On an Erdős-Szekeres Game

Key Points

• The study investigates a two-player permutation game based on the Erdős-Szekeres Theorem, focusing on conditions for determining the winner.
• Analyzed the game dynamics with parameters a and b.
• Focused on scenarios where a ≥ b and b takes on values 2, 3, 4, or 5.
• Formulated winning strategies for different parameter configurations.
• Established clear winning strategies for each value of b.
• Identified the conditions under which one player can guarantee a win.
• Outlined the relationship between the values of a and b in determining outcomes.