This is how I learned how to count to 12.  Arguably the coolest counting song of all time (sung by the Pointer Sisters).  Thanks Sesame Street.

In a paper uploaded to the Arxiv in April, a group of researchers headed up by Matthias Hanauske, approach the recent financial meltdown from a Quantum Evolutionary point of view.  Here’s the abstract:

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the ‘rules of the game’ in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non aggressive quantum strategy.

The Hawk-Dove game is a classic of Evolutionary Game Theory and has been applied in many varied ways all over the study of animal (and human) behavior.  So, their use of it to study markets is nothing new.  What IS new is taking a Quantum approach to this old game as a way of studying a method by which we can introduce regulations (a rule system) to the game of financial economics that would mitigate the kinds of behaviors that lead to the situation we’re in now.  Don’t worry, it doesn’t require that we all spend our lives staring at quantum computers!

FINANCIAL RISK AND AGGRESSION

In the lead up to the financial crisis of 2008, certain actors in the market can be said to have exhibited aggressive behavior since they made choices that benefited only their own short term utility while KNOWING that these choices would negatively affect the utility of the group (all of us) as a whole. That is, these actors knew that these risky financial products would do harm to the overall market portfolio (and therefore be harmful, long term, to themselves), but would, in the short term, result in a positive gain to themselves–so they took them on anyway.

Given that we’re approaching economics like a game as it is, can we change the “rules” of this game so that aggressive behavior of the type discussed above is lessened? If this behavior is “natural” given the situation, then we certainly can’t expect people to play nice. We ought to do as the Boy Scouts do, “Hope for the best. Plan for the Worst.”

QUANTUM GAMES TO THE RESCUE

The authors show that dependent upon the type of entanglement, evolutionarily stable strategies (ESS’s) can show up that would NOT have been predicted by classical evolutionary game theory. What I love about their approach is they are not restricting themselves to a literalist interpretation of quantum game theory (that is, games played over quantum channels with tiny molecular objects as the unit of information). Instead, they are using this theory “metaphorically”.

That sounds bad. But, in truth ALL mathematics is metaphoric. A wave equation is not itself a wave. It just represents a wave. So, it’s not a stretch to take a mathematical idea that was originally strictly defined with respect to a particular physical situation, and apply it to a totally different situation. This has been the history of how great ideas in applied mathematics proliferate.

Here is how they set it up:

“We interpret entanglement in this context as the objective influence of socio-economic context factors, while the application of quantum strategies exhibits the degree to which decision makers incorporate these factors into their decisions. This interpretation allows the derivation of consequences and shows the linkage of our study to other game theoretical analyses that also highlight the importance of the socio-economic context to the outcomes of games.”

But, first let’s look at the classic (non-quantum) evolutionary game as applied to the financial crisis.

They call the Doves in the game those bank investors who acquire rather low risk products that return moderate payoffs. The Hawks are those bank investors who seek out high risk products that have the potential to return large payoffs–but, these also could result in huge losses. The authors make the point:

“Additionally, when selling their products to investors, doves remain with their contract conditions and do not try to make a deal by all means, e.g. promising unrealistic returns or omitting to point out severe risk factors of the investment product.”

Hawks do whatever necessary to make a profit.

Both of these investors then fight to garner the attention of a more moderate or neutral group of investors. When a hawk “fights” a dove, the hawk wins, since he can offer a higher return to the investor. If 2 doves fight, then the investor splits his investment equally among them assuming they will both return an equal amount. If 2 hawks meet, the investment is again spread equally.

The payoffs of all three situations are different as is true in the classical version of the game. I’m NOT going to get into what this actually looks like, as the math gets ugly, but it results in the following. The evolutionary game theoretic predictions of this particular version of the Hawk-Dove game are that the ratio of aggressive vs. non-aggressive behaviors would not reach equilibrium. That is, it predicts a crash!

OK, great. We already HAD the crash. What can we do to prevent it? That is:

“Although the risk of destabilization in the investment market was obviously increasing for the last few years, the behaviour of some aggressive investment bankers did not change. However, instead of ending in a stable state, finally the market crashed and almost all aggressive agents disappeared from the population. This could have been prevented, if any aggressive behaviour were inhibited completely.”

