Job scheduling, cooperation, and control

This paper studies one machine job scheduling situations where clients can have more than one job to be processed and where a job can be of interest for different players. Corresponding cooperative games are introduced and a result on balancedness is provided.     

On shortest path games

A class of cooperative TU-games arising from shortest path problems is introduced and analyzed. Some conditions under which a shortest path game is balanced are obtained. Also an axiomatic characterization of the Shapley value for this class of games is provided.     

Stability and monotonicity in newsvendor situations

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.     

Results on rotation symmetric bent functions

In this paper we analyze the combinatorial properties related to the Walsh spectra of rotation symmetric Boolean functions on even number of variables. These results are then applied in studying rotation symmetric bent functions. For the first time we could present an enumeration strategy for all the 10-variable rotation symmetric bent functions.     

Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity

So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cases. The basic construction is that of symmetric Boolean functions and applying linear transformation on the input variables of these functions, one can get a large class of non-symmetric functions too. Moreover, we also study several other modifications on the basic symmetric functions to identify interesting non-symmetric functions with maximum annihilator immunity. In the process we also present an algorithm to compute the Walsh spectra of a symmetric Boolean function with O(n²) time and O(n) space complexity. We use the term “Annihilator Immunity” instead of “Algebraic Immunity” referred in the recent papers [3–5, 9, 18, 19]. Please see Remark 1 for the details of this notational change     

Further properties of several classes of Boolean functions with optimum algebraic immunity

Based on a method proposed by the first author, several classes of balanced Boolean functions with optimum algebraic immunity are constructed, and they have nonlinearities significantly larger than the previously best known nonlinearity of functions with optimal algebraic immunity. By choosing suitable parameters, the constructed n-variable functions have nonlinearity for even for odd n, where Δ(n) is a function increasing rapidly with n. The algebraic degrees of some constructed functions are also discussed.      

On balanced games with infinitely many players: Revisiting Schmeidler's result

We consider transferable utility cooperative games with infinitely many players and the core understood in the space of bounded additive set functions. We show that, if a game is bounded below, then its core is non-empty if and only if the game is balanced. This finding generalizes Schmeidler (1967) “On Balanced Games with Infinitely Many Players”, where the game is assumed to be non-negative. We also generalize Schmeidler's (1967) result to the case of restricted cooperation too.     

Cooperation under interval uncertainty

In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called ψ ^α-values are introduced and characterizations are given.