AN ANALYSIS OF THREE-MOVE FINITE GAMES

Abstract

The complexity of possible information patterns increases with the number of moves available to the players. If it is assumed that a move is made with either complete or no knowledge about the other move, a 2move game has only two possible patterns of information. Either there is perfect information, and thus one move precedes the other, or there is no information, in which case the moves are in effect made simultaneously. In each case the game has a value and optimal strategies,- - a pure strategy in the case of perfect information, and generally mixed strategies if the moves are made simultaneously. A 3-move game, i. e., one in which two moves are made by one player and one by the other, introduces many additional types of information patterns. Again, it is assumed that information, if any, about a preceding move is complete. At the time of his second move, the player with two moves may have forgotten his first move or the information known at this first move. The effect of this introduction of imperfect recall is to yield a game without a value. Further, in these cases it is generally impossible to express the 3-move game in normal form.

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Document Details

Document Type
Technical Report
Publication Date
Oct 16, 1951
Accession Number
AD0603990

Entities

People

  • M. Dresher
  • O. Helmer
  • R. M. Wagner

Organizations

  • RAND Corporation

Tags

Readers

  • Brain and Cognitive Science; Experimental Psychology; Cognitive Neuroscience
  • Game Theory.
  • Systems Analysis and Design