Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value

We provide a new and concise characterization of the Banzhaf value on the (linear) space of all TU-games on a fixed player set by means of two transparent axioms. The first one is the well-known Dummy player axiom. The second axiom, called Strong transfer invariance, indicates that a player's payoff is invariant to a transfer of worth between two coalitions he or she belongs to. To prove this result we derive direct-sum decompositions of the space of all TU-games. We show that, for each player, the space of all TU-games is the direct sum of the subspace of TU-games where this player is dummy and the subspace spanned by the TU-games used to construct the transfers of worth. This decomposition method has several advantages listed as concluding remarks

A system-theoretic approach to multi-agent models

A system-theoretic model for cooperative settings is presented that unifies and ex- tends the models of classical cooperative games and coalition formation processes and their generalizations. The model is based on the notions of system, state and transi- tion graph. The latter describes changes of a system over time in terms of actions governed by individuals or groups of individuals. Contrary to classic models, the pre- sented model is not restricted to acyclic settings and allows the transition graph to have cycles. Time-dependent solutions to allocation problems are proposed and discussed. In par- ticular, Weber’s theory of randomized values is generalized as well as the notion of semi-values. Convergence assertions are made in some cases, and the concept of the Cesàro value of an allocation mechanism is introduced in order to achieve convergence for a wide range of allocation mechanisms. Quantum allocation mechanisms are de- fined, which are induced by quantum random walks on the transition graph and it is shown that they satisfy certain fairness criteria. A concept for Weber sets and two dif- ferent concepts of cores are proposed in the acyclic case, and it is shown under some mild assumptions that both cores are subsets of the Weber set. Moreover, the model of non-cooperative games in extensive form is generalized such that the presented model achieves a mutual framework for cooperative and non-co- operative games. A coherency to welfare economics is made and to each allocation mechanism a social welfare function is proposed

Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.

Complaint, compromise and solution concepts for cooperative games

This thesis mainly focuses on solution concepts for cooperative games. We investigate the solution concepts concerning the complaints of players. Motivated by the work the procedural values, we study the formation of the grand coalition and define a new kind of complaint for individual players. We then reveal that the solutions for both models coincide with the ENSC value either based on the lexicographic criterion or the least square criterion. We propose the so called alpha-ENSC value by considering the egoism of players. We implement the alpha-ENSC value by means of optimization and also the satisfier of a set of properties. Following the similar idea, we propose two kinds of complaints for coalitions and define the optimal compromise values based on the lexicographic criterion. It turns out that the optimal compromise values coincides with the ENSC value and the CIS value under corresponding complaint. We show an application of the previous mentioned method. We introduce and axiomatize a class of cost sharing methods for polluted river sharing systems that consists of the convex combinations of the known Local Responsibility Sharing (LR) method and the Upstream Equal Sharing (UES) method. We also deals with the solution concepts based on the compromise between the ideal and minimal payoffs for players, which is inspired by the definition of the tau value but in a more general way. We reveal the relations between the general compromise value with several well known solution concepts. Furthermore, we investigate the solution concepts for cooperative games with stochastic payoffs. We focus on a subset of all allocations and introduce the stochastic complaint for players. Under the least square criterion, the most stable solutions and the fairest solutions are proposed. Moreover, the optimal solution stays the same whether the optimization model depends on the coalitions or individual players

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp