game theory

Game: COL (Partiza Position: A graph with each vertex labeled with one of the following. n The general initial position is for all vertices in a graph is uncolored. Moves: Left crosses off an uncolored or a filled vertex. Right crosses off an uncolored or an outlined vertex. The restriction is no player may cross off a vertex that is adjacent to a vertex that he or she has previously crossed off. So after each mo vertices adjacent to the vertex just crossed off are changed as given in the table below. 1 [The rules essentially state that two adjacent wertices cannot be crossed off with the same color.] Sample game: A portion of a game on five vertices in a line with Left moving first is below. Right wins in four moves. Notation: The same game above is represented more compactly by removing the vertices that have been crossed off or forbidden (along with any edges that are attached to them). Problem 6-4 (a continuation of Problem 5-4). A library of COL and SNORT positions for lines of order 3. Determine the outcome classes of each game. [Instructor's Note: No justification required.] Game: COL (Partiza Position: A graph with each vertex labeled with one of the following. n The general initial position is for all vertices in a graph is uncolored. Moves: Left crosses off an uncolored or a filled vertex. Right crosses off an uncolored or an outlined vertex. The restriction is no player may cross off a vertex that is adjacent to a vertex that he or she has previously crossed off. So after each mo vertices adjacent to the vertex just crossed off are changed as given in the table below. 1 [The rules essentially state that two adjacent wertices cannot be crossed off with the same color.] Sample game: A portion of a game on five vertices in a line with Left moving first is below. Right wins in four moves. Notation: The same game above is represented more compactly by removing the vertices that have been crossed off or forbidden (along with any edges that are attached to them). Problem 6-4 (a continuation of Problem 5-4). A library of COL and SNORT positions for lines of order 3. Determine the outcome classes of each game. [Instructor's Note: No justification required.]