computer solution to the game of pure strategy计算机解决纯策略的游戏.pdf
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Games 2012, 3, 150-156; doi:10.3390/g3040150
OPEN ACCESS
games
ISSN 2073-4336
/journal/games
Article
Computer Solution to the Game of Pure Strategy
Glenn C. Rhoads and Laurent Bartholdi
University of Maryland, University College, 3501 University Blvd. East, Adelphi, MD, USA;
E-Mail: glenn.rhoads@
¨
Mathematical Institute, Georg-August University, Bunsenstraße 3-5, D-37073 Gottingen, Germany;
E-Mail: laurent.bartholdi@
Received: 25 August 2012; in revised form: 11 October 2012 / Accepted: 1 November 2012 /
Published: 8 November 2012
Abstract: We numerically solve the classical “Game of Pure Strategy” using linear
programming. We notice an intricate even-odd behaviour in the results of our computations
that seems to encourage odd or maximal bids.
Keywords: goofspiel; game theory; linear programming; dynamic programming
1. Introduction
Simple, two-player games are important models for human decision making. They should have
sufficiently elementary rules so that they can be studied both theoretically and empirically, yet be
sufficiently rich to involve a non-trivial amount of human psychological experience.
We study, and solve numerically, the “Game of Pure Strategy”. The solution is not implementable by
a human, but only by a computer. The game is a model of decision making based on bidding, which is
an important paradigm in game theory, because it can easily be shown (see below) that no deterministic
strategy ma
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