Premium
The learning of strategies in a simple, two‐person zero‐sum game without saddlepoint
Author(s) -
Fox John
Publication year - 1972
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830170305
Subject(s) - minimax , adversary , fictitious play , zero (linguistics) , variance (accounting) , repeated game , strategy , mathematical economics , outcome (game theory) , skewness , simple (philosophy) , affect (linguistics) , zero sum game , exploit , computer experiment , game theory , psychology , computer science , mathematics , econometrics , economics , statistics , communication , linguistics , philosophy , accounting , epistemology , computer security
Abstract Subjects play a 2 × 2 zero‐sum game without saddlepoint against a computer program opponent; the computer program either follows its minimax mixed strategy or adopts a (pre‐defined) nonrational mixed strategy. It is found that there is a significant trend in the strategy choice behavior of subjects playing against a rational opponent such that these subjects tend to approach their optimal strategy mixture. Since subjects playing opposite a rational opponent cannot affect the expected outcome of the game, the relationship between subjects' play and the variance and skewness of payoffs (interpreted as components of the riskiness of the game) is explored. Subjects whose opponent is a computer program which plays nonoptimally appear to be able to learn to exploit their opponent's departure from rational play. There is some evidence that subjects may respond to random fluctuations in the computer's play.