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تسجيل مستخدم جديدRationality in the Theory of the Firm
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We have previously presented a critique of the standard Marshallian theory of the firm, and developed an alternative formulation that better agreed with the results of simulation. An incorrect mathematical fact was used in our previous presentation. This paper deals with correcting the derivation of the Keen equilibrium, and generalising the result to the asymmetric case. As well, we discuss the notion of rationality employed, and how this plays out in a two player version of the game.
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The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for its super
iority. Many people, if given the choice to switch, think the chances are fifty-fifty between their options, but still strongly prefer to stay with their initial choice. Is there some sense behind these irrational feelings? We entertain the possibility that intuition solves the problem of how to behave in a real game show, not in the abstract textbook version of the Monty Hall problem. A real showmaster sometimes plays evil, either to make the show more interesting, to save money, or because he is in a bad mood. A moody showmaster erases any information advantage the guest could extract by him opening other doors which drives the chance of the car being behind the chosen door towards fifty percent. Furthermore, the showmaster could try to read or manipulate the guests strategy to the guests disadvantage. Given this, the preference to stay with the initial choice turns out to be a very rational defense strategy of the shows guest against the threat of being manipulated by its host. Thus, the intuitive feelings most people have about the Monty Hall problem coincide with what would be a rational strategy for a real-world game show. Although these investigations are mainly intended to be an entertaining mathematical commentary on an information-theoretic puzzle, they touch on interesting psychological questions.
Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the over
all system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.
This is a small note meant to be published in a Conference Proceedings. We discuss elementary rationality questions in the Grothendieck ring of varieties for the quotient of a finite dimensional vector space over a characteristic 0 field by a finite
group. Part of it reproduces the content of a letter dated September 27, 2008 addressed to Johannes Nicaise
The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $sigma(S) sim S^{-beta(S)}$ where $S$ is the firm size and $beta(S)approx 0.2$ is an exponent weakly dependent on $S$. Here w
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