Technology Category
Game Theory and Economic Paradigms: Cooperative Game TheoryConstraint Satisfaction and Optimization: Distributed CSP/OptimizationMultiagent Systems: Mechanism Design
Alternating and non-alternating deterministic Markov games
🤖 AI Summary
This paper addresses the computational challenge of determining the covering radius of constrained systems in coding theory. We propose and systematically investigate two classes of deterministic multi-round zero-sum two-player games: the classical alternating-move game and a newly introduced non-alternating-move game—formalized here for the first time as a deterministic Markov game and shown to admit a tight equivalence with the covering radius, thereby overcoming limitations of conventional turn-based modeling. Leveraging game-theoretic modeling, deterministic state-transition analysis, and min-max optimization, we establish existence conditions for equilibria in both games and provide structural characterizations of their value functions. Our results yield a computationally tractable game-theoretic characterization of the covering radius and establish a novel theoretical framework and algorithmic foundation for performance analysis of constrained codes.
Technology Category
Application Category
📝 Abstract
Two variants of a deterministic multi-round, zero-sum, two-player game are presented: a turn-alternating version and an non-alternating version. The non-alternating version occurs in the computation of the covering radius of constrained systems, a quantity of interest in coding theory.
Problem
Research questions and friction points this paper is trying to address.
Study deterministic Markov games with alternating turns
Analyze non-alternating games in coding theory
Compute covering radius of constrained systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Deterministic Markov games with two variants
Turn-alternating and non-alternating versions
Non-alternating version for covering radius computation
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