 Trees are used to represent sequential games, because they show the order in which actions are taken by the players. However, games are sometimes represented on matrices rather than trees. This is the second type of mathematical object used to represent games. Matrices, unlike trees, simply show the outcomes, represented in terms of the players’ utility functions, for every possible combination of strategies the players might use. For example, it makes sense to display the river-crossing game from  Section 1  on a matrix, since in that game both the fugitive and the hunter have just one move each, and each chooses their move in ignorance of what the other has decided to do. Here, then, is part of the matrix: