Question

(e pointa) Two national foot ball teams, Swemark and Denden, are playing each other in the group stage of the European championships. The points they have secured in the games they have already played mean that if one team wins they will go forward to the knock out stage of the competition and the other team will not. However if they make a draw they will both go through to the next stage at the expense of another national side. The supporters and players of the Swemark and Denden sides are on friendly terms and would like both their teams to qualify but neither wants the other side to qualify at the expense of their own. (a) (2 points) At the start of the game players need to decide between going for a win and going for a draw. The dilemma for the players is that if one team decides to go for a draw but the other side goes for a win the team going for a draw is likely to lose. If both teams go for a win the game could still end in a draw but the players will be exhausted and will have less chance of winning in the knockout stage. Of course, nothing is this predictable in sports but assuming that if both teams go for a draw the game ends in a draw construct a payoff matrix to represent the strategic game played by Swemark and Denden. Is the game you have constructed a prisoners' dilemma? (b) (2 points) Now imagine that for both Swemark and Denden to go forward to the knockout stage they need to make a draw in which they both score 2 or more goals and that there are 10 minutes of the game left to play. At this stage of the game Denden are leading 2-1. Should the Denden side ease up to allovw the Swemark side to score or not? Why might easing up be a risky strategy for the Denden players?

Answer 1

Answer (a) : A situation in a game where both the players are dependent on the decision taken by the other player in such a way that the decision taken by a player will impact the other player’s win or loosing of the game. Such a situation is referred to as the Poisoner’s Dilemma. In the case given here, the decisions of both the teams, Swemark and Denden fully depend on one another , as if one chooses to win, the other will loose and will be out of the next stage. Thus , this situation corresponds to Prisoner’s matrix.

                             Let us see the pay off matrix for Swemark and Denden as below :

                        (Note : In the above payoff matrix, 1 indicates the Win for the team, and 0 indicates the loose ). From the above matrix, we can see that If Swemark goes for a Win, then there are three possibilities , either Swemark wins and Denden looses , Swemark looses and Denden wins or both end the game in a draw. The same applies for Denden too. If Denden goes for a Win, then there are also three possibilities , either Swemark wins and Denden looses , Swemark looses and Denden wins or both end the game in a draw. The other possibility is that both the teams go for a draw, where by they both go ahead to the next stage.

Answer (b) : Since Denden are ahead of the game by 2 goals to 1 , Denden should not easy up, but go for the win. This is because, easing up for Sweamark at this final 10 minutes could cost dearly for Denden, as if Swemark takes the advantage of this and gets 2 goals instead of 1, that would mean that Denden would be out of the tournament. Since, the tournament is on the line, Denden should therefore not take the risk of easing up at this stage. It should just ensure that they don’t suffer any goals, and they straight forward go through to the next stage.