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Playing for RealGame Theory$
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Ken Binmore

Print publication date: 2007

Print ISBN-13: 9780195300574

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780195300574.001.0001

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 Planning Ahead

 Planning Ahead

Chapter:
(p.143) 5 Planning Ahead
Source:
Playing for Real
Author(s):

Ken Binmore (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195300574.003.0005

This chapter consolidates the ideas necessary to understand the strategic form of a game. Payoff functions are introduced, and strategic forms of versions of Duel and Russian Roulette illustrate the idea. Matrices and vectors are reviewed because of their use with payoff matrices. Strong and weak domination are defined. The iterated deletion of dominated strategies is illustrated using the game of Duel. The iterated deletion of dominated strategies is related to backward induction. Problems of credibility and commitment are discussed in the context of subgame-perfect equilibria in simple Cournot and Stackelberg games. The application of subgame-perfect equilibria is discussed when players may only be boundedly rational.

Keywords:   strategic form, bimatrix game, payoff function, matrix, credibility, Cournot game, Stackelberg game, bounded rationality, holdup problem, Centipede Game

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