World Cup Game Theory What economics tells us about penalty kicks.
http://www.slate.com/id/2144182/
Often times in making life decisions, our decisions are influenced by external factors. Most commonly, they can be influenced by the decisions with whom we interact. As discussed in class, Game Theory can be defined by these interactions among decision-makers and by three situational aspects: first, there must be a set of players (participants), secondly, each of these players has a set of strategies to choose from, and thirdly, there is a payoff for each strategy. An important element to consider in game theory is one’s uncertainty of the fellow decision-makers thoughts. Therefore, the two parties cannot collaborate together to form the most favorable outcome to get the highest payoffs; one must make a decision without such knowledge, making the situation much more complicated and uncertain.
Game Theory presents itself in many life situations, from sporting events to the interaction of bidders on eBay. As discussed in the article above, game theory plays a major role in the event of penalty kicks in a soccer game. By looking at the basics of game theory, it can help to explain the behavior of athletes in certain situations. This case demonstrates the three aspects of a game: the players include the goalie and the opposing kicker, the strategies—whether to kick right or left, and the payoffs—scoring the goal or stopping the other team from scoring. The payoffs can be seen in the chart below depending on which direction the kicker decides to aim and which direction the goalie decides to move.
Kicker Payoffs Goalie Payoffs
L2 R2
| -1, +1 | +1, -1 |
| +1, -1 | -1, +1 |
L1
R1
After looking at the payoffs for this game, there is no clear strategy. Therefore, other factors must come into account. For example, the kicker may decide to kick in the direction in which he has more power. However, if the goalie anticipates this decision for the same reason, he may still be unsuccessful. There is no dominant strategy in this game. Similarly to the “Matching Pennies” game discussed in class, the players must randomize their decisions and, as the article states, the player’s strategies accordingly are completely unpredictable.