Keynesian beauty contest
Encyclopedia
A Keynesian beauty contest is a concept developed by John Maynard Keynes
and introduced in Chapter 12 of his work, General Theory of Employment Interest and Money
(1936), to explain price fluctuations
in equity
markets
.
A naïve strategy would be to choose the six faces that, in the opinion of the entrant, are the most beautiful. A more sophisticated contest entrant, wishing to maximize the chances of winning a prize, would think about what the majority perception of beauty is, and then make a selection based on some inference from their knowledge of public perceptions. This can be carried one step further to take into account the fact that other entrants would each have their own opinion of what public perceptions are. Thus the strategy can be extended to the next order, and the next, and so on, at each level attempting to predict the eventual outcome of the process based on the reasoning of other rational agent
s.
Keynes believed that similar behavior was at work within the stock market
. This would have people pricing shares not based on what they think their fundamental value
is, but rather on what they think everyone else thinks their value is, or what everybody else would predict the average assessment of value is.
National Public Radio's Planet Money
tested the theory by having its listeners select the cutest of three animal videos. The listeners were broken into two groups. One selected the animal they thought was cutest, and the other selected the one they thought most participants would think was the cutest. The results showed significant differences between the groups. Fifty percent of the first group selected the kitten compared to seventy-six percent of the second selecting the kitten. Individuals in the second group were generally able to disregard their own preferences and accurately make a decision based on the preferences of others. The results were considered to be consistent with Keynes's theory.
. For instance in the p-beauty contest game (Moulin 1986), all participants are asked to simultaneously pick a number between 0 and 100. The winner of the contest is the person(s) whose number is closest to p times the average of all numbers submitted, where p is some fraction, typically 2/3 or 1/2. If p<1 the only Nash equilibrium solution is for all to guess 0. By contrast, in Keynes's formulation, p=1 and there are many possible Nash equilibria.
In play of the p-beauty contest game (where p differs from 1), players exhibit distinct, boundedly rational levels of reasoning as first documented in an experimental test by Nagel (1995). The lowest, `Level 0' players, choose numbers randomly from the interval [0,100]. The next higher, `Level 1' players believe that all other players are Level 0. These Level 1 players therefore reason that the average of all numbers submitted should be around 50. If p=2/3, for instance, these Level 1 players choose, as their number, 2/3 of 50, or 33. Similarly, the next higher `Level 2' players in the 2/3-the average game believe that all other players are Level 1 players. These Level 2 players therefore reason that the average of all numbers submitted should be around 33, and so they choose, as their number, 2/3 of 33 or 22. Similarly, the next higher `Level 3' players play a best response
to the play of Level 2 players and so on. The Nash equilibrium of this game, where all players choose the number 0, is thus associated with an infinite level of reasoning. Empirically, in a single play of the game, the typical finding is that most participants can be classified from their choice of numbers as members of the lowest Level types 0, 1, 2 or 3, in line with Keynes' observation.
In another variation of reasoning towards the beauty contest, the players may begin to judge contestants based on the most distinguishable unique property found scarcely clustered in the group. As an analogy, imagine the beauty contest where the player is instructed to choose the most beautiful six faces out of a set of hundred faces. Under special circumstances, the player may ignore all judgment-based instructions in a search for the six most unique faces (interchanging concepts of high demand and low supply). Ironic to the situation, if the player finds it much easier to find a consensus solution for judging the six ugliest contestants, he may apply this property instead of beauty to in choosing six faces. In this line of reasoning, the player is looking for other players overlooking the instructions (which can often be based on random selection) to a transformed set of instructions only elite players would solicit, giving them an advantage. As an example, imagine a contest where contestants are asked to pick the two best numbers in the list: {1, 2, 3, 4, 5, 6, 7, 8, 2345, 6435, 9, 10, 11, 12, 13}. All judgment based instructions can likely be ignored since by consensus two of the numbers do not belong in the set.
(This contest has been held in Spektrum der Wissenschaft, November 1997, with results as PDF. Both links in German; Google translation.)
John Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
and introduced in Chapter 12 of his work, General Theory of Employment Interest and Money
General Theory of Employment Interest and Money
The General Theory of Employment, Interest and Money was written by the English economist John Maynard Keynes. The book, generally considered to be his magnum opus, is largely credited with creating the terminology and shape of modern macroeconomics...
(1936), to explain price fluctuations
Market trend
A market trend is a putative tendency of a financial market to move in a particular direction over time. These trends are classified as secular for long time frames, primary for medium time frames, and secondary for short time frames...
in equity
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
markets
Stock market
A stock market or equity market is a public entity for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.The size of the world stock market was estimated at about $36.6 trillion...
.
