There are 4 towns X, Y, Z, V located at the vertices of a square as below and two runners A and B. A begins his run in town X while B begins his run in town Z. Each of the runners can run to one of the towns which are located closest to the town the runner starts from (they must run, i.e., cant remain in the town they start from). If the runners meet at the finish, A wins, otherwise B wins. Write down the pay-off matrix for this game. If we allow each player the option of not running (i.e., the starting town will be the same as the finish town), what would be the new pay-off matrix? Analyze both situations for potential equilibrium pairs.

X Y

Z V