computer solution to the game of pure strategy计算机解决纯策略的游戏.pdf

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