Search results for "Certainty"

On the Efficiency of Affine Invariant Multivariate Rank Tests

1998

AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.

The Poincaré inequality is an open ended condition

2008

Let p > 1 and let (X,d,µ) be a complete metric measure space with µ Borel and doubling that admits a (1,p)-Poincare inequality. Then there exists e > 0 such that (X,d,µ) admits a (1,q)-Poincare inequality for every q > p - e, quantitatively.

BARGAINING WITH COMMITMENT UNDER AN UNCERTAIN DEADLINE

2006

We consider an infinite horizon bargaining game in which a deadline can arise with positive probability and where players possess an endogenous commitment device. We show that for any truncation of the game, the equilibrium agreement can only take place if the deadline arises within this finite horizon. Since the deadline is an uncertain event, the equilibrium exhibits agreements which are delayed with positive probability.

Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality

2018

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …

Codification schemes and finite automata

2000

This paper is a note on how Information Theory and Codification Theory are helpful in the computational design both of communication protocols and strategy sets in the framework of finitely repeated games played by boundedly rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds of Neyman¿s (1998) work on finitely repeated games played by finite automata.

On the propagation of error in certain non-linear algorithms

1959

Recursive and bargaining values

2021

Abstract We introduce two families of values for TU-games: the recursive and bargaining values. Bargaining values are obtained as the equilibrium payoffs of the symmetric non-cooperative bargaining game proposed by Hart and Mas-Colell (1996). We show that bargaining values have a recursive structure in their definition, and we call this property recursiveness. All efficient, linear, and symmetric values that satisfy recursiveness are called recursive values. We generalize the notions of potential, and balanced contributions property, to characterize the family of recursive values. Finally, we show that if a time discount factor is considered in the bargaining model, every bargaining value h…

Values of games with probabilistic graphs

1999

Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.

REPEATED GAMES WITH PROBABILISTIC HORIZON

2005

Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite s…

Efficient linear fusion of partial estimators

2018

Abstract Many signal processing applications require performing statistical inference on large datasets, where computational and/or memory restrictions become an issue. In this big data setting, computing an exact global centralized estimator is often either unfeasible or impractical. Hence, several authors have considered distributed inference approaches, where the data are divided among multiple workers (cores, machines or a combination of both). The computations are then performed in parallel and the resulting partial estimators are finally combined to approximate the intractable global estimator. In this paper, we focus on the scenario where no communication exists among the workers, de…