## Notes

A (biased) sampling from my bookshelf: Shoenfield’s

*Mathematical Logic*: “Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians”; Enderton’s*A Mathematical Introduction of Logic*: “Symbolic logic is a mathematical model of deductive thought”; and Chiswell and Hodges*Mathematical Logic*: “In this course we shall study some ways of proving statements.”That is, if, according to player

*i*’s beliefs, strategy*s*is optimal for player*j*, then*i*cannot rule out*all*states where player*j*follows strategy*s*.I am assuming that the set of states is finite, so that individual states can be assigned a non-zero probability.

I assume that the reader is familiar with the standard formulation of common knowledge: An event

*E*is commonly known provided everyone knows*E*, everyone knows that everyone knows*E*, everyone knows that everyone knows*E*, and so on*ad infinitum*.Note that the framework used in [20] differs in small but important ways from the epistemic-probability models introduced in this paper. These technical details are not important for the main point I am making here, and, indeed, this argument can be made more formal using epistemic probability models.

This follows from the well-known fact that a strategy is weakly dominated iff it does not maximize expected utility with respect to any probability that assigns non-zero probability to all of the opponent’s choices.

Well, I do restrict attention to games with a finite set of players and and finite sets of actions for each player.

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Pacuit, E. On the use (and abuse) of Logic in Game Theory.
*J Philos Logic* **44**, 741–753 (2015). https://doi.org/10.1007/s10992-015-9356-8

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DOI: https://doi.org/10.1007/s10992-015-9356-8