Feels Like it Was Yesterday

Stay safe everyone. 

End of an Era

On August 13 Judit Polgar announced that she was retiring from competitive chess.  This came as a shock to most people who follow chess – it certainly came as a shock to me though I have heard on several occasions that Judit wanted to put more emphasis on raising her family.  On her website she said that she was going to spend more time with her children and developing her foundation (The Judit Polgar Chess Foundation promotes pioneering cognitive skills development for school children). 

Judit is often described as the strongest female chess player ever and I have no reason to doubt that assessment.  At the peak of her career, Judit was one of the strongest players of either gender.  Her highest ELO ranking was a staggering 2735 and she was ranked #8 overall in the world in 2005.  According to Wikipedia, she has been the #1 rated female chess player in the world since 1989 (!). Judit typically played in the general tournaments – she actually never competed for the women’s world championship. Over her career, she has defeated a slew of famous players including Magnus Carlsen (the current world #1 and current chess champion), Viswanathan Anand (the previous world #1), Anatoly Karpov, Boris Spassky, … the list goes on and on. [1]

There is a famous anecdote that Gary Kasparov once described Judit as a “circus puppet” and asserted that women chess players should stick to having children. I’m not actually sure where this story comes from – it was relayed by The Guardian in 2002 without further elaboration. The statement is so over the top that I wonder whether it’s actually true.  It’s might be true – chess players are known for making zany statements like this from time to time (Bobby Fischer comes to mind). Perhaps Kasparov was trying to stir up some controversy … who knows. In any case, Kasparov asked for it and he got it.  In 2002 Polgar beat Kasparov and added to her trophy room.  Kasparov was the worlds #1 ranked player at the time. 

Another fascinating aspect of Judit’s chess life is that her father, Laszlo Polgar, apparently decided to use his children to “prove” that geniuses are “made, not born.” He made a conscious effort to train his children in chess starting when they were each very young. Perhaps Laszlo was right, in addition to Judit, her sisters Susan and Sofia are also established chess grandmasters. 

Speaking for myself, Judit has been my favorite active chess player for a while now.  Her style is somewhat of an anachronism – she is known for a hyper aggressive, dramatic playing style.  She often sacrifices pieces trying to gain initiative and attacking positions. For the most part, men’s chess is actually much tamer – many of the best male players are “positional” players who grind out games looking for small advantages which they eventually convert for a win (Alexey Shirov is a counter-example – see below). Stylistically, Judit reminds me a lot of Mikhail Tal – perhaps the greatest chess tactician of all.

Below is a video of one of Judit’s most famous games. In the game Judit plays against Alexey Shirov. The game commentary is by Mato Jelic. If you are interested in learning more about chess or about Judit’s games, Mato’s youtube channel is a great place to start. Among other things, Mato has a great collection of Judit Polgar’s games with commentary. 

 

[1] Here’s a funny quote from Judit about her sister Susan. “My sister Susan — she was 16 or 17 — said that she never won against a healthy man. After the game, there was always an excuse: ‘I had a headache. I had a stomach ache.’ There is always something.”  

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More Thoughts on Agent Based Models

My recent post on Agent Based Models (ABMs) generated a few interesting responses and I thought I would briefly reply to a couple of them in this post.  In particular, two responses came from people who actually have direct experience with ABMs.

Rajiv Sethi posts a response on his own blog.  Some excerpts:

Chris House has managed to misrepresent the methodology so completely that his post is likely to do more harm than good.

[Well that doesn’t sound too good …]

Agents can be as sophisticated and forward-looking in their pursuit of self-interest in an ABM as you care to make them; they can even be set up to make choices based on solutions to dynamic programming problems, provided that these are based on private beliefs about the future that change endogenously over time.

What you cannot have in an ABM is the assumption that, from the outset, individual plans are mutually consistent. That is, you cannot simply assume that the economy is tracing out an equilibrium path. The agent-based approach is at heart a model of disequilibrium dynamics, in which the mutual consistency of plans, if it arises at all, has to do so endogenously through a clearly specified adjustment process. This is the key difference between the ABM and DSGE approaches [.]

In a similar vein, in the comments section to the earlier post, Leigh Tesfatsion offered several thoughts many of which fit squarely with Rajiv’s opinion.  Professor Tesfatsion uses ABMs in a multiple settings including economics and climate change – I’m quite sure that she has much more experience with such models that I do (I basically don’t know anything beyond a couple of papers I’ve encountered as a referee here and there).  Here are some excerpts from Leigh’s comments:

Agents in ABMs can be as rational (or irrational) as their real-world counterparts…

The core difference between agent modeling in ABMs and agents in DSGE models is that agents in ABMs are required to be “locally constructive,” meaning they must specify and implement their goals, choice environments, and decision making procedures based on their own local information, beliefs, and attributes. Agent-based modeling rules out “top down” (modeler imposed) global coordination devices (e.g., global market clearing conditions) that do not represent the behavior or activities of any agent actually residing within the model. They do this because they are interested in understanding how real-world economies work.

Second, ABM researchers seek to understand how economic systems might (or might not) attain equilibrium states, with equilibrium thus studied as a testable hypothesis (in conjunction with basins of attraction) rather than as an a priori maintained hypothesis.

I was struck by the similarity between Professor Sethi and Professor Tesfatsion’s comments. The parts of their comments that really strike me are (1) the agents in an ABM can have rational rules; (2) in an ABM, there is no global coordination imposed by the modeler. That is, agents behaviors don’t have to be mutually consistent; and (3) ABMs are focused on explaining disequilibrium in contrast to DSGE models which operate under the assumption of equilibrium at all points.

