-how, mathematical good judgment and social neuroscience.
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Extra resources for The Language of Game Theory: Putting Epistemics into the Mathematics of Games
Management Science, 14, 159–182, 320–334, 486–502. Keisler, HJ and BS Lee (2011). Common assumption of rationality. edu/∼keisler. Kohlberg, E and J-F Mertens (1986). On the strategic stability of equilibria. Econometrica, 54, 1003–1038. Mertens, J-F and S Zamir (1985). Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory, 14, 1–29. January 8, 2014 9:7 xxxiv 9in x 6in The Language of Game Theory b1636-fm Adam Brandenburger Nash, J (1950). Non-cooperative games.
What can be thought of as an output in conventional game theory becomes an input in EGT. Conventionally, we start with a Nash equilibrium — say, one in which Ann chooses the strategy Up and Bob chooses the strategy Left. We can associate beliefs with this pair of strategies: Ann assigns probability 1 to Bob’s choosing Left and Bob assigns probability 1 to Ann’s choosing Up. ) The solution concept is interpreted as telling us what beliefs the players hold. In short, beliefs emerge as an output of the analysis.
In general, a belief model has a set of states for each player, and a relation for each player that speciﬁes when a state of one player considers a state of the other player to be possible. The concepts of assumption and belief have natural deﬁnitions in such a model. Given a belief model, we next consider a language used by the players to formulate their beliefs about the other players. 4 Thus, completeness is relative to a language. Completeness for a given language 2 For an earlier — and weaker — impossibility result, see Brandenburger (2003).
The Language of Game Theory: Putting Epistemics into the Mathematics of Games by Adam Brandenburger