Advertising coordination games of a manufacturer and a retailer while introducing a new product

Two kinds of vertical cooperative advertising program are considered in a distribution channel constituted by a manufacturer and a retailer, where the manufacturer pays part of the retailer’s advertising costs. In the first participation scheme, the manufacturer chooses his/her advertising participation rate in the retailer’s advertising effort and then each player determines the advertising effort that maximizes his/her profit. In the second scheme, the retailer chooses the manufacturer’s participation rate and then the manufacturer determines the advertising efforts of both players with the objective of maximizing the manufacturer’s profit. Each participation scheme corresponds to a special Stackelberg game: the manufacturer is the leader of the first, while the retailer is the leader of the second. The Stackelberg equilibrium advertising efforts and participation rate in both games are provided. Then the equilibrium strategies of the two players in the analyzed scenarios are compared with the Nash equilibrium in the competitive framework. Finally, the conditions which suggest a special kind of agreement to a player are analyzed. This work was supported by the Italian Ministry of University and Research and the University of Padua.     

Does stock return predictability affect ESO fair value?

Executive Stock Options (ESOs) are modified American options that cannot be valued using standard methods. With a few exceptions, the literature has discussed the ESO fair value by assuming unpredictable stock returns which are not supported by the available empirical evidence. In this paper we obtain the fair value of American ESOs when stock returns are predictable and, specifically, driven by the trending Ornstein–Uhlenbeck process of Lo and Wang (1995). We solve the executive’s portfolio allocation problem for a simple buy-and-hold strategy when his wealth can be distributed between a risk-free asset and a market portfolio. This problem is jointly solved with the executive’s optimal exercise policy. We find that executives tend to wait longer the higher the predictability, independently of the composition of executive’s asset menu. We have also analyzed the implications under the FAS123R proposals for the ESO fair value and found that, even for low autocorrelations, there is a meaningful mispricing when unpredictable returns are erroneously assumed.     

S-convexity revisited (fuzzy): long version

In this revisional article, we criticize (strongly) the use made by Medar et al., and those whose work they base themselves on, of the name ‘convexity’ in definitions which intend to relate to convex functions, or cones, or sets, but actually seem to be incompatible with the most basic consequences of having the name ‘convexity’ associated to them. We then believe to have fixed the ‘denominations’ associated with Medar’s (et al.) work, up to a point of having it all matching the existing literature in the field [which precedes their work (by long)]. We also expand his work scope by introducing s ₁-convexity concepts to his group of definitions, which encompasses only convex and its proper extension, s ₂-convex, so far. This article is a long version of our previous review of Medar’s work, published by FJMS (Pinheiro, M.R.: S-convexity revisited. FJMS, 26/3, 2007).     

A model of the executive's decision processes in new product development

This paper introduces the concept of fuzziness to deal quantitatively with the imprecision of the meaning of the executive's judgment stated in a natural language and presents a model of the executive's decision processes for the new product introduction which contain fuzzy-2 states, fuzzy-2 information systems, fuzzy-2 information signals, fuzzy-2 strategy are presented. The committee decision problem under fuzzy-2 constraints is dealt with.     

Choosing the equilibrium behavior in an infinitely repeated 2 × 2 game for conservative and innovative gamers

We examine an infinitely repeated 2 × 2 game in which each gamer in every next round chooses his own pure strategy based on the results of a random experiment; the random experiment is generated by gamer’s own arbitrary mixed strategy, which with high probability (but generally different from 1) gives the gamer a choice of strategy appropriate to his type of behavior: conservative or innovative.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultiple objective linear programming (MOLP) problems is developed and compared to other interactive MOLP methods. The decision maker (DM)’s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for ‘utility efficiency’ for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of ‘strength of preference ’ is developed for the assessment of the DM’s unknown utility function where he can express his preference for a pair of extreme points as ‘strong ’, ‘weak ’, or ‘almost indifferent ’. The problem of ‘inconsistency of the DM’ is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed. All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

The method of integral relations for computing blunt body flows with a detached shock wave

Dorodnicyn’s classical work concerning the method of integral relations is given in his original presentation. Developments of the method provided by Dorodnicyn’s students are outlined. Belotserkovskii’s 1956 paper concerning a technique for computing the detached shock wave in flow over a cylinder is presented in full (with comments and numerical results). A technique for the study of flow characteristics for space vehicles of particular shapes is described. The breakthrough character of techniques proposed more than 50 years ago is demonstrated, and their (still important) philosophy is assessed.     

On coordination of supply chain based on information asymmetry of effort level and fuzzy market environment

The agent’s private information contributes greatly to a person to make principal decision in the supply of a chain coordination. Therefore, it is a great issue for him to design an effective incentive mechanism in order to get the true information from the agent in his principle making. Assuming that the demand depend upon an agent’s effort level and the fuzzy market condition, the author in this paper researches and analyzes the principle-agent problem under fuzzy information asymmetry condition by using the theory of principal-agent as well as incentive mechanism.     

Work effort, consumption, and portfolio selection: when the occupational choice matters

We consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market including the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility. The power utility case is discussed as well. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two positions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibility to benefit from her work effort by acquiring own-company shares. This gives insight into aspects of optimal contract design. Our framework is applicable to the pharmaceutical and financial industry, and the IT sector.     

Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper

The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of~q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler’s constant. The main tools are Euler-type integrals and hypergeometric series. 2000 Mathematics Subject Classification Primary—11Y60; Secondary—11J72, 33C20, 33D15 The work of the second author is supported by an Alexander von Humboldt research fellowship Dedication: To Leonhard Euler on his 300th birthday.     

A convergence theorem of Rosen’s gradient projection method

Since Rosen’s gradient projection method was published in 1960, a rigorous convergence proof of his method has remained an open question. A convergence theorem is given in this paper. Part of this author’s work was done while he studied at the Department of Mathematics, University of California at Santa Barbara, and was supported by the National Science Foundation under Grant No. MCS83-14977. Part of this author’s work was done while he visited the Computer Science Department, University of Minnesota, Minneapolis, and was supported by the National Science Foundation under Grant No. MCS81-01214.     

$\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions

We prove that C²\mathcal{C}^{2} surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass (Invent. Math. 176:617–636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls by contracting maps in a approach combining hyperbolic theory and Yomdin’s theory.     

Jacobi and Kummer’s ideal numbers

In this article we give a modern interpretation of Kummer’s ideal numbers and show how they developed from Jacobi’s work on cyclotomy, in particular the methods for studying “Jacobi sums” which he presented in his lectures on number theory and cyclotomy in the winter semester 1836/37.     

Discovery of a lost factoring machine

Despite the importance of the work of Eugène Carissan and the remarkable machine he built, very few people were aware of his work. Perhaps this was because both Pierre and Eugène died within 5 years of the exhibition of the machine in Paris in 1920. Indeed, when D. H. Lehmer began to construct his first automatic sieve in 1926, he had never heard of Carissan’s sieve, and he remained ignorant of it until 1989. Lehmer’s 1926 sieve, which was in some ways much less sophisticated than Carissan’s, made use of bicycle chains driven by an electric motor. It was his first attempt of many. Each time he built a new sieve, the most advanced technology was used: photoelectric cells in 1932,16-mm movie film in 1936, and delay lines in 1965 for the DLS-127 (later DLS-157). For an account of all of this, see [18].     

W. Charles Holland, 75<Superscript>th</Superscript> birthday

This issue of Mathematica Slovaca is in honour of W. Charles Holland’s 75th birthday. We present here a brief account of some of his research (to date) and a couple of brief personal sketches of the man.     

“Naturadeus”, a metaphor of the Perfect Diamond

In this essay, the author outlines his re-construction of Spinoza’s ontological monism by re-presenting the system of Ethica, ordine geometrico demonstrata, in an “intuitive” model of the Perfect Diamond, called NATURADEUS. So, for example, ordo et connexio idearum et rerum, is presented to the inner eye in the forms of two parallel structures, of rays and of facets within the NATURADEUS, respectively. The conceptual background of the proposed model is mostly analytic, the author essays to develop some ideas of Jonathan Bennett’s Spinoza’s metaphysics (especially “transattributive mode identity”), with strong emphasis on ethical issues of ontological monism or pantheism. This essay is written as a dialogue between master Bruno and his student John (physically absent at the moment). More philosophical dialogues of this kind can be found on the author’s web page and in his book Four Seasons (in Slovenian, 2002).     

The computational complexity of bilevel assignment problems

In bilevel optimization problems there are two decision makers, the leader and the follower, who act in a hierarchy. Each decision maker has his own objective function, but there are common constraints. This paper deals with bilevel assignment problems where each decision maker controls a subset of edges and each edge has a leader’s and a follower’s weight. The edges selected by the leader and by the follower need to form a perfect matching. The task is to determine which edges the leader should choose such that his objective value which depends on the follower’s optimal reaction is maximized. We consider sum- and bottleneck objective functions for the leader and follower. Moreover, if not all optimal reactions of the follower lead to the same leader’s objective value, then the follower either chooses an optimal reaction which is best (optimistic rule) or worst (pessimistic rule) for the leader. We show that all the variants arising if the leader’s and follower’s objective functions are sum or bottleneck functions are NP-hard if the pessimistic rule is applied. In case of the optimistic rule the problem is shown to be NP-hard if at least one of the decision makers has a sum objective function.     

Optimal incentive contracts under relative income concerns

We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral biases: envy, jealousy, or admiration toward the other coworkers’ compensation. We assume workers care about their relative position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303–328, 1987). We model team production by agents in which each agent’s effort generates an observable signal and depends on efforts of other agents. One of the important findings is that an agent’s optimal effort is negatively impacted by the behavioral biases in other agents’ judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica 69(1):1–35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits high pay-for-performance sensitivity.     

A Priori knowledge contextualised and Benacerraf’s dilemma

In this article, I discuss Hawthorne’s contextualist solution to Benacerraf’s dilemma. He wants to find a satisfactory epistemology to go with realist ontology, namely with causally inaccessible mathematical and modal entities. I claim that he is unsuccessful. The contextualist theories of knowledge attributions were primarily developed as a response to the skeptical argument based on the deductive closure principle. Hawthorne uses the same strategy in his attempt to solve the epistemologist puzzle facing the proponents of mathematical and modal realism, but this problem is of a different nature than the skeptical one. The contextualist theory of knowledge attributions cannot help us with the question about the nature of mathematical and modal reality and how they can be known. I further argue that Hawthorne’s account does not say anything about a priori status of mathematical and modal knowledge. Later, Hawthorne adds to his account an implausible claim that in some contexts a gettierized belief counts as knowledge.