A Rough View on Incomplete Information in Games

In both game theory and in rough sets, the management of missing and contradicting information is regarded as one of the biggest challenges with significant practical relevance. In game theory, a distinction is made between imperfect and incomplete information. Imperfect information is defined when a player cannot identify the decision node it is presently at. Incomplete information refers to a lack of knowledge about the future actions of one’s opponent, e.g., due to missing information about its payoffs. In rough set theory, missing and contradicting information in decision tables has been extensively researched and has led to the definition of lower and upper approximations of sets. Although game theory and rough sets have already addressed missing and contradicting information thoroughly little attention has been given to their relationship. In the paper, we present an example how games with imperfect information can be interpreted in the context of rough sets. In particular, we further detail Peters’ recently proposed mapping of a game with incomplete information on a rough decision table.

[1]  George A. Akerlof.  The Market for “Lemons”: Quality Uncertainty and the Market Mechanism , 1970 .

[2]  Duoqian Miao,et al.  Analysis on attribute reduction strategies of rough set , 1998, Journal of Computer Science and Technology.

[3]  Jerzy W. Grzymala-Busse,et al.  Rough Set Theory with Applications to Data Mining , 2011 .

[4]  J. Tirole.  The Theory of Industrial Organization , 1988 .

[5]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[6]  Georg Peters.  A Rough Perspective on Information in Extensive Form Games , 2016, IJCRS.

[7]  Jiuping Xu,et al.  A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs , 2010, Int. J. Math. Math. Sci..

[8]  David M. Kreps,et al.  Game Theory and Economic Modelling , 1992 .

[9]  J. D. Morrow.  Game Theory for Political Scientists , 1994 .

[10]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[11]  Jingtao Yao,et al.  Game-Theoretic Rough Sets , 2011, Fundam. Informaticae.

[12]  William Perrizo,et al.  Big Data Analytics in Bioinformatics and Healthcare , 2014 .

[13]  R. Selten,et al.  Game theory and evolutionary biology , 1994 .

[14]  Jingtao Yao,et al.  Game-Theoretic Risk Analysis in Decision-Theoretic Rough Sets , 2008, RSKT.

[15]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[16]  J. Harsanyi.  Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points , 1968 .

[17]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.