Advances in Mathematical Economics by Shigeo Kusuoka & Toru Maruyama

Author:Shigeo Kusuoka & Toru Maruyama
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

5.2 Yet Another Counterexample

In order to develop the counterexample, we return to Lemma 2(ii), and work with the measurable the measure-preserving map from to the usual Lebesgue interval guaranteed therein. Use this map to formulate the following KRS-like game, .

We can now appeal to Lemma 2(iii) to assert that

Claim 2

There does not exist a PSNE in the game .

But now one is on a roll. One can ask whether the non-existence of a PSNE in the KRS-like game can be is resolved in precisely the same way that the non-existence issue for the KRS game was resolved. This is to check whether a further extension of the extended Lebesgue interval would subdue the new example. This can be done by a consideration of the following game,

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