# GAME THEORY keynsian beauty contest

The experiment executed in the seminar was very simple. Players had to choose a number between 0 and 100. The objective is to choose a number based on your guess of the mean guesses of the group and multiply it by 2/3. It is called the Beauty contest Experiment because it was based on a theory John Maynard Keynes proposed on the relationship of the stock market with beauty contests conducted in newspapers of his time. In this report I will examine the logic behind choosing the best response strategy in theory and compare it with the actual results of the experiment conducted. From the comparison I will provide justification for why the theory is different from reality by also comparing it to examples in real life. To understand the underlying logic of the game’s strategy one must understand the Nash Equilibrium. Princeton University’s Website (an excellent source since John Nash the person who came up with the Equilibrium attended that university) defines Nash Equilibrium as “a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash Equilibrium.”1 The fundamental question now is to what extent is the concept of Nash equilibrium relevant and effective in the Beauty Contest Experiment and does it in fact exist. A definitive answer for the later question is easy because by mathematical logic there is. Simply said if all the players choose 0, no player could have been better off and no one has the incentive to change their strategy if the other players don’t change theirs. In Mathematical terms, a total of zero will yield an average of 0, and 2/3 of that is also 0 meaning guesses will be 100% accurate. This mathematical line of reasoning is valid for any number lower or greater than 1 to be multiplied by the mean. Logical reasoning uses infinite level of reasoning which did not usually exist in humans as evident by the experiment results which I will later discuss. Unlike pure mathematical reasoning, human reasoning varies significantly from player to player. There are several levels of reasoning of which some are empirically illogical while others are to some degree logical (See diagram below for details for reasoning level ‘k-level reasoning’ ”. Levels of reasoning increase proportionally with the assumed average level of reasoning of the group. It is important to note that an increased level of reasoning does not mean a better strategy and that is the main difference between pure mathematical reasoning and human reasoning. Effective human reasoning must take into account the predictability of other players. So a strategic player is one that is skillful at determining the average level of reasoning of the group. While in contrast pure mathematical reasoning assumes that the group will use perfect mathematical reasoning. Mathematical reasoning is not effective a single player to use in a group of humans.

Determining the average level of reasoning of the group is difficult and to some degree requires intuition rather than logic. This process changes a lot with each round of the experiment. This is because players must take into account that other players will employ similar strategies as they are and thus they would want to remain a step further. This recurring process could explain why in round 3 results showed lower averaged guesses than round 2. The concept of this process is referred to as iterated elimination of weakly dominated strategy. It is evident to occur according to the Graph in Fig1. Fig1: Table showing average guesses by each group

As you can see, guesses tend to...

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