A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

Important, unimportant a critical anticipation of the assumptions of legal positivism in Alice in Wonderland

Almost a full century separates Lewis’ Alice in Wonderland (1865) and the second, lengthier and more elaborate edition of Hans Kelsen’s Pure Theory of Law (1960; first edition published in 1934). And yet, it is possible to argue that the former anticipates and critically addresses many of the philosophical assumptions that underlie and are elemental to the argument of the latter. Both texts, with the illuminating differences that arise from their disparate genre, have as one of their key themes norms and their functioning. Wonderland, as Alice soon finds out, is a world beset by rules of all kinds: from the etiquette rituals of the mad tea-party to the changing setting for the cricket game to the procedural insanity of the trial with which the novel ends. Pure Theory of Law, as Kelsen emphatically stresses, has the grundnorm as the cornerstone upon which the whole theoretical edifice rests2. This paper discusses some of the assumptions underlying Kelsen’s argument as an instance of the modern worldview which Lewis satirically scrutinizes. The first section (Sleepy and stupid) discusses Lewis critique of the idea that, to correctly apprehend an object (in the case of Kelsen’s study, law), one has to free it from its alien elements. The second section (Do bats eat cats?) discusses the notion of systemic coherence and its impact on modern ways of thinking about truth, law and society. The third section (Off with their heads!) explores the connections between readings of systems as neutral entities and the perpetuation of political power. The fourth and final section (Important, Unimportant) explains the sense in which a “critical anticipation” is both possible and useful to discuss the philosophical assumptions structuring some positivist arguments. It also discusses the reasons for choosing to focus on Kelsen’s work, rather than on that of Lewis’ contemporary, John Austin, whose The Province of Jurisprudence Determined (published in 1832) remains influential in legal debates today.

Extinction, pollution, and the sustainable use of exhaustible and renewable resources

Single ownership of natural resources is conunon in many developing countries and socialist economies. The sole owner is usually the .state or society at large, and governments are responsible for either distributing exploitation rights or engaging in exploitation through their own corporations. • Under this circumstance, the notion of externality may not fully explain pollution problems existent in these nations. This paper studies the case where a single agent owns both exhaustible and renewable resources, and attempts to maximize its welfare. The resources are either perfect or imperfect substitutes. Initially, exhaustible resource extraction does not affect the renewable resource, and sustainable growth is attainable. A lactor of pollution flowing from the extraction of the nc.nrenewable resource into the growth of the renewable resource is introduced. The continuous exploitation of the exhaustible resource leads to the " optimal " extinction of the renewable resource, and sustainable growth is no longer reached. Regulation from a supra governmental agency such as an multinational institution may prove to be of utmost importance, if sustainability is to be achieved. The paper is divided into five sections. Section two provides a brief survey of the relevant literature. Section three presents the model without pollution. This factor is introduced in section four. The final section discusses some possible approaches for attaining sustainable growth, and contains the concluding remarks .