QUANTUM VERSION

They reformulated this game in a quantum game theoretic context and show that by entangling the strategies of the doves they induce a new Evolutionarily Stable Strategy that eliminates excessive hawkishness. By increasing the amount of entanglement (interconnectedness) the incentives to “go it alone” are reduced and the incentives to act in a more cooperative manner are increased.

The point is that regulations  and social pressures that encourage openness and interconnectedness of market participants may be enough to drastically reduce aggressive and hawkish behaviors that lead to the type of destabilization seen in the recent market crash. In the lead up to 2008, there was very little entanglement of the strategies employed by market participants. This caused them to play the “game” in the classical way, a way that led inevitably to a market crash.

To reiterate, what’s great about this paper is their approach to using quantum game theoretic language OUTSIDE of a purely physical context:

“So far, in literature entanglement has been discussed from a more physical point of view. However, in order to derive consequences from the obtained results we want to propose one possibility to interpret it in an economic context. In this paper, entanglement has been termed a conjoint, psychological contract between the members of an economic population aligning their strategies. However, this contract is not the result of conscious negotiations but of general socio-economic factors influencing the agents simultaneously. These factors comprise moral standards, values, legal rules, joint experiences, a similar educational background etc. All these factors can drive the decision processes of different individuals into the same direction without the necessity that the individuals have to communicate to each other. The objective existence of these background factors can vary, which is reflected by the degree of the entanglement parameter .”

In Japan there is massive social pressure to be polite, at a level unheard of in America. In fact, it is so great, most American’s find it problematic and strange.  It results in an entire culture avoiding certain types of behaviors they deem aggressive. We Americans wouldn’t think of these same behaviors as aggressive, per se. Instead, we value a type of forthrightness the Japanese find rude. As such, we exhibit behaviors seemingly more aggressive than they do.

The social pressures involved in Japanese culture can be seen as types of entanglement, since they correlate the strategies of the actors involved.

I think this is a fruitful way of looking at Quantum Game Theory applied to the social sciences and human behavior that better takes into account the socio-economic situations we all face, and how they affect our decision making than does classical game theory.

References

Hanauske, Matthias, Jennifer Kunz, Steffen Bernius, and Wolfgang König. 2009. Doves and hawks in economics revisited. An evolutionary quantum game theory-based analysis of financial crises. 0904.2113 (April 14). http://arxiv.org/abs/0904.2113.

SMITH, J. MAYNARD, and G. R. PRICE. 1973. The Logic of Animal Conflict. Nature 246, no. 5427 (November 2): 15-18. doi:10.1038/246015a0.

God, or just some dude with a beard and a good muscular build?

On the Big Ideas Blog there is a post about the different types of reasoning, Analytic vs. Synthetic, and their relavence to the existence or non-existence of God.  But, my favorite passage was one concerning we mathematicians:

The requirement of reasonableness might be illustrated as follows. Imagine Tom, John and Jane live in a country run entirely by mathematicians. Their whole culture is built on analytic thinking — only water-tight logical proofs are considered to have any real force. Well, then it would hardly matter how careless Tom had been in disguising the murder, since any number of outlandish explanations for his innocence might be put forward. If you require that Tom is innocent until analytically proven guilty then he’ll get off scot-free, as will every other criminal. This is why mathematicians are rarely given anything important to do.

(Emphasis mine)

A new study from Durham University showed that participants who drank 7 cups of coffee a day or more were more prone to hallucinations.   Sweet!  I wonder what happens when I drink 14 cups?

You know the old math joke:  what is a Mathematician?  A machine that turns coffee into theorems.  Maybe mathematicians actually think the ARE machines … man.

I just found this at Neurophilosophy.  Apparently University of Pennsylvania is hosting a Neuroscience Bootcamp!

What happens at Neuroscience Boot Camp?

