The definition of fictitious play may depend on first move rules, initial beliefs, weights assigned to initial beliefs, and tie-breaking rules determining the particular best replies chosen at each stage. Using the original definition of Brown (1951) in which the first moves are chosen arbitrarily and no tie-breaking rules are assumed, we give an example of a fictitious play process in a 2 × 2 ...

We propose a new learning model for finite strategic-form two-player games based on fictitious play and Walley’s imprecise Dirichlet model (1996, J. Roy. Statistical Society B 58, 3–57). This model allows the initial beliefs of the players about their opponent’s strategy choice to be near-vacuous or imprecise instead of being precisely defined. A similar generalization can be made as the one pr...

— The use of fictitious noise processes to improve the robustness of controllers based on linear quadratic Gaussian synthesis is studied in this paper. By constructing the noise process so that its effective energy is primarily in the frequency bands where robustness is lacking, improvements can be made without changing the CIOSed–100D characteristics outside those frequency bands. Specifically...

As an example, I consider a published N-body model for the Galactic bulge and disc, and fictitious l, b, v measurements, and recover (with error estimates) the spatial and velocity scales of the model and the orientation of the bar. The fictitious data are actually derived from the model by assuming the mass scale and the solar position, but their size and extent mimics a recent survey of OH/IR...

String theory requires additional degrees of freedom to maintain world–sheet reparameterisation invariance at the quantum level. These are often interpreted as extra dimensions, beyond the 4 space-time. I discuss a class of quasi-realistic string models in which all the untwisted geometrical moduli are projected out by GSO projections. In these models the extra dimensions are fictitious, and do...

In this paper, we present a statistical approach for phoneme extraction based on universal constraint. Inspired by former phonological studies, we assume a fictitious point in each phoneme that exhibits the most stable information to explain the phoneme’s existence. With the universal constraint of phoneme definitions, the point is statistically estimated by an iterative procedure to maximize t...

An analytically extended PM model with fictitious PM arrays is presented in the paper for solving the field problem of PM electric machines in three dimensions. To consider the effect of finite core length, each PM array is assumed to face a fictitious core array together with the actual armature core. By using the analytic approach and the PM model presented, the three-dimensional field proble...

We propose and study a domain decomposition method which treats the constraint of displacement continuity at the interfaces by augmented Lagrangian techniques and solves the resulting problem by a parallel version of the Peaceman-Rachford algorithm. We prove that this algorithm is equivalent to the fictitious overlapping method introduced by P.L. Lions. We also prove its linear convergence inde...

Successful coordination is a common and important social problem. Achieving it relies on the players’ ability to accurately anticipate future choices from known information. Individuals may not only lack this cognitive ability, but differ in it. Fictitious Play is an adaptive behavior where a myopic best response to the historical play of an opponent is selected. I consider the interaction betw...

The analysis of macroeconomic variables for current situation in Iran indicates a Conundrum. Solving this puzzle is vital for Central Bank of Iran in order to choose an appropriate approach for monetary policy and banking supervision. Increase in liquidity growth rate, significant decrease of inflation rate and interest rate rigidity are the three sides of this puzzle. This study designs an inn...