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An optimal strategy for repeated n ‐person games
Author(s) -
Wilson Atholl L.
Publication year - 2007
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.3830080404
Subject(s) - strategy , repeated game , stochastic game , set (abstract data type) , selection (genetic algorithm) , control (management) , mathematical economics , sequential game , computer science , game theory , strategic dominance , extensive form game , operations research , economics , artificial intelligence , mathematics , programming language
An n‐person game, in which each player chooses a strategy from a finite set and each then receives a payoff based on the strategies selected, is called completely nonco‐operative when the players have no opportunity to co‐ordinate their choices of strategy. Here this is taken to imply that no matter how many times such a game is repeated, no player has any indication (even probabilistically) about any other player's future choices. Many game theorists, in common with businessmen, military commanders, statesmen, and others who are habitually concerned with competitive game strategies, often assume that the player should select strategies which will allow him to make predictions about his opponents' future moves on the basis of past behavior, and thus exercise control over them. This paper presents a method of strategy selection whereby the player makes no attempt to predict his opponents' strategy or to control it, and yet succeeds as well, on the average, as if he knew in advance the probabilities of selection of each strategy.