  The classical Erdos-Szekeres theorem states that a convex $k$-gon exists in
every sufficiently large point set. This problem has been well studied and
finding tight asymptotic bounds is considered a challenging open problem.
Several variants of the Erdos-Szekeres problem have been posed and studied in
the last two decades. The well studied variants include the empty convex
$k$-gon problem, convex $k$-gon with specified number of interior points and
the chromatic variant.
  In this paper, we introduce the following two player game variant of the
Erdos-Szekeres problem: Consider a two player game where each player playing in
alternate turns, place points in the plane. The objective of the game is to
avoid the formation of the convex k-gon among the placed points. The game ends
when a convex k-gon is formed and the player who placed the last point loses
the game.
  In our paper we show a winning strategy for the player who plays second in
the convex 5-gon game and the empty convex 5-gon game by considering convex
layer configurations at each step. We prove that the game always ends in the
9th step by showing that the game reaches a specific set of configurations.