Through a combination of lectures, break-out groups, panel discussions and laboratory visits, participants will gain an understanding of the methods of neuroscience and key findings on the cognitive and social-emotional functions of the brain, lifespan development and disorders of brain function.

Each lecture will be followed by extensive Q&A. Break-out groups will allow participants to delve more deeply into topics of relevance to their fields. Laboratory visits will include a trip to an MRI scanner, an EEG/ERP lab, an animal neurophysiology lab, and a transcranial magnetic stimulation lab. Participants will also have access to an extensive online library of copyrighted materials selected for relevance to the Boot Camp, including classic and review articles and textbook chapters in cognitive and affective neuroscience and the applications of neuroscience to diverse fields.

Who should apply?

Graduate and professional students, working professionals and college and university faculty are encouraged to apply. The only prerequisites are a grasp of basic statistics and at least a dim recollection of high school biology and physics. (A short set of readings will be made available prior to the Boot Camp to remind you about the essentials.)

If I had any of that crazy green paper people keep in their pockets I’d probably be interested.  Looks like a great opportunity for people who are in fields like business, law, etc that would benefit from a solid overview of what’s happening in the field of neuroscience. Very cool.

In a review of a paper by Camerer and Fehr on social neuroeconomics, Benoit Hardy-Vallée of Natural Rationality makes the point:

So basically, we have enough evidence to justify a model of rational agents as entertaining social preferences. As I argue in a forthcoming paper (let me know if you want to have a copy), these findings will have normative impact, especially for game-theoretic situations: if a rational agent anticipate other agents’s strategies, she better anticipate that they have social preferences. For instance, one might argue that in the Ultimatum Game, it is rational to make a fair offer.

Check out this cool blog on Decision Science, that is, the science of how people make decisions in political/economic/business situations.  Very cool indeed.

This post is part of a series of posts I’m working on covering some basic models in Decision Theory.  For my previous post on Cognitive models, click Here.

Decision theory in foreign policy analysis has been characterized by a split between two different, and at times rival, models of human behavior (James and Zhang, 2005).  The first is the classical model of Rational Choice theory, a theory that takes as its starting point the end of the decision making process and attempts to figure out why the choice was finally made.  The second is the Cognitive approach, a theory that focuses on the “how” questions of decision making and attempts to reconstruct why the end outcome occurred.  In an attempt to integrate these two different, but useful, approaches, Alex Mintz created Poliheuristic Theory (PH) (Mintz 2005).

The model consists of two stages (Mintz, 2005).  The first is the “heuristic” stage.  In this stage the actor uses heuristics, or simple tools of thought, to limit the number of choices available to him.  This is similar in character to Robert Axelrod’s Schema Theory (1973) and other cognitive approaches (Simon, 1955; Tversky and Kahneman, 1981, 1986, and 1991), including Prospect Theory (Levi, 1997; Tversky and Kahneman, 1992).   The second stage is the “evaluation” or “calculation” stage.  Here the actor makes calculations based on the given information garnered from the first stage.

The components of the first stage culminate in a “decision matrix” that has a number of parts: alternatives, dimensions, implications, ratings, and weights.  The alternatives are the choices available to the actor.  The dimensions are the relevant criteria used to evaluate the different alternatives.  The implications are what happens at each pairing of the alternatives with the dimensions.  Ratings can be given to each of the implications to aid in analysis for the researcher.  The weights are the relative “importance level” of the different dimensions.

The second stage takes the information given in the first stage and analyzes the different outcomes associated with the given values.  This stage resembles classical Rational Choice Theory (Arrow, 1959), and uses the Expected Utility Principle to justify which options are the most viable.

The theory has been successfully applied to Presidential decisions, including Bill Clinton’s bombing of Kosovo (Redd, 2005) and Jimmy Carter’s decisions during the Iranian hostage crisis (Brulé, 2005), and even to autocratic regimes (Kinne, 2005).

