Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation...
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games....
In the Shapley-Scarf economy each agent is endowed with one unit of an indivisible good (house) and wants to exchange it for another, possibly the most preferred one among the houses in the market. In this economy, core is always nonempty and a core allocation can be found by the famous Top Trading Cycles algorithm. Recently, a modification of this economy, containing Q >= 2 types of goods (say, houses and cars for Q=2) has been introduced. We show that if the number of agents is 2, a complete...
We introduce a type of isomorphism among strategic games that we call local isomorphism. Local isomorphisms is a weaker version of the notions of strong and weak game isomorphism introduced in [J. Gabarro, A. Garcia and M. Serna, Theor. Comput. Sci. 412 (2011) 6675–6695]. In a local isomorphism it is required to preserve, for any player, the player’s preferences on the sets of strategy profiles that differ only in the action selected by this player. We show that the game isomorphism problem for...
We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which I or II...
Some possibilities of fuzzification of the von Neumann-Morgenstern solution of cooperative games with transferable utility (TU games) are briefly investigated. The fuzzification based on the transformation of individual fuzzy TU game into a fuzzy class of (deterministic) TU games with their own specific solutions is discussed.
We consider the two-sided eigenproblem over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.