Kensaku Kikuta

Rendezvous search on a star graph with examination costs

We discuss some of the problems that arise when two teams attempt to rendezvous on a star graph while minimizing a cost arising from three components: movement, time and searching. The intuitive strategy is to meet at the center, but in some circumstances this strategy is not optimal and the participants must employ the alternative strategy of meeting at a node. There is also the question of what tactics to employ on the first move. We derive procedures by which two participants can arrive at an optimal solution.

Search games on networks with travelling and search costs and with arbitrary searcher starting points

The authors analyze two-person zero-sum search games of the following type. Play takes place on a network; the hider must choose a node and remain there while the searcher can choose the node at which he starts. To detect the hider, the searcher needs to conduct a search at the node chosen by the hider. Searching a node involves a cost which can vary from node to node. In addition to the search costs, the searcher also incurs travelling costs represented by distances on the edges. The costs are known to both players and the searcher wants to minimize his total costs. An upper bound for the value of the game is obtained and a lower bound when the network has all its edge lengths the same. Restricting attention to networks which have all their edges of the same length, the upper, and lower bounds are shown to coincide for some networks including Hamiltonian ones. Some results for the star and line networks are also given.

Technical Note---An Ambush Game with a Fat Infiltrator

This paper concerns a two-person zero-sum game between an infiltrator and a defender. The infiltrator wants to pass through a channel, while the defender wants to detect the infiltrator by laying static underwater devices across the channel. Previous work assumed the infiltrator has zero width. We consider an extension when the infiltrator has a positive width, and a proportion of its width needs to be detected by the underwater devices for a positive identification. We show that the positive-width problem reduces to the zero-width problem by an appropriate transformation.

Search games on a network with travelling and search costs

The authors analyse two-person zero-sum search games in which play takes place on a network and in discrete time. The hider first chooses a node and remains there for the duration of the game. The searcher then chooses a node and searches there. At each subsequent time instant the searcher moves from the node he occupies to an adjacent node and decides whether or not to search it. Play terminates when the searcher is at the node chosen by the hider and searches there. The searcher incurs costs in moving from one node to another and also when a node is searched. The searcher wants to minimize the costs of finding the hider and the hider wants to maximize them. The paper has two main strands. The first investigates these games on directed, not necessarily strongly connected, networks; previous work has tended to concentrate on undirected networks. The second complements previous work on undirected networks by obtaining results for the case when the search cost is the same for all nodes.

Two point one sided rendezvous

In a rendezvous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider two seekers in the plane. This is a one sided problem since Seeker 1 begins at a predetermined point O. Seeker 2 begins at one of a finite set of points xi with probability pi. We first discuss the general situation and then consider the specific case when Seeker 2 can begin from one of two points.

Analysis of an Intentional Fault Which Is Undetectable by Local Checks under an Unfair Scheduler

We consider a malicious unfair adversary which generates an undetectable fault by local checks, called an intentional fault. Though the possibility of such a fault has ever been suggested, details of its influence and handling are unknown. We assume the intentional fault in a self-stabilizing mutual exclusion protocol, a hybrid of previously proposed ones that complement each other. In the hybrid protocol, we can cope with the fault by using optional strategies, whether or not sending a minor token, which plays a role of preventing the contamination from spreading. We construct a payoff matrix between a group of privileged processes and an adversary, and consider a multistage two-person zero sum game. We interpret the game in two ways: whether it continues or replays the game after an ME(mutual exclusion)-violating repair, in which more than one unexpected privileges are given. For each case, we evaluate the ability of malicious unfair adversary by using a mixed strategy. Our idea is also considered as a general framework for strengthening an algorithm against an intentional fault.

Open Problems on Search Games

We discuss two classic search games: Isaacs’ princess and monster game, and Dresher’s high-low guessing game. Despite the fact that these games were introduced decades ago, there are still numerous open problems around them.

Price stabilization in networks: what is an appropriate model?

We consider a simple network model for economic agents where each can buy commodities in the neighborhood. Their prices may be initially distinct in any node. However, by assuming some rules on new prices, we show that the distinct prices will converge to unique by iterating buy and sell operations. First, we present a protocol model in which each agent always bids an arbitrary price in the difference between his own price and the lowest price in the neighborhood, called max price difference. Next, we derive the condition that price stabilization occurs in our model. Furthermore, we consider game (auction) theoretic price determination by assuming that each agents value is uniformly distributed over the max price difference. Finally, we perform a simulation experiment. Our model is suitable for investigating the effects of network topologies on price stabilization.

TWISTED DUAL GAMES AND THEIR PROPERTIES

We define a duality of solutions in coalitional games that we call a twisted duality. This twisted duality extends the rule of self-duality in bankruptcy problems. After showing that the prekernel and prenucleolus exhibit twisted duality, we define a twisted reduced game property and characterize the prekernel and prenucleolus by axioms including this property. We note that the Shapley value satisfies twisted duality, and we define another twisted reduced game property by and characterize the Shapley value by axioms including this property.

An Inflation / Deflation Model for Price Stabilization in Networks

We consider a simple network model for economic agents where each can buy goods in the neighborhood. Their prices may be initially distinct in any node. However, by assuming some rules on new prices, we show that the distinct prices will reach an equilibrium price by iterating buy and sell operations. First, we present a protocol model in which each agent always bids at some rate in the difference between his own price and the lowest price in the neighborhood. Next, we show that the equilibrium price can be derived from the total funds and the total goods for any network. This confirms that the inflation / deflation occurs due to the increment / decrement of funds as long as the quantity of goods is constant. Finally, we consider how injected funds spread in a path network because sufficient funds of each agent drive him to buy goods. This is a monetary policy for deflation. A set of recurrences lead to the price of goods at each node at any time. Then, we compare two injections with half funds and single injection. It turns out the former is better than the latter from a fund-spreading point of view, and thus it has an application to a monetary policy and a strategic management based on the information of each agent.