When does one of the central ideas in economics work?

February 20, 2019, University of Oxford
Noughts and crosses -- the games people play. Credit: University of Oxford

The concept of equilibrium is one of the most central ideas in economics. It is one of the core assumptions in the vast majority of economic models, including models used by policymakers on issues ranging from monetary policy to climate change, trade policy and the minimum wage. But is it a good assumption? In a forthcoming Science Advances paper, Marco Pangallo, Torsten Heinrich and Doyne Farmer investigate this question in the simple framework of games, and show that when the game gets complicated this assumption is problematic. If these results carry over from games to economics, this raises deep questions about when economics models are useful to understand the real world.

Kids love to play tic-tac-toe, but when they are about 8 years old they learn that there is a strategy for the second player that always results in a draw. This strategy is what is called an in economics. If all the players in the game are rational they will play an equilibrium strategy. In economics, the word rational means that the player can evaluate every possible move and explore its consequences to their endpoint and choose the best move. Once kids are old enough to discover the equilibrium of tic-tac-toe they quit playing because the same thing always happens and the game is really boring. One way to view this is that, for the purposes of understanding how children play tic-tac-toe, rationality is a good behavioral model for eight year olds but not for six year olds.

In a more complicated game like chess, rationality is never a good behavioral model. The problem is that chess is a much harder game, hard enough that no one can analyze all the possibilities, and the usefulness of the concept of equilibrium breaks down. In chess no one is smart enough to discover the equilibrium, and so the game never gets boring. This illustrates that whether or not rationality is a sensible model of the behavior of real people depends on the problem they have to solve. If the problem is simple, it is a good behavioral model, but if the problem is hard, it may break down.

Theories in economics nearly universally assume equilibrium from the outset. But is this always a reasonable thing to do? To get insight into this question, Pangallo and collaborators study when equilibrium is a good assumption in games. They don't just study games like tic-tac-toe or chess, but rather they study all possible games of a certain type (called normal form games). They literally make up games at random and have two simulated players play them to see what happens. The simulated players use strategies that do a good job of describing what real people do in psychology experiments. These strategies are simple rules of thumb, like doing what has worked well in the past or picking the move that is most likely to beat the opponents recent moves.

Pangallo and his colleagues demonstrate that the intuition about tic-tac-toe vs. chess holds up in general, but with a new twist. When the game is simple enough, rationality is a good behavioral model: players easily find the equilibrium strategy and play it. When the game is more complicated, whether or not the strategies will converge to equilibrium depends on whether or not the game is competitive. If the incentives of the players are lined up they are likely to find the equilibrium , even if the game is complicated. But when the incentives of the players are not lined up and the game gets complicated, they are unlikely to find the equilibrium. When this happens their strategies always keep changing in time, usually chaotically, and they never settle down to the equilibrium. In these cases equilibrium is a poor behavioral model.

A key insight from the paper is that cycles in the logical structure of the game influence the convergence to equilibrium. The authors analyze what happens when both players are myopic, and play their best response to the last move of the other player. In some cases this results in convergence to equilibrium, where the two players settle on their best move and play it again and again forever. However, in other cases the sequence of moves never settles down and instead follows a best reply cycle, in which the players' moves keep changing but periodically repeat - like "ground hog day" over and over again. When a game has best reply cycles convergence to equilibrium becomes less likely. Using this result the authors are able to derive quantitative formulas for when the players of the game will converge to equilibrium and when they won't, and show explicitly that in complicated and competitive games cycles are prevalent and convergence to equilibrium is unlikely. Many of the problems encountered by actors are too complicated to model easily using a normal form game. Nonetheless, this work suggests a potentially serious problem. Many situations in economics are complicated and competitive. This raises the possibility that many important theories in economics may be wrong: If the key behavioral assumption of equilibrium is wrong, then the predictions of the are likely wrong too. In this case new approaches are required that explicitly simulate the behavior of the players and take into account the fact that real people are not good at solving complicated problems.

Explore further: The reason we lose at games

More information: "Best reply structure and equilibrium convergence in generic games" Science Advances (2019). advances.sciencemag.org/content/5/2/eaat1328

Related Stories

The reason we lose at games

January 7, 2013

If you have ever wondered why you never seem to win at skill-based games such as poker or chess, there might be a very good reason. Writing in PNAS, a University of Manchester physicist has discovered that some games are ...

What computer science can teach economics

November 9, 2009

(PhysOrg.com) -- Computer scientists have spent decades developing techniques for answering a single question: How long does a given calculation take to perform? Constantinos Daskalakis, an assistant professor in MIT’s ...

Outside competition breeds more trust among coworkers

September 19, 2018

Working in a competitive industry fosters a greater level of trust amongst workers, finds a new study from the University of British Columbia, Princeton University and Aix-Marseille University, published today in Science ...

Recommended for you

Machine learning identifies links between world's oceans

March 21, 2019

Oceanographers studying the physics of the global ocean have long found themselves facing a conundrum: Fluid dynamical balances can vary greatly from point to point, rendering it difficult to make global generalizations.

How fluid viscosity affects earthquake intensity

March 21, 2019

Fault zones play a key role in shaping the deformation of the Earth's crust. All of these zones contain fluids, which heavily influence how earthquakes propagate. In an article published today in Nature Communications, Chiara ...