On the first point (1) I agree with Rajiv and Leigh on the basic principle. Agents in an ABM could be endowed with rational behavioral rules – that is, they could have rules which are derived from an individual optimization problem of some sort. The end result of an economic optimization problem is a rule – a contingency plan that specifies what you intend to do and when you intend to do it. This rule is typically a function of some individual state variable (what position are you in?). In an ABM, the modeler specifies the rule as he or she sees fit and then goes from there. If this rule were identical to the contingency plan from a rational economic actor then the two modelling frameworks would be identical along those dimensions. However, in an ABM there is nothing which requires that these rules adhere to rationality. The models could accommodate rational behavior but they don’t have to. To me this still seems like a significant departure from standard economic models that typically place great emphasis on self-interest as a guiding principle. In fact, the first time I read Rajiv’s post, my initial thought was that an ABM with a rational decision rule would be essentially a DSGE model. All actions in DSGE models are based on private beliefs about the system. Both the system and the beliefs can change over time.  I for one would be very interested if there were any ABMs that fit Rajiv’s description that are in use today.

The second point (2) on mutual consistency is interesting. It is true that in most DSGE models, plans are indirectly coordinated through markets.  Each person in a typical economic model is assumed to be in (constant?) contact with a market and each confronts a common price for each good.  As a result of this common connection, the plans of individuals in economic models are assumed to be consistent in a way that they are not in ABMs.  On the other hand, there are economic models that do not have this type mutual consistency.  Search based models are the most obvious example.  In many search models, individuals meet one-on-one and make isolated bargains about trades.  There are thus many trades and exchanges occurring in such model environments and the equilibria can feature many different prices at any point in time.  This might mean that search / matching models are a half-way point between pure Walrasian theories on the one hand and ABMs on the other.

The last issue (3) that Rajiv and Leigh brought up was the idea that ABMs seek to model “disequilibrium” of some sort. I suspect that this is somewhat more an issue of terminology rather than substance but there may be something more to it.  Leigh’s comment in particular suggests that she is reserving the term “equilibrium” for a classical rest point at which the system is unchanging. I mentioned to her that this doesn’t match up with the term “equilibrium” in economics. In economic models (e.g., DSGE models) equilibria can feature erratic dynamic adjustment over time as prices and markets gradually adjust (e.g., the New Keynesian model) or as unemployment and vacancies are gradually brought into alignment (e.g., the Mortensen Pissarides model) or as capital gradually accumulates over time (e.g., the Ramsey model).  Indeed, the equilibria can be “stochastic” so that they directly incorporate random elements over time. There is no supposition that an equilibrium is a rest point in the sense that (I think) she intends.  When I mentioned this she replied:

As for your definition of equilibrium, equating it with any kind of “solution,” I believe this is so broad as to become meaningless. In my work, “equilibrium” is always used to mean some type of unchanging condition that might (or might not) be attained by a system over time. This unchanging condition could be excess supply = 0, or plans are realized (e.g., no unintended inventories), or expectations are consistent with observations (so updating ceases), or some such condition. Solution already means “solution” — why debase the usual scientific meaning of equilibrium (a system at “rest” in some sense) by equating it with solution?

I suspect that in addition to her background in economics, Professor Tesfatsion also has a strong background in the natural sciences and is somewhat unaccustomed to terminology used in economics and prefers to use the term “equilibrium” as it would be used in say physics.[1] In economics, an outcome which is constant and unchanging would be called a “steady state equilibrium” or a “stationary equilibrium.”  As I mentioned above, there are non-stationary equilibria in economic models as well.  Even though quantities and prices are changing over time, the system is still described as being “in equilibrium.”  The reason most economists use this terminology is subtle.  Even though the observable variables are changing, agents’ decision rules are not – the decision rules or contingency plans are at a rest point even though the observables move over time.

Consider this example. Suppose two people are playing chess. The player with the white pieces is accustomed to playing e4. She correctly anticipates that her opponent will respond with c5 – the Sicilian Defense. White will then respond with the Smith-Morra Gambit to which black with further respond with the Sicilian-Scheveningen variation. Both players have played several times and they are used to the positions they get out of this opening. To an economist, this is an equilibrium.  White is playing the Smith-Morra Gambit and black plays the Sicilian-Scheveningen variation. Both correctly anticipate the opening responses of the other and neither wants to deviate in the early stages of the game. Neither strategy changes over time even though the position of the board changes as they play through the first several moves. (In fact this is common to see in competitive chess – two players who play each other a lot often rapidly fire off 8-10 moves and get to a well-known position.)

In any case, I’m not sure that this means economists are “debasing” the usual scientific meaning of equilibrium or not but that’s how the term is used in the field.

One last point that came up in Rajiv’s post which deserves mention is the following:

A typical (though not universal) feature of agent-based models is an evolutionary process, that allows successful strategies to proliferate over time at the expense of less successful ones.

This is absolutely correct.  I didn’t think to mention this in the earlier post but I clearly should have done so.  Features like this are used often in evolutionary game theory.  In those settings, we gather together many individuals and endow them with different rules of behavior.  Whether a rule survives, dies, proliferates, etc. is governed by how well it succeeds at maximizing an objective.  Rajiv is quite correct that such behavior is common in many ABMs and he is right to point out its similarity with learning in economic models (though it is not exactly the same as learning).

[1] A reader pointed out that Leigh Tesfatsion’s Ph.D. is in economics and so she is well aware of non-stationary equilibria or stochastic equilibria. My original post incorectly suggested that she might unaware of economic terminology (Sorry Leigh). Leigh prefers to reserve the term “equilibrium” for a constant state as it is in many other fields. Her choice for terminology is fine as long as she and I are clear as to what were are each talking about.