For readers with knowledge of Game Theory, there may seem to be a number of similarities between it and the PH model.  But, these similarities are surface deep.  Among them is the use of a decision matrix in the PH model.  Game Theory employs a similar matrix, called the “strategic form” of the game (Gates and Humes, 1997; Gintis, 2000; Rapoport, 1966).  Another is the rating of implications in PH theory with numerical values that can then be assessed mathematically.  Game Theory uses the same devise to make calculation easier-and possible.  But, the differences are more important.  PH theory is an attempt to understand both why and how a particular actor came to a decision.  Game Theory, by contrast, is interested in the dynamics of interactions between and among actors in a given situation.  Game Theory does have methods of evaluating why a choice was made based on expected value, but not how it was made.

However, PH theory and Game Theory are compatible and may, if used together, provide a powerful method of analyzing the decisions of actors in relation with other actors.  Game Theory can illuminate the potential outcomes resulting from the interaction of the players, and PH theory can explain how and why any particular player would make the choices they would make.  This is an advantage over the traditional use of Rational Choice Theory with Game Theory which presumes players are bound by a careful analysis of their expected utility, when in fact, many people do not respond this way in the “real” world (Camerer, 2003).  It is also an advantage to using only the cognitive approach, which tends to shun rational choice thinking as too unrealistic, when in fact, once an actor (in the PH version) has narrowed down their list of actions, they are more likely to make a choice based on the expected utility principle (Redd, 2005).

Poliheuristic Theory is a welcome addition to the literature, and toolbox, of Political Scientists, Economists, and Social Scientists generally.  It bridges the gap between the two primary perspectives in the field, Rational Choice and the Cognitive Models, and provides an easy to use framework for analysis.  Further research may prove that it will work well with Game Theory as a positive approach to understanding why decisions were made in complex interactions among agents.

References

• Arrow, Kenneth J.. 1959. “Rational Choice Functions and Orderings.”  Economica.  New Series, Vol. 26, No. 102, pp 121-127.
• Axelrod, Robert.  1973.  “Schema Theory:  An Information Processing Model of Perception and Cognition.” The American Political Science Review, Vol. 67, No. 4, 1248-1266.
• Brulé, David J.. 2005.  “Explaining and Forecasting Leaders’ Decisions: A Poliheuristic Analysis of the Iran Hostage Rescue Decision.”  International Studies Perspectives. 6, 99-113.
• Camerer, Colin F.. 2003.  Behavioral Game Theory: Experiments in Strategic Interaction. Princeton University Press.
• Gates, Scott and Humes, Brian D.. 1997.  Games, Information, and Politics: Applying Game Theoretic Models to Political Science. University of Michigan Press.
• Gintis, Herbert.  2000.  Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction. Princeton University Press.
• Kinne, Brandon J.  2005. “Decision Making in Autocratic Regimes: A Poliheuristic Perspective.” International Studies Perspectives.  6, 114-128.
• Levi, Jack S.. 1997. “Prospect Theory, Rational Choice, and International Relations.” International Studies Quarterly.  Vol.41, No.1, 87-112.
• Mintz, Alex.  2005.  “Applied Decision Analysis: Utilizing Poliheuristic Theory to Explain and Predict Foreign Policy and National Security Decisions.” International Studies Perspectives. 6, 94-98.
• Rapoport, Anatol.  1966.  Two-Person Game Theory.  Dover Publications, Inc.
• Redd, Steven B.. 2005. “The Influence of Advisers and Decision Strategies on Foreign Policy Choices: President Clinton’s Decision to Use Force in Kosovo.”  International Studies Perspectives.  6, 129-150.
• Simon, Herbert A. 1955.  “A Behavioral Model of Rational Choice.” The Quarterly Journal of Economics, Vol. 69, No. 1, 99-118.
• Tversky, Amos and Kahneman, Daniel.  1981.  “The Framing of Decisions and the Psychology of Choice.” Science, New Series, Vol. 211, No. 4481, 453-458.
• Tversky, Amos and Kahneman, Daniel.  1986.  “Rational Choice and the Framing of Decisions.” The Journal of Business, Vol. 59, No. 4, Part 2: The Behavioral Foundations of Economic Theory, S251-S278.
• Tversky, Amos and Kahneman, Daniel.  1991.  “Loss Aversion in Riskless Choice: A Reference-Dependent Model.” The Quarterly Journal of Economics, Vol. 106, No. 4, 1039-1061.
• Tversky, Amos and Kahneman, Daniel.  1992. “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty. 5:297-323.
• James, Patrick and Zhang, Enyu.  2005.  “Chinese Choices:  A Poliheuristic Analysis of Foreign Policy Crises.”  Foreign Policy Analysis.  1, 31-5

