Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms

The cooperative luminescence and absorption properties of Yb³⁺ doped aluminosilicate glass optical fibres and preforms are investigated in detail. In accordance with previous investigations, both the visible cooperative luminescence and the infrared luminescence decay measurements have been resolved into a single exponential decay component. We show that for a glass with similar Yb³⁺ dopant concentration but more Al³⁺, the glass emits less visible luminescence. Absorption loss measurements completed on fibre samples revealed a broad absorption in the 350-500 nm range, which we propose is due to a combination of Yb²⁺ absorption and cooperative absorption from Yb³⁺ ion pairs.     

A goodwill model with predatory advertising

We investigate the dynamic advertising policies of two competing firms in a duopolistic industry, assuming a predatory phenomenon between their advertising campaigns. The resulting model is a differential game which is not linear-quadratic. We show that there exists a Markovian Nash equilibrium, and that it leads to time constant advertising strategies. According to this model, predatory advertising produces a negative externality: the interference between the advertising campaigns decreases the total demand of the market.     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.     

A parallel search game

We answer in negative a question of Gál and Miltersen [Proc 30th Int Coll Automata, Languages, and Programming (ICALP) 2003, pp. 332–344] about a combinatorial game arising in the study of time‐space trade‐offs for data structures. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Sequencing games with repeated players

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations. In max-RP sequencing situations it is assumed that each player’s cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing games. Moreover, it is seen that min-RP sequencing games are convex. We thank two referees for their valuable suggestions for improvement. Financial support for P. Calleja has been given by the Ministerio de Educación y Ciencia and FEDER under grant SEJ2005-02443/ECON, and by the Generalitat de Catalunya through a BE grant from AGAUR and grant 2005SGR00984.     

Noncooperative stochastic games under a n-stage local contraction assumption

We consider a class of noncooperative stochastic games with general state and action spaces and with a state dependent discount factor. The expected time duration between any two stages of the game is not bounded away from zero, so that the usual N-stage contraction assumption, uniform over all admissible strategies, does not hold. We propose milder sufficient regularity conditions, allowing strategies that give rise with probability one to any number of simultaneous stages. We give sufficient conditions for the existence of equilibrium and ∈-equilibrium stationary strategies in the sense of Nash. In the two-player zero-sum case, when an equilibrium strategy exists, the value of the game is the unique fixed point of a specific functional operator and can be computed by dynamic programming.     

Persuasive advertising under Bertrand competition: A differential game

We investigate a linear state differential game of advertising, under Cournot and Bertrand competition. A unique saddlepoint equilibrium exists if the marginal cost of advertising is sufficiently low. Bertrand competition entails more intense advertising than Cournot competition, since increasing market size is more important to firms when competition is tough.     

Periodical states and marching groups in a closed owari

Owari is an old African game that consists of cyclically ordered pits that are filled with pebbles. In a sowing move all the pebbles are taken out of one pit and distributed one by one in subsequent pits. Repeated sowing will give rise to recurrent states of the owari. Bouchet studied such periodical states in an idealised setup, where there are infinitely many pits. We characterise periodical states in owaris with finitely many pits. Our result implies Bouchet's result.     

A note on coalitional manipulation and centralized inventory management

In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies this property. The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN.     

Dual-Role Based Pricing in a Dynamic and Competitive Environment

The dual role of price, as a product attribute signaling quality and as a measure of sacrifice, serving as a benchmark for comparing the utility gains from superior product quality, is now well established in the marketing and economic literature. However, knowledge about their long-run impact and the influence of competition on these effects still remains very sparse. In the current paper, with reference to a dynamic and competitive framework, an analytical model is proposed to help determining optimal decision rules for price incorporating both roles. The main results are as follows: (i) The optimal pricing policy is determined as a Nash equilibrium strategy. (ii) The resulting equilibrium price is higher than an equilibrium that disregards the carryover price effects. (iii) For a symmetric competition, we provide normative rules on how firms should set prices as a function of the perceived quality; particularly, how the price should be set initially, when there is little product familiarity and the perceived quality is low, and how this price should vary as the perceived quality increases. (iv) At steady state, we find that the level of equilibrium margin, in percentage terms, decreases with the elasticity of demand with respect to the brand price, but this decrease is moderated by the elasticity of demand with respect to the brand perceived quality, the cross elasticity of demand with respect to the competitor’s perceived quality and the effect of the competitor’s current price on the firm’s perceived quality deterioration. The author thanks Konstantin Kogan for helpful discussions and comments.