Abstract-Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players' skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of games by players across a broad FIDE Elo range, and is in principle applicable to any scenario where high-value decisions are being made under pressure.

We introduce resource-bounded betting games, and propose a generalization of Lutz's resource-bounded measure in which the choice of next string to bet on is fully adaptive. Lutz's martingales are equivalent to betting games constrained to bet on strings in lexicographic order. We show that if strong pseudo-random number generators exist, then betting games are equivalent to martingales, for measure on E and EXP. However, we construct betting games that succeed on certain classes whose Lutz measures are important open problems: the class of polynomial-time Turing-complete languages in EXP, and its superclass of polynomial-time Turing-autoreducible languages. If an EXP-martingale succeeds on either of these classes, or if betting games have the "finite union property" possessed by Lutz's measure, one obtains the non-relativizable consequence * CWI,

The classes W [t] of the Downey-Fellows W hierarchy are defined, for each t, by fixed-parameter reductions to the weighted-assignment satisfiability problem for weft-t circuits. This paper proves that for each t ≥ 1, W [t] equals the closure under fixed-parameter reductions of the class of languages L definable by formulas of the form φ = (∃U)ψ, where U is a set variable and ψ is a first-order formula in t prenex form. This is a fixed-parameter analogue of Fagin's well-known characterization of NP by second-order existential formulas. An equivalent form of this result states that the fixed-parameter "slices" L k of L are definable by a family { φ k } of first-order formulas in t prenex form, subject to the restriction that the quantifier blocks in φ k after the leading existential block are independent of k. Whether this restriction can be removed is connected to open problems in other recent papers on the W hierarchy.

Abstract. This paper studies the population of chess players and the distribution of their performances measured by Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970's is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players' average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model's Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems.Note.

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