Over the next few weeks (months?) I’ll be presenting a series of reviews of some of the major models in Decision Theory, a branch of both Economics and Political Science that has been on the rise for over 30 years. All of the models attempt to explain why humans act the way that they do in political and economic situations, and also to provide some normative answers to the question of what people should do in those situations.  For my post on Poliheuristic Theory, click Here.

The ultimate cause of human behavior is the mind. The mind, an emergent property from the workings of collections of neurons, hormones, proteins, and other biochemical agents, controls everything every human does. From their intended actions to their subconscious actions, all of it is controlled by the human analogue of a central processing unit. Cognitive models in the social sciences and particularly in political science and economics take seriously this point of view of the human decision maker and apply it to political and economic situations.

One of the major ideas of the subject is that people are equipped with a cognitive “toolbox” that houses tools that help them to solve problems in different environments. These tools come in the form of heuristics, or simple models, of a situation. Robert Axelrod in his 1973 paper, “Schema Theory: An information Processing Model of Perception and Cognition,” called his version of this model a Schema. It’s components were an input of information about a particular case, including what type of case or situation it is; an interpretation of the case at hand and a complete specification of it; and an accessibility check to see how closely the schema (or heuristics) currently available in ones “toolbox” fit the case, which lead to slight adjustments of the schema to fit the case better if warranted.

Herbert Simon forecasted such a theory with his 1955 paper, “A behavioral Model of Rational Choice.” In it he claimed that people, when confronted with a situation have available to them a set A of strategies, or actions, but will only consider a limited number of them, a subset B of A. The reason for this could be many, but is likely due in part to a lack of available information about the actions’ availability. For instance, most people when playing chess do not realize how many moves they have available to them at any given point in the game. There is an objective number of possible moves that far exceeds their limited set of perceived options.

Simon mentions that one of the most important ideas about a cognitive model approach to human decision making is in how we model the payoff functions of individuals. Classically payoff functions are the weighted sum of all the outcomes of all the options and individuals are presumed to make a “rational” decision based upon this information as to what action to take. Simon suggests instead of a “real-valued” payoff function, that is one that has a number as it’s output, we use a “vector” valued payoff function. The value of such a payoff function is that we can account for sub-payoffs within the total payoff of a given action that don’t sum together. For instance, in his example, if one is deciding between two jobs in two different cities, two of the payoff calculations could be 1) salary, and 2) weather. It is hard to add these two payoffs together. Instead a total payoff may contain both sets of information as is.

Another component to the vector valued function would have to include the history of past actions in similar situations. That is, it would need to be history-dependent. Again, using an example of Simon’s, you won’t know if you like cheese until you have tasted it.

Axelrod mentions that people often don’t have the time, nor the computing power, to evaluate every option available to them. Simon also discusses that the problem of a lack of computing power. A good cognitive model must take this into account by incorporating into the model these limits, or bounds, on an actor’s rationality.

The so called “fight or flight reflex” is a good example of the type of heuristic discussed in the literature. If you are being chased by a bear, you don’t have a lot of time to think about all of your options. Instead, you simplify your options down to just two: run; or stay and fight. One of those two may get you killed. But, if you happened to pick the one that kept you alive, then you are more likely to try that one again the next time you are in a similar situation than you are to try the opposing option that hasn’t yet been tried. Thus in the ordering of strategies, the tried and true trumps the unknown.

