Each player simultaneously chooses a number from {1, 2, ..., 10} and writes it down on a piece of paper; then the players compare the two numbers. If the numbers differ by one, the player with the higher number pays the other player 2. If the players' choices differ by two, the player with the lower number pays 1 to the other player. If the numbers differ by 3 or more then the player with the highest number pays 2 to the other player. In the event of a tie, no money changes hands. Construct a game matrix which describes this game, and evaluate what each player's optimum strategies would be. [10 marks]