The parametric minimax problem, which finds the parameter value minimizing the weight of a solution of a combinatorial maximization problem, is a fundamental problem in sensitivity analysis. Moreover, several problems in computational geometry can be formulated as parametric minimax problems. The parametric search paradigm gives an efficient sequential algorithm for a convex parametric minimax problem with one parameter if the original non-parametric problem has an efficient parallel algorithm. We consider the parametric minimax problem with d parameters for a constant d, and solve it by using multidimensional version of the parametric search paradigm. As a new feature, we give a feasible region in the parameter space in which the parameter vector must be located. Typical results obtained as applications are: (1) Efficient solutions for some geometric problems, including theoretically efficient solutions for the minimum diameter bridging problem in d-dimensional space between convex polytopes. (2) Solutions for parametric polymatroid optimization problems, including an O(n log n) time algorithm to compute the parameter vector minimizing k-largest linear parametric elements with d dimensions.
We study synchronous phenomena in neural network models with neurons described by Hindmarsh–Rose (HR) equation. Those neurons generate periodic spikes, quasiperiodic spikes and chaotic spikes in some range of bifurcation parameters. We propose two models: a model with synaptic connections described by a gap junction (model 1) and a model with synaptic connections described by a first-order kinetics (model 2). We calculate numerically Lyapunov exponents and quadratic deviations of membrane potentials among the neurons. By increasing the strength of excitatory synapses, we find that a chaotic synchronization occurs for model 1, but does not for model 2 when the values of the bifurcation parameters for each neuron are set to those for the chaotic spikes. On the other hand, by increasing the strength of inhibitory synapses, it turns out that the periodic spikes are generated in antiphase for model 1, and the chaotic spikes and the periodic spikes are alternately generated in antiphase for model 2 for those values of the bifurcation parameters.
We propose an image segmentation algorithm under an expectation-maximum scheme using a Bethe approximation. In the stochastic image processing, the image data is usually modeled in terms of Markov random fields, which can be characterized by a Gibbs distribution. The Bethe approximation, which takes account of nearest-neighbor correlations, provides us with a better approximation to the Gibbs free energy than the commonly used mean-field approximation. We apply the Bethe approximation to the image segmentation problem and investigate its efficiency by numerical experiments. As a result, our approach shows better robustness and faster converging speed than those using the mean-field approximation.
Let H be the Heisenberg group and let Γ be the discrete subgroup of H with integer entries. We obtain a necessary and sufficient condition for a homogeneous metric g on H⁄Γ to be a critical point for the total scalar curvature functional I defined for the set A(M) of some proper homogeneous Riemannian metrics on H⁄Γ.
Special Section for the GSIS Workshop on Game Theoretic Analyses of Social Institutions
This study is intended to examine an efficient industrial garbage disposal system and an optimal policy to establish it. Industrial waste created in processes of all production is increasing every year. That increase is exacerbated by the shortage of disposal space, engendering frequent cases of illegal abandonment. We analyze environmental policies to restrain illegal abandonment and to establish a social optimum under the two-region model that incorporates transboundary movements of industrial garbage. Although a subsidy policy is an optimal policy in the one-region model, it is not optimal policy in the two-region model because of a subsidy-reducing game.
This paper presents an examination of a lobbying game between a government with informational superiority and a special interest group (SIG), which is a lobbyist. This informational superiority of the government allows the application of an analytical method of ordinary contract theory in this game. Results of these analyses show that, for a SIG whose population is sufficiently small, although the government has informational superiority to the SIG, the government is unable to prevent the SIG from distorting policy excessively by endowing a political contribution to the government. However, for a SIG whose population is sufficiently large, the government’s informational superiority can stanch the SIG inducement of a larger policy by endowing a political contribution to the government. In this case, government disclosure is not always socially desirable.
This study focused on real world conflicts over the allocation of costs in cases where several municipalities jointly maintain local bus transportation services. Traditionally, agreement over allocation of costs is reached through discussions between municipalities, which can be divided into two stages without any assistance from knowledge of game theory. Two points were analyzed during the study: the structure of the game and the concept of fairness behind each case. We described real situations using cooperative game theory and interpreted the games as consisting of two stages including the proposition of cost allocation methods followed by the seeking of acceptable allocations. The fair allocation concepts behind each case were identified and disruption nucleolus was shown to be among the most plausible concepts. These results were used to illustrate the procedure to allocate the costs, which was concluded as being useful to resolve conflicts over the allocation of costs of local bus transportation services jointly maintained by several municipalities.
In infrastructure planning, more and more citizens are participating in decision making process. Such process is often called “participatory planning.” This paper focuses on the aspect of participatory planning as an “institutionalized” conflict. In an institutionalized conflict, only a few players can take actions. Other citizens can observe a development of the conflict, but they can affect the process only indirectly. Players try to behave according to the preferences of their “supporters.” In such a conflict, players need to communicate with supporters to know their preferences. However, players and supporters cannot necessarily share the knowledge about interaction of players’ behaviors (strategies), and they tend to use more simplified mechanisms. Under such simplified mechanisms, players may take different behavior principles, and a final outcome of a conflict can be changed. In this paper, an institutionalized conflict in participatory planning is assumed, and an appropriate opinion-summarizing mechanism between players and supporters is examined. First, the conflict in participatory planning is modeled as non-cooperative game. Then, the relationship between an opinion-summarizing mechanism and an outcome of the conflict is analyzed, and the mechanism based on preference on actions may lead to an inefficient outcome. It is also shown that the effect of opinion-summarizing mechanisms depends on the structure of a conflict.
A simple link-formation game is developed to analyze efficiency of construction of network infrastructures, especially road networks, under locally-distributed authorities of network construction decision. In the model, three serially-located local governments (nodes) are eligible to provide its own roads (links) to connect to the neighboring nodes aiming at minimizing the provision cost while satisfying local demand for connection. Inefficiency of equilibrium network provision by distributed authority is clarified. The intervention by central authority with some ‘cooperation rule’ under which links have to be constructed through some bargaining (cooperation) by the both-end nodes is introduced. Its effects on network efficiency are also analyzed. Population distribution and other conditions that the cooperation rule remedies inefficiency are then clarified.
It is pertinent to build an effective external audit system to prevent manipulations in the analysis of project evaluation. In reality, it is difficult for an external auditor to understand details of the analysis. Hence, it is likely that he would misinterpret and penalize the analysts even though they have not manipulated the analysis. The possibility of misinterpretation gives analysts the disincentive for participating in project evaluation business. In the long term, this would hinder the implementation of socially desirable projects. This paper tries to derive the optimal structure of external audit system of project evaluation focusing on the quality of audit. We modify and analyze the principal=agent=auditor model which we suggested in Fukumoto and Tsuchiya (2004).
In this paper, a model is proposed to analyze how a dispute resolution process can be controlled by third parties’ adjudications in construction projects. We analyze the effects of introducting two alternatives, Dispute Adjudication Board (DAB) and Dispute Review Board (DRB) into the dispute resolution process under the FIDIC standard conditions of construction contract. The model explains how the differences between DAB and DRB affect the efficiency of the dispute resolution process. Differences between dispute resolution processes in FIDIC and GCW, the standard conditions of construction contract in Japan, are also analyzed. The following conclusions are obtained. 1) DAB and DRB are efficient in settling disputes by agreement if the possibility of their errors is sufficiently small. 2) DAB is more likely to cause arbitration than DRB. 3) The GCW does not provide less efficient dispute resolution procedure than the old FIDIC. When the Japanese construction market becomes completely open to foreign contractors disputes may be followed by arbitration more often under the GCW model than under the FIDIC with no third parties’ adjudication.