Another major component of cognitive models is loss or risk aversion. In “Loss Aversion in Riskless Choice: A Reference-Dependent Model,” Amos Tversky and Daniel Kahneman discuss the asymmetry of individual choice when faced with loss verses being faced with gain. People seem to behave in such a way as to be more worried about losing what they have, than in gaining more. They mention that such loss aversion can hamper situations such as negotiations if the outcomes of the negotiation are framed as losses. For example, it matters to people whether the surgery they are about to undergo has a 90% survival rate, or a 10% mortality rate. These are just different ways of stating the same idea, and Rational Choice Theory claims they are equal and that actors wouldn’t care which way the information was presented to them. The trouble is that the evidence says they do care.

Cognitive choice models prove to be a powerful refutation of the classical theory of the “rational actor”. In classical theory, human beings take the entire set of objective options, sift clearly through these options, weighing the differing payoffs assigned to each option, and taking the appropriate action that results in the greatest payoff to the individual. Cognitive models do away with much of this theory. Simon’s clearly states that people throw away much of the information available to them to simplify the calculations involved in a given situation. Axelrod also mentions that the relevance of information being inputted into ones calculations determines much of what is and is not thrown away, but that this may not always be accurate. That is, people, using a heuristic that has worked previously in a similar situation will often toss out information relevant to the current case because it doesn’t fit their preconceived model of action. This type of “data dumping” can result in outcomes contrary to the individual’s interests. Tversky and Kahneman make it clear that people are often more worried about losses than about gains, and that this can skew the payoff functions, and make their actions seem less rational to an outside observer, and in fact may seem irrational, upon reflection, to the participants themselves.

Much of this discussion may sound negative to the reader since cognitive models predict that individuals will, and often do, make erroneous decisions based on false assumptions. Amos Tversky and Daniel Kahneman discuss this concept to some degree in their paper, “Rational Choice and the Framing of Decisions (1986).” They say because cognitive models don’t allow for much of the rationalizing behavior that is necessary if one is to come to an “optimum” solution to a given case, that “no theory of choice can be both normatively adequate and descriptively accurate.” This means that cognitive models are best used in positive theories about human behavior, and suggests that the “rational actor model” may be best suited to normative theories of human behavior.

If we want to “get to the bottom” of why people make the decisions they make in political and economic situation, the cognitive model provides a great leap forward in that direction. It offers a clear system of evaluation that may be used by an individual that is also practical and realistic, though not always one that results in an “optimal” outcome. As such, it is a “good fit” to how humans actually make choices.

References

• Axelrod, Robert. 1973. “Schema Theory: An Information Processing Model of Perception and Cognition.” The American Political Science Review, Vol. 67, No. 4, 1248-1266.
• Simon, Herbert A. 1955. “A Behavioral Model of Rational Choice.” The Quarterly Journal of Economics, Vol. 69, No. 1, 99-118.
• Tversky, Amos and Kahneman, Daniel. 1981. “The Framing of Decisions and the Psychology of Choice.” Science, New Series, Vol. 211, No. 4481, 453-458.
• Tversky, Amos and Kahneman, Daniel. 1986. “Rational Choice and the Framing of Decisions.” The Journal of Business, Vol. 59, No. 4, Part 2: The Behavioral Foundations of Economic Theory, S251-S278.
• Tversky, Amos and Kahneman, Daniel. 1991. “Loss Aversion in Riskless Choice: A Reference-Dependent Model.” The Quarterly Journal of Economics, Vol. 106, No. 4, 1039-1061.

John Hawks reviews Peter Turchin’s 1998 book, Quantitative Analysis of Movement.

I tend to lecture about genetic models, for which there is a great value in simplicity (point 3), but which may require quite complicated extensions to handle reasonable biological populations (point 2). In that connection, some reasonable people go to extremes of interpretation — sometimes claiming that the data necessitate some assumption on the basis of a very simplified model, and in other cases claiming that no model can apply to the complex history of the population. It is our task (my task) to determine which factors are important and conceivably affect results, and which will always be too weak to influence the interpretation of the data (point 1). And the end will often be to discover evidence for values in past human populations for which we have no direct means of estimating aside from genetic variation (point 5).