Resource location games

In this paper, we introduce and analyze resource location games. We show core non-emptiness by providing a set of intuitive core allocations, called Resource-Profit allocations. In addition, we present a sufficient condition for which the core and the set of Resource-Profit allocations coincide. Finally, we provide an example showing that when the sufficient condition is not satisfied, the coincidence is not guaranteed.     

Boundary blow-up rate and uniqueness of the large solution for an elliptic cooperative system of logistic type

This paper ascertains the blow-up rates of each of the components of a singular boundary value problem related to a cooperative system of logistic type, in order to establish the uniqueness of the large solution. Astonishingly, the cooperative coupling does not change the blow-up rates of the uncoupled system provided these blow-up rates are sufficiently close, though it changes exactly one of them, keeping invariant the other, when they are bounded away. This seems to be the first time where this change of behavior has been documented in the literature.     

Cooperative catalysis: Condensation-aromatization for synthesis of 2-(4-nitrophenyl)-1H-benzimidazole by silica immobilized Brønsted-Lewis acidic ionic liquid (Si-BLAIL)

Herein, pleasing the advantageous of both Brønsted and Lewis acidic site of Si-BLAIL the condensation-aromatization reaction has been carried out. The striking distinctiveness of work is optimum reaction condition, easy work-up, high yield, catalyst recyclability, non-inertness of reaction flask, simple catalyst loading method. The decreases in the amount of catalyst and reaction time shows good to high (71%–93%) yield suggests about the involvement of some interesting mechanism such as cooperative catalysis. The mechanism has been hypothesizes as, the Si-BLAIL increase the efficiency of condensation reaction possibly by providing the proton in 2-position of cationic imidazolium ring of BLAIL through the hydrogen bond interaction with carbonyl group and nucleophilic activation during aromatization by hydrogen bond acceptor ability of Lewis adduct anion of BLAIL. The catalyst Si-BLAIL shows massive affirm for industrial applications. The Si-BLAIL has identified as the best acid catalyst for 2-(4-nitrophenyl) benzimidazole synthesis with additional benefits of cooperative catalysis.     

Performance evaluation of improved double-threshold energy detector over Rayleigh-faded sensing and imperfect reporting channels

Cognitive radio (CR) has been viewed as a promising solution to spectrum scarcity. In order to design a reliable CR system, many improvements have been proposed to enhance spectrum sensing performance of secondary users (SUs) in a CR network (CRN). Sensing reliability and transmission throughput of SUs are two important performance criteria, which should be optimized to enhance signal protection of primary user (PU) as well as spectrum utilization rate. In this paper, we consider Rayleigh-faded sensing channels and SUs use improved energy detector (IED) to make their local decisions. The final decision is made in a fusion center (FC) through the cooperative spectrum sensing (CSS) scheme with erroneous reporting channels. We show that the improved double-threshold energy detector (IDED) outperforms the conventional energy detector (CED) in terms of the total error rate. Furthermore, we evaluate the transmission throughput of the CRN through various ED schemes with detection constraints over both perfect and imperfect reporting channels. We show that the IDED has the highest achievable throughput among different ED schemes over imperfect reporting channels.     

An evolutionary game theory model of binary opinion formation

A basic characteristic of most opinion models is that people tend to agree or compromise in the opinion interaction, which could be hopefully described by cooperative games in the evolutionary game theory framework. This paper presents game theory methods to model the formation of binary opinions: cooperative games are proposed to model the interaction rules of general people who tend to find an agreement; minority games are proposed to model the behaviors of contrarians; opinion preference is considered by varying the payoff values. The Majority Voter model could be restored from the proposed games. The game theory models show evolutionary results similar to traditional opinion models. Specially, the evolution of opinions with consideration of contrarians is in accordance with the Galam model. Furthermore, influences of evolving rule, network topology and initial distribution of opinions are studied through numerical simulations. Discussions about methods to promote or hinder the consensus state at the best equilibrium point are given.     

Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited

Analytic solutions for optimal collision avoidance strategies are of great importance when setting and validating air traffic rules and as a benchmark when validating automated proximity management and collision avoidance systems. Such a solution for optimal air collision avoidance strategies for a coplanar cooperative encounter between two identical aircraft (or ships) was first presented by Merz (Proc. Joint Automatic Control Conf., Pap. 15-3:449–454, 1973; Navigation 20(2):144–152, 1973). Unfortunately, Merz provided only a very brief indicative justification for his solution. This paper presents a rigorous analysis of the problem. New results include a characterization of a complete set of extremals, justification for optimal strategies and an analysis of the properties of the regions of different optimal strategies. A simple, practical and sufficiently accurate closed form approximation for dispersal curves that partition the plane of initial positions into the regions of different optimal strategies is also presented. We thank the anonymous referees and our colleagues Drs. R.S. Anderssen and R. Jarrett for helpful comments and suggestions.     

Values of games with graph restricted communication and a priori unions

Two new values for transferable utility games with graph restricted communication and a priori unions are introduced and characterized. Moreover, a comparison between these and the Owen graph value is provided. These values are used to analyze the distribution of power in the Basque Parliament emerging from elections in April 2005.     

Pooling,pricing and trading of risks

Exchange of risks is considered here as a transferable-utility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced merely in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.     

Global attractivity of positive periodic solutions for nonlinear impulsive systems

In this paper, the existence, uniqueness and global attractivity of positive periodic solutions for nonlinear impulsive systems are studied. Firstly, existence conditions are established by the method of lower and upper solutions. Then uniqueness and global attractivity are obtained by developing the theories of monotone and concave operators. And lastly, the method and the results are applied to the impulsive n$n$-species cooperative Lotka–Volterra system and a model of a single-species dispersal among n$n$-patches.     

An acyclic relation for comparison of bargaining powers of coalitions and its interrelationship with bargaining set

This paper proposes a method to compare bargaining power of coalitions within the framework of games in coalition form with transferable utility. The method is expressed by a relation on the set of all coalitions in a game, the relation which is defined based on the players’ bargaining power. It is shown in this paper that the newly defined relation satisfies acyclicity. Also, it is verified in this paper that the set of all individually rational payoff configurations under which all coalitions have the equal bargaining power coincides with the bargaining set. Some examples demonstrate how the newly proposed method works.