Mixed Strategy and Bluffing
Many people know bluffing to be a strategic move based on psychology. However, for those studying game theory, bluffing is pure mathematics. Bluffing is a strategical method of demonstrating one’s unpredictability. By increasing one’s unpredictability, one is able to manipulate or trick the opposition. However, this has to be done at strategically advantageous times, following a certain probability p, so that one’s unpredictability will not be, for a lack of a better term, predictable. As professor Kalai describes in the article, “If I bluffed all the time, obviously my bluffing would be ineffective. But it’s not effective to under-bluff, either, because then I’m not making enough use of my reputation as a non-bluffer. If you never bluff, or bluff very rarely, you can use this reputation to bluff more effectively and increase your long-term winnings.” This constant and systematic bluffing is used in mixed strategy to optimize one’s advantage by randomizing just enough to keep that advantage working effectively. By accessing both one’s advantage and keeping in mind that the opponent will also access one’s advantage, randomization from bluffing can guarantee a long-term unpredictability.
This idea of bluffing is very similar to the in class example of penalty kicks about mixed strategy when discussing game theory. In mixed strategy, one’s strategy is at its most effectiveness when it takes into account the opposition’s strategy as well. In the penalty kick example, a Nash Equilibrium was unable to attained. However, by assigning p to be the probability that the kicker will go left and q to be the probability that the goalie will go left, one can calculate new payoff numbers by accessing both one’s own advantages as well as the opposition’s advantages. However, with the strategy of bluffing, one can optimize one’s own advantage by maximizing the unpredictability.
Article URL: To Bluff or Not to Bluff