Game Theory

Randomized Strategies

In game theory, randomized strategy is a strategy that you randomly make you decision and doesn’t have any theory or fact to support your decision.

In the game we played in the class, there is no Nash equilibrium that could result in best outcome no matter what ever our counter party bid. In that game, if my counter party chooses left, I should choose down. If my counter party chooses right, I should choose up. Thus, my best response varies based on the choice of my counter party. To speak in a theoretical way, we should call this dynamic gaming, which means that we need to continuously adjust our strategy

In order to perform well in that game, the most important thing we need to do is to figure out the bidding strategy of our counter party. It may seems like that we could nothing in such a game since our counter party will make their choices randomly. However, randomly choice by human being may not to be a perfect randomly process. People may have specific habit of preference on making their choices. Some people may prefer to begin with the option on the left side while others may prefer the option on the right side. Similarly, some people may prefer the button on the top while others may prefer the button down. Furthermore, it is possible to guess the next choice of our counter party based on their past choices. For example, if I choose down and the counter party chooses left, then I make a bigger profit than him. Then, in the next round, most people tend to change their choice to the right. If I keep on choosing down, I will suffer from a loss. Thus, the best response is to choose top in the next round. However, there is a possibility that your counter party is not smart enough to figure that they have been disadvantaged by the current choice. Then they will keep on choosing the left. In that case, my best response should be stick to my original choice. There is also a possibility that the counter party is very smart and already...