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Games with recurring certainty

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Abstract

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.
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... We believe that the next steps are, first, to see whether the syntactical fragments studied for SL with perfect information, such as One-Goal or Boolean-Goal Strategy Logic, can be transferred to BSL and then to ESL, and see whether they enjoy better complexity properties. The second natural move would be to look at structures which are known to work well with multiple agents with imperfect information: hierarchical knowledge [7,20], recurring common knowledge of the state [6]. . . ...
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... The present article extends a previous report [13] presented at the Workshop on Strategic Reasoning. ...
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