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Games with Unknown Past
Author(s) -
Khoussainov Bakhadyr,
Yakhnis Alexander,
Yakhnis Vladimir
Publication year - 1998
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19980440206
Subject(s) - determinacy , mathematics , tree (set theory) , class (philosophy) , isomorphism (crystallography) , root (linguistics) , combinatorial game theory , bounded function , type (biology) , mathematical economics , discrete mathematics , theoretical computer science , computer science , combinatorics , game theory , sequential game , artificial intelligence , chemistry , mathematical analysis , ecology , linguistics , philosophy , crystal structure , biology , crystallography
We define a new type of two player game occurring on a tree. The tree may have no root and may have arbitrary degrees of nodes. These games extend the class of games considered by Gurevich‐Harrington in [5]. We prove that in the game one of the players has a winning strategy which depends on finite bounded information about the past part of a play and on future of each play that is isomorphism types of tree nodes. This result extends further the Gurevich‐Harrington determinacy theorem from [5].