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Knowledge Games
Author(s) -
Van Ditmarsch Hans
Publication year - 2001
Publication title -
bulletin of economic research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.227
H-Index - 29
eISSN - 1467-8586
pISSN - 0307-3378
DOI - 10.1111/1467-8586.00134
Subject(s) - action (physics) , computer science , sequential game , set (abstract data type) , frame (networking) , combinatorial game theory , mathematical economics , state (computer science) , game theory , repeated game , extensive form game , common knowledge (logic) , function (biology) , screening game , artificial intelligence , mathematics , epistemic modal logic , algorithm , telecommunications , physics , quantum mechanics , evolutionary biology , multimodal logic , programming language , description logic , biology
The subject of epistemic logic is firmly entrenched in game theory, including the analysis of common knowledge and of public announcements, such as in ‘hat problems’. How to analyse communications to sub groups of the public, and the effects of such common knowledge of a subgroup on the information state of a larger group, has only recently come into fruition. Knowledge games are introduced to provide a comfortably concrete vehicle for the study of such interactions. This paper introduces the concepts of knowledge game, deal of cards, knowledge game state, game action, and action execution. A deal of cards is a function from cards to players. A knowledge game state is represented by a pointed multiagent S5 model on the set of card deals where all players hold the same number of cards as in the actual deal. A game action combines a question with an answer, and is represented by a pointed multiagent S5 frame on the set of possible answers. The execution of a game action in a knowledge game state corresponds to the computation of a pointed multiagent S5 model that is a restriction of the direct product of the corresponding action frame and game model.