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Équité et jeu de Saint-Pétersbourg

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  • Daniel Zajdenweber

Abstract

[fre] Equité et jeu de Saint-Petersbourg. . S'il est joué un grand nombre de fois, le jeu de Saint-Pétersbourg n'est plus qu'un cas particulier d'une loi faible des grands nombres généralisée. Le gain moyen de n parties du jeu tend en probabilité vers 1/2 Logn (en base 2), un résultat connu depuis la fin du XIXè siècle au moins, mais dont la démonstration est relativement récente. L'usage de simulations montre que la solution équitable du jeu est réaliste, car les ordres de grandeur de n ne sont pas gigantesques. Le jeu est donc jouable, même si les joueurs sont averses au risque.. L'article montre que les distributions des tailles de certains sinistres, recensés par les compagnies d'assurances, sont du type « Saint-Pétersbourg ». Le jeu est donc un modèle réaliste. Les conséquences économiques du jeu sont analysées et des stratégies pour gérer les risques statistiques à espérance infinie sont proposées. [eng] Fairness and the petersburg game . . When played in a large number of trials, the Petersburg game is only a special case of a generalized weak law of large numbers. The average gain of n trials tends in probability to l/2Logn (basis 2), a resuit already known since the end of the XIX th. century, at least, but the demonstration of which is relatively recent. Simulation evidences show that the fair solution is realistic, because the magnitude of n is not gigantic, hence the game is playable, even for risk-averse gamblers.. The paper shows that the size-distributions of some insurance claims belong to the « Petersburg » type, hence the game may be a realistic model. Economie consequences are analyzed and strategies to cope with statistical hazards without expectation are presented.

Suggested Citation

  • Daniel Zajdenweber, 1994. "Équité et jeu de Saint-Pétersbourg," Revue Économique, Programme National Persée, vol. 45(1), pages 21-46.
  • Handle: RePEc:prs:reveco:reco_0035-2764_1994_num_45_1_409508
    DOI: 10.3406/reco.1994.409508
    Note: DOI:10.3406/reco.1994.409508
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