Your overconfidence is your weakness… or is it?
http://news.nationalgeographic.com/news/2011/09/110914-optimism-narcissism-overconfidence-hubris-evolution-science-nature/
This article sheds light on an interesting question: can game theory prove that overconfidence is actually beneficial in certain situations? As it turns out, the answer is “yes.” According to an analysis of game theory mechanics, overconfidence is good in situations where the benefits of succeeding outweigh the cost of losing. When there is uncertainty about the true strength of the opponent, overconfidence always pays off. A simple example can be used to illustrate this situation. If there are two players in a game, A and B, and the benefit of winning far exceeds the cost of losing, the game can be drawn up like so:
. B1 B2
A1 ?,? 10x,0
A2 0,10x 0,0
where “1” represents an aggressive strategy and “2” represents a cautious strategy. If both players play a cautious strategy (A2,B2), neither player will gain or lose anything. If one player plays an aggressive strategy and one plays a cautious strategy, the aggressive player will win an amount given by 10x and the cautious player will not gain or lose anything. Viewing the game from the point of view of player A, let us assume that he is uncertain about the strength of player B. This means that player A does not know if he will win against player B if both players take an aggressive strategy. However, assuming the prize for winning is 10x and the cost of losing is only -x, player A should arguably still play an aggressive strategy. If player B plays a cautious strategy or player B is weaker than player A, player A will win by playing A1. If player A plays an aggressive strategy and player B is stronger than player A, player A will lose, but the cost will only be -x compared to a possible benefit of 10x. This is a simple game that incorporates the ideas in the article.
This article brought an interesting new aspect into my understanding of game theory: uncertainty. Since most examples use situations in which both players know the costs and rewards for themselves and their opponents, this required a new type of analysis. Though it cannot be said that A1 is a dominant strategy for player A in the above example, it can be argued that it is the best logical strategy with the given information. This type of game is applicable in many real-life situations. One might be war: if the strength of the enemy is unknown but the reward of winning far exceeds the cost of losing, an aggressive strategy is the best strategy. This might mean that the opponent could be caught off guard and surrender (a play of B2 in the above example) or that the opponent will try to attack as well but will be weaker. Both scenarios give a positive outcome. Thus, overconfidence is beneficial. Games involving some uncertainty about the opponent’s strength are very common in real life.
Therefore, game theory can be used to at least make a viable argument that overconfidence is beneficial.