The Game of Synchronized Domineering 1st edition by Alessandro Cincotti, Hiroyuki Iida ISBN 3540876076 9783540876076

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Product details:

ISBN 10:       3540876076
ISBN 13: 978-3540876076
Author:       Alessandro Cincotti, Hiroyuki Iida  

In synchronized games players make their moves simultaneously rather than alternately. Synchronized Domineering is the synchronized version of Domineering, a classic two-player combinatorial game. We present the solutions for all the m ×n boards with m ≤ 6 and n ≤ 6. Also, we give results for the n ×3 boards, n ×5 boards, and some partial results for the n ×2 boards. Future research is indicated.

The Game of Synchronized Domineering 1st Table of contents:

Chapter 1: Introduction
1.1 Overview of Domineering
1.2 The Concept of Synchronized Domineering
1.3 Motivation and Objectives of the Study
1.4 Importance of Game Theory in Combinatorial Games
1.5 Structure of the Paper

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Chapter 2: Background and Related Work
2.1 Classic Domineering: Rules and Strategies
2.2 Combinatorial Game Theory: Key Concepts
2.3 Previous Work on Domineering and Synchronized Games
2.4 Related Combinatorial Games and Their Analysis
2.5 Computational Complexity in Game Theory

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Chapter 3: Formal Definition of Synchronized Domineering
3.1 Rules and Mechanics of Synchronized Domineering
3.2 Board Configurations and Player Moves
3.3 Symmetry and Synchronized Moves
3.4 Theoretical Framework for Analyzing Synchronized Domineering
3.5 Notation and Terminology Used in the Game

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Chapter 4: Strategy and Analysis of Synchronized Domineering
4.1 Winning and Losing Positions in Synchronized Domineering
4.2 Strategy for Player 1 and Player 2
4.3 Optimal Strategies and Decision Making
4.4 Grundy Numbers and the Theory of Nimbers
4.5 Illustrative Examples of Synchronized Domineering Strategies

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Chapter 5: Computational Complexity and Algorithmic Considerations
5.1 Complexity of Solving Synchronized Domineering
5.2 Dynamic Programming Approaches to Analyze the Game
5.3 Approximation Algorithms for Synchronized Domineering
5.4 Efficient Search Methods in Large Game Spaces
5.5 Complexity Comparison with Other Combinatorial Games

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Chapter 6: Game-Theoretic Properties of Synchronized Domineering
6.1 Nash Equilibria in Synchronized Domineering
6.2 Strategy Profiles and Dominance
6.3 Relation to Other Game-Theoretic Concepts (e.g., Minimax, Zero-Sum)
6.4 Optimal Play and Perfect Information
6.5 Extensions of Synchronized Domineering: Multi-Player and Stochastic Variants

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Chapter 7: Applications and Implications of Synchronized Domineering
7.1 Educational Applications in Game Theory
7.2 Algorithmic Game Theory and Computational Complexity
7.3 Applications in Real-World Scenarios (e.g., Resource Allocation)
7.4 Synchronized Domineering as a Model for Coordination Problems
7.5 Games with Multiple Synchronized Moves in Practical Contexts

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Chapter 8: Experimental Evaluation and Simulations
8.1 Simulation of Synchronized Domineering on Various Boards
8.2 Empirical Analysis of Strategy Efficiency
8.3 Comparing Algorithmic Performance in Strategy Execution
8.4 Evaluating Player Behavior and Decision Making in Simulated Games
8.5 Results and Insights from Experimental Data

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Chapter 9: Challenges and Open Problems
9.1 Unresolved Challenges in Synchronized Domineering Analysis
9.2 Possible Extensions to the Game’s Rules and Mechanics
9.3 Exploring Multi-Agent and Cooperative Game Extensions
9.4 Open Problems in Computational Game Theory
9.5 Future Directions for Research in Synchronized Domineering

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Chapter 10: Conclusion
10.1 Summary of Key Findings
10.2 Impact on the Field of Combinatorial Game Theory
10.3 Contributions to Strategy and Game Analysis
10.4 Final Remarks on Synchronized Domineering
10.5 Outlook for Future Research and Applications

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