Real Life Situation
I created a matrix for two popular cereal brands: Kellogg's Corn Flakes and Cheerios. One can often see some toys or activities that are included with a box of cereal. This will increase the demand for this particular product because children (who are the main focus of cereal brands) want toys and things to play with.
The numbers represent the profit in millions. If both companies decided to put toys into their boxes, their revenue would not change because there are still the same amount of people buying the same product but the cost of producing the toys has to be taken into account and so there is a decrease in profit. If both companies decide to not put toys into their boxes, the profit will not increase or decrease. However if one firm does put toys into their boxes, they will effectively 'steal' some of the consumers of the other company and their profits will increase exponentially while the company who did not put toys into their boxes have a decrease in profit.
Game Theory Games
One of the games I played on the website was called battle of the sexes. A husband and wife wish to choose an evening activity, and have two options: going to the ballet (B) and watching football (F). They both prefer to choose the same activity, but while the wife (player 2) prefers F, the husband (player 1) prefers B. These were the rules to that game.
Although it wasn't specified, we can assume that the numbers represent happiness points. If I was the wife, I would always choose F because I would either get 2 points or 0 points opposed to the 1 point or 0 points I would get for choosing B. For the husband I always chose F because of the same reasons. There was a dominant strategy for each respective player but there was no Nash equilibrium because if one player's choice was set in stone, the other player may change to get some happiness points out of the situation.