MATHEMATICAL ENGINEERING TECHNICAL REPORTS Implications of contrarian and one-sided strategies for the fair-coin game
نویسندگان
چکیده
We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [8]. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n−1/2). This is achieved by a very simple contrarian strategy of Skeptic. This type of result, bounding the rate of convergence from below, contrasts with more standard results of bounding the rate of SLLN from above by using momentum strategies. We also derive a corresponding one-sided result.
منابع مشابه
Implications of contrarian and one-sided strategies for the fair-coin game
We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [8]. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n−1/2). This is achieved by a very simple co...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS A Game-Theoretic Proof of Erdos-Feller-Kolmogorov-Petrowsky Law of the Iterated Logarithm for Fair-Coin Tossing
We give a game-theoretic proof of the celebrated Erdős-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing. Our proof, based on Bayesian strategy, is explicit as many other game-theoretic proofs of the laws in probability theory.
متن کاملMATHEMATICAL MODELLING FOR DICE FINDER GAME PROBLEM
Play is often episodic and mission-centric, with a series of challenges culminating in a final puzzle or enemy that must be overcome. Multiple missions played with the same characters may be related to each other in a plot arc of escalating challenges. The exact tone, structure, pace and end (if any) vary from game to game depending on the needs and preferences of the players, as in [9]. "THE C...
متن کاملThe Effect of Game Strategies on the Physiological, Physical, and Technical Loads of Soccer Players
Background. The study aims to determine position-specific loads by different tactical strategies. Eighty Turkish Super League U21 players (19.35 ± 1.6 years, 179.4 ± 2.3 cm, 75.6 ± 4.1 kg; M ± SD) were involved in this study. Objectives. The players completed eight different 11v11 training games. While one team practiced the ball possession and “defense as a team” strategy, the other team impl...
متن کاملA game theory approach for determining optimum strategy of claim resolution in construction projects
Claim is a big challenge for the contractors and the owners in construction projects. Claims are considered to be one of the most disruptive events of a project. A suitable claim resolution strategy can prevent the damages to the project and the involved parties. In this research, a mathematical model using game theory is presented to find the optimum strategy for resolving cost-related claims ...
متن کامل