14 comments

Adjust slider to filter visible comments by rank

Display comments: newest first

marcush
5 / 5 (2) Feb 20, 2019
Sounds like an important study...
Shakescene21
5 / 5 (2) Feb 20, 2019
"...If these results carry over from games to economics, this raises deep questions about when economics models are useful to understand the real world..."

That's a huge "If" and I don't think game theory based on two-person win-lose games has much relevance to macroeconomics. Macroeconomics involves millions of economic agents and hundreds of equilibria within hundreds of sub-systems, as well as general equilibria.

In Microeconomics there are some areas where game theory might be useful, especially for price setting where there are only a few sellers in a market. But economic problems are usually much more than a win-lose game in a static world.

Shakescene21
5 / 5 (2) Feb 20, 2019
"...Theories in economics nearly universally assume equilibrium from the outset. But is this always a reasonable thing to do?..."

Although undergraduate textbook presentations of economic theories may often start from "eqilibrium", this is done to make it easier to understand. In real-world economic analysis it is understood that economies are seldom able to reach equilibrium before underlying conditions change and push the economy toward another equilibrium. So base-year data is usually adjusted with a trend factor, or a moving average, or other techniques. Similar adjustments are typically done in microeconomic forecasting if the economist is worth his salt.

Even if economic systems rarely reach an equilibrium situation, the equilibrium provides the best forecast of where the economy is heading.
Researcher
3 / 5 (2) Feb 20, 2019
@Shakescene21 - I disagree. If you look at the variables in Macroeconomic systems there is always what can be viewed as a positive and a negative. There is always a counterpart. Similar to a two person game. For instance you can call savings as a positive. The negative could be inflation. As inflation eats savings. EG 1 dollar saved in 1960 today you could not buy a fresh breath of air with it (if you could find one). According to the Bureau of Labor Statistics (US) consumer price index, prices in 2016 are 710.83% higher than average prices throughout 1960. I use one thing on each side here as an example. In Macroeconomics groups of variables can be considered as positive and negative. Of course the positive and negative changes sides depending of your point of view. But once that point of view is established its locked in. Which means the fluidity becomes stable. Game theory comes into play. (excuse the pun :)
Researcher
1 / 5 (2) Feb 20, 2019
What the world of economics needs is a replacement for the keynesian economics theory. Its old and tired. There are much better systems that are much fairer and stops a lot of issues with Keynes theory.
Da Schneib
1 / 5 (2) Feb 20, 2019
@Research, problem is no one has disproven Keynesian economics. That which is old is strong.
Da Schneib
1 / 5 (2) Feb 20, 2019
All that is gold doth not glitter
Not all those who wander are lost
The old that is strong doth not wither
Deep roots are not touched by the frost

From the ashes, a fire shall be woken
A light from the shadows shall spring
Renewed shall be sword that was broken
And the crownless again shall be king
Squirrel
3 / 5 (2) Feb 21, 2019
Looks like George Soros is right https://economist...eor.html
Macrocompassion
3 / 5 (2) Feb 21, 2019
Actually macroeconomics is nothing like as complicated as most people imagine. its a matter of how our social situation is conceived. Without making the following simplification we will never properly learn about how it all works.

We need to accept it as being a system and then to explore the number of different KINDS of business transactions and exchanges that occur. Of course we all perform a number of these deals in varying degrees, but instead of looking at the activities of each individual, we should examine the various activities that are possible. I have done this in my paper SSRN 2865571 "Einstein's Criterion Applied to Logical Macroeconomics Modeling", where only 10 are found to be required. The rest as they say, is history!
Macrocompassion
5 / 5 (1) Feb 21, 2019
Without a trend towards equilibrium our social system is unstable and likely to reach a crisis. Of course this has happened in 2007 with the investment bank having to be bailed out. But suppose the US government could not do this, the it would appear that an impossible situation would occur.

It is my claim that our social system has inherent stability although it hardly ever reaches an equilibrium situation, due to a continuous series of disturbances and policy changes. A theoretical model of our system might be in equilibrium were it not for the actual nature of fluctuation and business variation. So all the time there is a search taking place for getting closer to equilibrium. The is the application of Adam Smith's "inviable Hand" and Leon Walras's "Tantonnement" or grouping activity.
EnricM
1 / 5 (1) Feb 21, 2019
Looks like George Soros is right https://economist...eor.html


Ahh, Evil!! (((People))) ROFLMAO
julianpenrod
5 / 5 (1) Feb 21, 2019
Among other things, no "economics theory" ever helped prevent financial disasters. If they described the way things behaved in "economics", they would be able to. But there are a number of aspects "economists" don't want to admit really control world economies. Among other things, in any finite hierarchical system, say of physical wealth or physical power, there is always a top level. They own all physical wealth that isn't tied down. They can say conditions are whatever they want to say and the gullible will buy it. They can cut off money distribution and say it's something else. They can claim businesses are doing well or badly and so many will accept it without question. They are the New World Order, the ones who never lose money, no matter what happens.
Da Schneib
1 / 5 (1) Feb 21, 2019
Then you get to try to convince a billion Chinese communists. And that's only the beginning of your problems.
torbjorn_b_g_larsson
not rated yet Feb 21, 2019
Looks like George Soros is right https://economist...eor.html


One example is an anecdote, not data.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.