Game+Theory+9


 * __The Runner's Dilemma__**

You are a cross country runner assigned to run a 1 mile long race. However, being the lazy and unmotivated individual you are, you want to complete the race with the least possible amount of effort, but don't want to make a complete ass out of yourself. Also, the prize that awaits the winner outweighs your unwillingness to work (not having to repeat the race).


 * Rules**: For the best possible result, each runner would have to walk the race at an even pace, allowing for each individual to have an equal chance of winning but with little/no effort being put forward. As each person would tie, every racer would recieve the award for first.


 * Materials needed**:
 * 2+ runners
 * a course on which the race can be completed


 * Predicted results**: At least one of the runners will end up running some part of the race in order to gain an advantage on the other runners. Eventually, this will lead to all of the runners working as hard as possible in order to obtain the prize. The end result: all of the runners will be tired and only one of them will have the prize.
 * || Runner B: walk || Runner B: run ||
 * Runner A: walk ||  A & B: not tired w/ prize || A:not tired without prize B:tired w/ prize ||
 * Runner A: run || A: tired w/ prize B:not tired without prize || A & B: tired and only one has the prize ||

To put it bluntly, the dominant strategy is to suck it up and run the race as fast as you can to try and get the prize. This applies to all the runners, no matter how many there are. Therefore, the nash equlibrium exists because every runner shares the same dominant strategy of trying as hard as possible.