Computing power indices: Multilinear extensions and new characterizations

Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n-person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.     

Evaluation of firm’s loss due to incomplete information in real investment decision

We investigate the effect of incomplete information in a model where a start-up with a unique idea and technology pioneers a new market but will eventually be expelled from the market by a large firm’s subsequent entry. We evaluate the start-up’s loss due to incomplete information about the large firm’s behavior. We clarify conditions under which the start-up needs more information about the large firm. The proposed method of evaluating the loss due to incomplete information could also be applied to other real options models involving incomplete information.     

一类二元对策问题

讨论一类二元对策问题.在对策双方能力不同的情况下,推导对策双方获胜的充要条件和获胜方获胜的具体对策方案.文后的应用实例说明,本文所讨论的问题具有一定的应用价值.     

Alliances, partnerships and the Banzhaf semivalue

The coordination of strategies in a cooperative game, when some players decide to act together, is the basis of the partnership notion. Nevertheless, in some situations, it may be more convenient to form an effective coalition or alliance. In this work, we consider the Banzhaf semivalue and use it to discuss the convenience to form either partnerships or alliances, especially in simple games. Throughout the paper, some mathematical properties of the Banzhaf semivalue, in relation with the partnership formation, are derived.     

Coordination mechanisms for inventory control in three-echelon serial and distribution systems

This paper is concerned with the coordination of inventory control in three-echelon serial and distribution systems under decentralized control. All installations in these supply chains track echelon inventories. Under decentralized control the installations will decide upon base stock levels that minimize their own inventory costs. In general these levels do not coincide with the optimal base stock levels in the global optimum of the chain under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. To remove this cost inefficiency, two simple coordination mechanisms are presented: one for serial systems and one for distribution systems. Both mechanisms are initiated by the most downstream installation(s). The upstream installation increases its base stock level while the downstream installation compensates the upstream one for the increase of costs and provides it with a part of its gain from coordination. It is shown that both coordination mechanisms result in the global optimum of the chain being the unique Nash equilibrium of the corresponding strategic game. Furthermore, all installations agree upon the use of these mechanisms because they result in lower costs per installation. The practical implementation of these mechanisms is discussed.     

An algorithm of evolutionarily stable strategies for the single-population evolutionary game

In this paper, we study the single-population evolutionary game and construct an algorithm to find evolutionarily stable strategies. Finally, by an example, we illuminate the computing process of algorithm.     

Numerical techniques for finding equilibrium in von Neumann’s model

Numerical methods for finding an equilibrium position in von Neumann’s multisector economy model are proposed. They can be implemented using computers with floating-point arithmetic. The proposed methods are based on reducing the problem to solving the corresponding matrix games.     

On the Sociobiology of Hawks and Doves. A phase diagram for integration and segregation

Competing groups in a population will be integrated or segregated depending on their contest strategies. In this work a population of a fixed proportion of hawks and doves is supposed to be able to employ two different contest strategies, one more competitive than the other one. Energies are derived for populations employing these strategies and these energies depend on the availability of the resource for which hawks and doves compete. The energy for the less competitive strategy is lower than the other one when the resource is abundant. In that case hawks and doves can be in cohabitation in all proportions. If, however, the resource is scarce, the energy of the more competitive strategy is lower than the other one. In that case complete segregation of hawks and doves into colonies will result. The situation is akin to the phase pressure diagram of a binary solution with eutectic point, miscibility gap in the liquid phase and complete miscibility in the vapour phase. This revised version was published online in August 2006 with corrections to the Cover Date.     

An oligopoly model of dynamic advertising competition

An oligopoly model is presented that allows the determination of feedback Nash equilibrium advertising strategies for an oligopoly. Analyses of symmetric and asymmetric oligopolies with the model show that unit contribution and advertising effectiveness have positive effects on a competitor’s own advertising and steady-state sales, while discount rate and decay rate have negative effects. An asymmetric analysis further shows that unit contribution and advertising effectiveness affect positively, and discount rate and decay rate negatively, a competitor’s rivals’ advertising, but have effects in opposite directions regarding rivals’ steady-state sales. The symmetric and asymmetric analyses also show that steady-state sales per competitor decline with the number of competitors in the oligopoly, while total oligopoly steady-state sales increase. The model is applied empirically to the triopolistic competition involving Anheuser-Busch, SABMiller, and Molson Coors in the beer industry.     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用，获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后，新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.