Sufficient conditions for the existence of Nash equilibria in bimatrix games in terms of forbidden $2 \times 2$ subgames
In 1964 Shapley observed that a matrix has a saddle point in pure strategies whenever every its (Formula presented.) submatrix has one. In contrast, a bimatrix game may have no pure strategy Nash equilibrium (NE) even when every (Formula presented.) subgame has one. Nevertheless, Shapley’s claim can be extended to bimatrix games as follows. We partition all (Formula presented.) bimatrix games into fifteen classes (Formula presented.) depending only on the preferences of two players. A subset (Formula presented.) is called a NE-theorem if a bimatrix game has a NE whenever it contains no subgame from t. We suggest a method to construct all minimal (that is, strongest) NE-theorems based on the procedure of joint generation of transversal hypergraphs given by a special oracle. By this method we obtain all (six) strongest NE-theorems. Let us remark that the suggested approach, which may be called “math-pattern recognition”, is very general: it allows to characterize completely an arbitrary “target” in terms of arbitrary “attributes”.
This book constitutes the refereed proceedings of the 22st Annual European Symposium on Algorithms, ESA 2014, held in Wrocław, Poland, in September 2014, as part of ALGO 2014. The 69 revised full papers presented were carefully reviewed and selected from 269 initial submissions: 57 out of 221 in Track A, Design and Analysis, and 12 out of 48 in Track B, Engineering and Applications. The papers present original research in the areas of design and mathematical analysis of algorithms; engineering, experimental analysis, and real-world applications of algorithms and data structures.
Boolean games are a succinct representation of strategic games with a logical flavour. While they have proved to be a popular formalism in the multiagent community, a commonly cited shortcoming is their inability to express richer utilities than success or failure. In addition to being a modelling limitation, this parsimony of preference has made proving complexity bounds difficult. We address the second of these issues by demonstrating how cardinal utilities can be simulated via expected utility. This allows us to prove that RationalNash and IrrationalNashare NEXP-hard, and to translate hardness results for IsNash and DValue into the Boolean games framework.
Boolean games allow us to succinctly represent strategic games with binary payoffs in the case where the players' preferences have a structure readily expressible in propositional logic. Since their introduction, the computational aspects of Boolean games have been of interest to the multiagent community, but so far the focus has been exclusively on pure strategy equilibria. In this paper we consider the complexity of problems involving mixed strategy equilibria, such as the existence of an equilibrium satisfying a given payoff constraint. The results are obtained by the observation that a mixed strategy can hold enough information to encode the computation history of an exponential time Turing machine.
Boolean games are an expressive and natural formalism through which to investigate problems of strategic interaction in multiagent systems. Although they have been widely studied, almost all previous work on Nash equilibria in Boolean games has focused on the restricted setting of pure strategies. This is a shortcoming as finite games are guaranteed to have at least one equilibrium in mixed strategies, but many simple games fail to have pure strategy equilibria at all. We address this by showing that a natural decision problem about mixed equilibria: determining whether a Boolean game has a mixed strategy equilibrium that guarantees every player a given payoff, is NEXP-hard. Accordingly, the epsilon variety of the problem is NEXP-complete. The proof can be adapted to show coNEXP-hardness of a similar question: whether all Nash equilibria of a Boolean game guarantee every player at least the given payoff.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability
The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.
Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.