Hello Class- This is my blog post on an example of two teams in soccer using mixed strategies in a real world scenario. Below you will find a YouTube link that shows “Manchester United – Chelsea London Champions League Final 2008”. In this video you can fast forward to 2:55 of the video and at this point we can see that there is some type of confusion between the goalie and the kickers. This confusion is due to a mixed strategy of Manchester’s goalie responding to the actions of the other teams players. The goalie is adjusting his strategy due to what he expects the other players strategies to be. Manchester United’s goalkeeper learns of Chelsea’s kicking strategy. This strategy is of the kickers kicking to their natural side. Due to this the Chelsea players begin kicking to the opposite side- hence their unnatural side. Ex: If the kicking players natural side is right, they would kick the soccer ball to their left side. Manchester’s goal keeper notices this unnatural strategy, so on the last kick he points to the unnatural side of the kicker. This causes the kicker (Nicolas Anelka), to see that the goalie has learned of their strategy. Nicolas kicks to the natural side to confuse the goalkeeper. The problem is that the goalkeeper on Manchester (Van Der Sar) dives to the natural side and blocks the kicker. The reason why he was able to block the kick is because he increased his probability of the kicker kicking to the natural side. Through this example mixed strategy can be seen by each player playing a strategy that will take advantage of the expected probability of the other players strategy.

# Mixed Strategies in Soccer

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This is a great example of mixed-strategy game theory being used in real life. It is interesting to see just how random the outcome of a mixed strategy game can be. And, considering how each player assigns their own expected probability in relation to the other player’s strategies, it is easy to see why it is so difficult for coordination to occur. What was most interesting about this example is how the goalie was able to figure out which strategy the kickers were more likely to use. This in essence allowed the goalie to assign a much higher probability to the strategy and to achieve a higher degree of coordination. What is amazing is that the kickers adapted their strategy after noticing the goalie’s strategy, in order to create mis-coordination once again. The reason that the changing of strategies occurred is due to the additional information that the goalie and then the kickers were able to learn from the repeated interactions between each other. What is most astonishing to me is how the goalie used the simple tactic of pointing to one of the corners to give himself a much higher chance of coordinating with the kicker. What the goalie did was amazing in the sense that he pretended to show the kicker his decision, causing the kicker to make a snap decision to play the opposite strategy. But, since the goalie did not actually show his true strategy he was able to coordinate and stop the ball. The goalie effectively increased his odds by using the kicker’s snap decision making against him. Besides being a good textbook example of mixed-strategy, this situation gives great insight to what happens when players have multiple interactions with one another. It additionally shows how some information, the pointing to a corner, is not clearly represented in the model for mixed-strategy games.