# 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-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Lectures on the Theory of Games

• 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
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
• Bookmarks
• Highlights & Notes
• Citations
/ 107

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.