Robert Louis Stevenson's Bottle Imp: A strategic analysis

Kukushkin, Nikolai S. (2015): Robert Louis Stevenson's Bottle Imp: A strategic analysis.

Abstract

The background of Stevenson's story is viewed as a stylized model of participation in a financial pyramid. You are invited to participate in a dubious activity. If you refuse, you neither gain nor lose anything. If you accept, you will gain if you are able to find somebody who will take your place on exactly the same conditions, but suffer a loss otherwise. The catch is that there is a finite number of discrete steps at which the substitution can be done, so the agent who joins in at the last step inevitably loses. Clearly, rational agents will not agree to participate at any step. However, an arbitrarily small probability of a "bailout," in which case that last agent will get the same gain as every other participant, plus an appropriately asymmetric structure of private information, change everything, so the proposal will be accepted in a (subgame perfect) equilibrium, provided there are sufficiently many steps ahead.

• Item Type: MPRA Paper
• Language: English
• Keywords: financial pyramid; partitional information structure; game of incomplete information; game of perfect information
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design

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