Lectures on the Theory of Games

By Harold W. Kuhn | Go to book overview

Chapter Two
Matrix Games

2.1 Two Examples
The well-known game of Matching Pennies provides us with an example of a zero-sum two-person finite game with two moves. (Note that in this game, as in later examples, in order that only one player act at a move, we divide one natural simultaneous move into two consecutive moves.) In the first move, P1 chooses the alternative “heads” or “tails,” and in the second move, P2, in ignorance of P1's choice, chooses the alternative “heads” or “tails.” After the choices have been made, P2 pays P1 the amount 1 if they match or -1 if they do not match. We can summarize the rules without losing any essential information by the diagram:At the end of a play P2 pays P1 the amount shown. This diagram can be simplified considerably if we adopt the following conventions:
a. The rows (columns) of the matrix will correspond to possible choices for P1(P2).
b. Since there are only two moves in the game under consideration, a choice for P1 and a choice for P2, that is, a row and a column, determine a play uniquely. The matrix entry at the corresponding intersection gives the amount that P2 pays P1 at the end of the play.

-5-

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Lectures on the Theory of Games
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Author's Note vii
  • Preface ix
  • Chapter One - What is the Theory of Games? 1
  • Chapter Two - Matrix Games 5
  • Chapter Three - Extensive Games 59
  • Chapter Four - Infinite Games 81
  • Index 105
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