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## Robert V. Dodge

Print publication date: 2012

Print ISBN-13: 9780199857203

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780199857203.001.0001

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# The Two-by-Two Matrix

Chapter:
(p.44) Chapter 5 The Two-by-Two Matrix
Source:
Schelling's Game Theory
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199857203.003.0005

This chapter introduces the most basic game theory tool—the two-by-two matrix—and looks at how to read, construct, and illustrate real-life situations with the simple four-cell box. It uses Sugden's “banknote game” to demonstrate basic interaction at the simplest level, with two players each having one choice. It shows how the outcome of player's choices can be ranked in order by utility and the simple matrix yields a surprisingly large number of different outcomes, representing many different situations. Sequential and simultaneous plays are also discussed. The chapter introduces Schelling's “staggered” payoffs, then simple instructions teach how to determine the results of games, looking at “dominance” and finding “natural outcomes.” There is a brief introduction to randomization for games without natural outcomes. Pareto efficiency as an evaluation of a game's result is discussed, followed by the construction of a matrix to evaluate a situation. The final two matrix constructions are real life ones: one involving the decision to require hockey helmets in the National Hockey League and the other being the arms race between the U.S. and the Soviet Union. The supplement to this section is a column by Pulitzer Prize winning humorist Dave Barry, presenting his own version of strategy, entitled “How to Win Arguments.”

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