A History of Game Theory - Vol. 1

By Mary Ann Dimand; Robert W. Dimand | Go to book overview

4

STRATEGIC INTERDEPENDENCE

Bilateral monopoly

In a city that stands in the very centre of Africa, and is rarely visited by the casual tourist, the people had always bought eggs—a daily necessary in a climate where egg-flip was the usual diet—from a Merchant who came to their gates once a week. And the people always bid wildly against each other: so there was quite a lively auction every time the Merchant came, and the last egg in his basket used to fetch the value of two or three camels, or thereabouts. And eggs got dearer every week. And still they drank their egg-flip, and wondered where all their money went to.

And there came a day when they put their heads together. And they understood what donkeys they had been.

And next day, when the Merchant came only one Man went forth. And he said, ‘Oh, thou of the hook-nose and the goggle-eyes, thou of the measureless beard, how much for that lot of eggs?’

And the Merchant answered him ‘I could let thee have that lot at ten thousand piastres the dozen.’

And the man chuckled inwardly, and said ‘Ten piastres the dozen I offer thee, and no more, oh descendant of a distinguished grandfather!’

And the Merchant stroked his beard, and said ‘Hum! I will await the coming of thy friends.’ So he waited. And the Man waited with him. And they both waited together.

‘The manuscript breaks off here,’ said Mein Herr, as he rolled it up again….

(Lewis Carroll, Sylvie and Bruno Concluded)

Carroll’s novel, published in 1893 but by his account largely written by 1885, contains this passage describing an initial situation in which the egg merchant acts as a price-discriminating monopolist. When his customers recognize that they can combine to their advantage, however, both buyers and sellers have market power. That ‘the manuscript breaks off here’ could indicate two things: that Carroll did not know how to solve the problem, or the indeterminacy of price in such a situation. 1

This is a peculiarly appropriate passage with which to begin a discussion of treatments of what was termed ‘bilateral monopoly’. The indeterminacy of outcome in many situations in which strategic interdependence, rather than a market, operates became a theme of economists and remains a focus for game

-54-

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A History of Game Theory - Vol. 1
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface ix
  • 1 - Introduction 1
  • 2 - Strategic Interdependence 18
  • 3 - Strategic Interdependence 35
  • 4 - Strategic Interdependence 54
  • 5 - Lewis Carroll and the Game of Politics 84
  • 6 - Early Mathematical Models of Conflict 104
  • 7 - The Minimax Approach to Non-Cooperative Strategic Games from Waldegrave to Borel 120
  • 8 - From Games of Pure Chance to Strategic Games 131
  • 9 142
  • Notes 158
  • Bibliography 170
  • Index 184
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