The year is 1994, the setting is the Shell Carribean Cup. Greneda is playing against Barbados in the final match of the group round of the tournament. In order to move on in the tournament, Barbados needs to win by two goals, if they fail to do this then instead Greneda will move forward. In most tournaments we can model the match very simply and the soccer match would proceed as most matches do. Both teams would try to maximize the goals they score on the opponent while minimizing the goals scored against them. However this was not a normal match because of two seemingly insignificant rules. The first one was that all matches needed a winner, generally not a clause that adds any odd behavior to a match, but one that is not usually seen in the group stages of the tournament. The other rule was that all goals in overtime count for 2. In most cases these rules would not have impacted the way the two teams played very much but we can predict the issue if we analyze this match using game theory. The game is different depending on the state of the match. If the game is tied the game is simple. Each team can choose to try to score on the opponents goal, their own or they can not try to score (this may seem odd why we would say that these are the teams’ options but it will become apparent in a moment). In this case the payoff is the same. If they score in their own goal they will get a negative payoff and if they score in the opponents goal they get a positive payoff and if they don’t score then they will not get a payoff. Now in the match what ended up happening was that Barbados managed to be two goals ahead and then Greneda scored in the last 10 minutes. Lets analyze the various payoffs for this point. If Barbados score they will receive a positive payoff because they will be once again 2 goals ahead, if they don’t score they have a negative payoff because they will be knocked out of the tournament, but if they score an own goal they can force the match into overtime so that they get another chance to score there, and if they do, they move on. This is exactly what Barbados did. So with the score at 2-2 let us analyze the payoffs. If Barbados scores on either goal they will either win by less than one goal or lose, in both instances they are eliminated from the tournament. If they choose not to score though they get a positive payoff in the form of the opportunity to continue in the tournament by winning in overtime. For Greneda the payoff is the opposite. If they score in either goal they get to continue in the tournament, but if the score stays the same then they are eliminated. With both teams understanding this, the most incredible last ten minutes of a soccer match then transpired. Barbados spent the last 10 minutes of the match defending both goals while greneda tried in vain to score at either end.
I think that this is a great example of how seemingly insignificant rules in a ‘game’ can lead to very complicated and unintuitive behavior.