We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game is started by the breaker. This implies the same in the (2 : 1) biased game also in the maker-start game. It remains open to characterize the maker-win graphs...

We consider a Maker-Breaker type game on the square grid, in which each player takes t points on their tth turn. Maker wins if he obtains n points on a line (in any direction) without any of Breaker’s points between them. We show that, despite Maker’s apparent advantage, Breaker can prevent Maker from winning until about his nth turn. We actually prove a stronger result: Breaker only needs to c...

In research situations usually approached by Decision Theory, it is only considered one researcher who collects a sample and makes a decision based on it. It can be shown that randomization of the sample does not improve the utility of the obtained results. Nevertheless, we present situations in which this approach is not satisfactory. First, we present a case in which randomization can be an i...

Let P be a monotone increasing graph property, let G = (V,E) be a graph, and let q be a positive integer. In this paper, we study the (1 : q) Maker-Breaker game, played on the edges of G, in which Maker’s goal is to build a graph that satisfies the property P . It is clear that in order for Maker to have a chance of winning, G itself must satisfy P . We prove that if G satisfies P in some stron...

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns in claiming previously unclaimed edges of a given graph H . Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from achieving his goal. We define a function f on the integers and show that for every d-regular graph G on n vertices there is a graph H with at most f(d)n edges such ...

We estimate a structural model of herd behavior in …nancial markets. A sequence of traders exchanges an asset with a market maker. Trade occurs over many days. Herd behavior can arise despite the fact that the price is e¢ ciently set by the market maker. The price is updated too slowly by the market maker and there are periods in which traders choose the same action independently of their priva...

We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being “clever”. The reverse scenario is treated in a separate paper. We determine the sharp threshold bias of classical games played on the edge set of the complete graph Kn, such...

Laboratory seakeeping test under irregular wave load is essential for studying seakeeping performances of marine and offshore structures. One of the key techniques in such a sort of test is how to assure the quality of wave load. By assuring the quality of wave load, we mean that man-made irregular wave series exerting on a test model should have a given power spectrum. From a view of optimal c...

According to the most widely accepted classification the Multiobjective Mathematical Programming (MMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a-posteriori methods convey much more information to the d...

Getting the right data to the right decision-maker is a significant problem for many industrial companies. One of the main reasons is an overload of data. With the increasing amounts of industrial data this problem is becoming a bigger problem in the future. In order to address this challenge we propose the use of an Industrial Data Recommender System (IDRS). An IDRS recommends additional data ...