Abstract
This paper proposes a new framework for modelling certain duel-like games played in continuous time. The key difficulty is that the continuum with the natural order is not a well-ordered set, so problems arise while constructing normal forms for such games. The paper deals with zero-sum two-person games in which each player expends an initial stock of “resources” during a time interval. Such an expenditure can be “silent” (not observable by the opponent) or “noisy” (at each moment the opponent has full information about the history of the game), giving rise to three possible types of games, depending on whether the number of “noisy players” is 0, 1, or 2. Here, with the help of Zorn’s lemma, the normal forms of these games are precisely formulated, a modelling effort that includes identification and resolution of a technical difficulty in describing the strategy spaces for the noisy case.
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Radzik, T., Goldman, A.J. (2001). On Problems with Information in Some Games: Modelling the Strategies in Some Dynamic Games. In: Altman, E., Pourtallier, O. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0155-7_1
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DOI: https://doi.org/10.1007/978-1-4612-0155-7_1
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