Overview
Keynes described the action of rational agents in a market using an analogy based on a fictional newspaper contest, in which entrants are asked to choose a set of six faces from photographs of women that are the "most beautiful". Those who picked the most popular face are then eligible for a prize.A naïve strategy would be to choose the six faces that, in the opinion of the entrant, are the most beautiful. A more sophisticated contest entrant, wishing to maximize the chances of winning a prize, would think about what the majority perception of beauty is, and then make a selection based on some inference from their knowledge of public perceptions. This can be carried one step further to take into account the fact that other entrants would each have their own opinion of what public perceptions are. Thus the strategy can be extended to the next order, and the next, and so on, at each level attempting to predict the eventual outcome of the process based on the reasoning of other rational agent
Rational agent
In economics, game theory, decision theory, and artificial intelligence, a rational agent is an agent which has clear preferences, models uncertainty via expected values, and always chooses to perform the action that results in the optimal outcome for itself from among all feasible actions...
s.
“It is not a case of choosing those [faces] that, to the best of one’s judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.” (Keynes, General Theory of Employment Interest and Money, 1936).
Keynes believed that similar behavior was at work within the stock market
Stock market
A stock market or equity market is a public entity for the trading of company stock and derivatives at an agreed price; these are securities listed on a stock exchange as well as those only traded privately.The size of the world stock market was estimated at about $36.6 trillion...
. This would have people pricing shares not based on what they think their fundamental value
Intrinsic value (finance)
In finance, intrinsic value refers to the value of a security which is intrinsic to or contained in the security itself. It is also frequently called fundamental value. It is ordinarily calculated by summing the future income generated by the asset, and discounting it to the present value...
is, but rather on what they think everyone else thinks their value is, or what everybody else would predict the average assessment of value is.
National Public Radio's Planet Money
Planet Money
Planet Money is an American podcast and blog produced by NPR. The podcast launched on September 6, 2008 to cover the global financial crisis of 2008–2009 in the wake of the Federal takeover of Fannie Mae and Freddie Mac. It was created after the success of "The Giant Pool of Money", an episode of...
tested the theory by having its listeners select the cutest of three animal videos. The listeners were broken into two groups. One selected the animal they thought was cutest, and the other selected the one they thought most participants would think was the cutest. The results showed significant differences between the groups. Fifty percent of the first group selected the kitten compared to seventy-six percent of the second selecting the kitten. Individuals in the second group were generally able to disregard their own preferences and accurately make a decision based on the preferences of others. The results were considered to be consistent with Keynes's theory.
Subsequent theory
Other, more explicit scenarios help to convey the notion of the beauty contest as a convergence to Nash EquilibriumNash equilibrium
In game theory, Nash equilibrium is 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 own strategy unilaterally...
. For instance in the p-beauty contest game (Moulin 1986), all participants are asked to simultaneously pick a number between 0 and 100. The winner of the contest is the person(s) whose number is closest to p times the average of all numbers submitted, where p is some fraction, typically 2/3 or 1/2. If p<1 the only Nash equilibrium solution is for all to guess 0. By contrast, in Keynes's formulation, p=1 and there are many possible Nash equilibria.
In play of the p-beauty contest game (where p differs from 1), players exhibit distinct, boundedly rational levels of reasoning as first documented in an experimental test by Nagel (1995). The lowest, `Level 0' players, choose numbers randomly from the interval [0,100]. The next higher, `Level 1' players believe that all other players are Level 0. These Level 1 players therefore reason that the average of all numbers submitted should be around 50. If p=2/3, for instance, these Level 1 players choose, as their number, 2/3 of 50, or 33. Similarly, the next higher `Level 2' players in the 2/3-the average game believe that all other players are Level 1 players. These Level 2 players therefore reason that the average of all numbers submitted should be around 33, and so they choose, as their number, 2/3 of 33 or 22. Similarly, the next higher `Level 3' players play a best response
Best response
In game theory, the best response is the strategy which produces the most favorable outcome for a player, taking other players' strategies as given...
to the play of Level 2 players and so on. The Nash equilibrium of this game, where all players choose the number 0, is thus associated with an infinite level of reasoning. Empirically, in a single play of the game, the typical finding is that most participants can be classified from their choice of numbers as members of the lowest Level types 0, 1, 2 or 3, in line with Keynes' observation.
In another variation of reasoning towards the beauty contest, the players may begin to judge contestants based on the most distinguishable unique property found scarcely clustered in the group. As an analogy, imagine the beauty contest where the player is instructed to choose the most beautiful six faces out of a set of hundred faces. Under special circumstances, the player may ignore all judgment-based instructions in a search for the six most unique faces (interchanging concepts of high demand and low supply). Ironic to the situation, if the player finds it much easier to find a consensus solution for judging the six ugliest contestants, he may apply this property instead of beauty to in choosing six faces. In this line of reasoning, the player is looking for other players overlooking the instructions (which can often be based on random selection) to a transformed set of instructions only elite players would solicit, giving them an advantage. As an example, imagine a contest where contestants are asked to pick the two best numbers in the list: {1, 2, 3, 4, 5, 6, 7, 8, 2345, 6435, 9, 10, 11, 12, 13}. All judgment based instructions can likely be ignored since by consensus two of the numbers do not belong in the set.
(This contest has been held in Spektrum der Wissenschaft, November 1997, with results as PDF. Both links in German; Google translation.)
External links
- The State of Long-Term Expectation, Ch 12. General Theory of Employment Interest and Money