Categories: world

When does one of the key ideas in the economy work?

Nuts and crosses – games people play. Credit: University of OxfordThe 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 politicians on issues ranging from monetary policy to climate change, trade policy and minimum wage. But is that a good assumption? In a forthcoming Science Advance paper, Marco Pangallo, Torsten Heinrich and Doyne Farmer are investigating this issue in the simple game frame and showing that when the game becomes complicated, this assumption is problematic. If these results change from game to economy, this raises deep questions about when finance models are useful for understanding the real world. Children love to play tic-tac-toe, but when they are about 8 years old they learn that there is a strategy for the other player that always results in a draw. This strategy is what is called a balance in the economy. If all players in the game are rational, they play a balance strategy. In economics, the word rational means that the player can evaluate all possible moves and explore the consequences for their end point and choose the best move. When the kids are old enough to discover the balance of tic-tac-toe they stopped playing because the same thing always happens and the game is very boring. One way to see this is that to understand how children play tic-tac-toe, rationality is a good behavior model for eight year olds…



Nuts and crosses – 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 politicians on issues ranging from monetary policy to climate change, trade policy and minimum wage. But is that a good assumption? In a forthcoming Science Advance paper, Marco Pangallo, Torsten Heinrich and Doyne Farmer are investigating this issue in the simple game frame and showing that when the game becomes complicated, this assumption is problematic. If these results change from game to economy, this raises deep questions about when finance models are useful for understanding the real world.

Children love to play tic-tac-toe, but when they are about 8 years old they learn that there is a strategy for the other player that always results in a draw. This strategy is what is called a balance in the economy. If all players in the game are rational, they play a balance strategy. In economics, the word rational means that the player can evaluate all possible moves and explore the consequences for their end point and choose the best move. When the kids are old enough to discover the balance of tic-tac-toe they stopped playing because the same thing always happens and the game is very boring. One way to see this is that to understand how children play tic-tac-toe, rationality is a good behavior model for eight year olds but not for six-year-olds.

In a more complicated game like chess, rationality is never a good behavior model. The problem is that chess is a much more difficult game, difficult enough because no one can analyze all possibilities, and the usefulness of the concept of equilibrium is broken down. In chess no smart enough to discover equilibrium, and so the game never gets boring. This illustrates that whether rationality is a sensible model for real people’s behavior depends on the problem they have to solve. If the problem is simple, it is a good behavior model, but if the problem is difficult it can break down.

The theories in the economy almost all take the balance from the beginning. But is it always a reasonable thing to do? In order to gain insight into this issue, Pangallo and employees study when equilibrium is a good assumption in games. They study not only games such as tic-tac-toe or chess, but rather study all the possible games of a certain type (called the normal form game). They literally play randomly and have two simulated players to play them to see what’s going on. The simulated players use strategies that do a good job describing which real people are doing in psychological experiments. These strategies are simple rules of thumb, such as doing what has worked well before or picking the trait that is most likely to hit the opponents’ latest move.

Pangallo and his colleagues show that the intuition of tic-tac-toe vs chess is generally, but with a new twist. When the game is simple enough, rationality is a good behavior model: players can easily find the balance strategy and play it. When the game is more complicated, whether the strategies will converge to equilibrium depends on whether the game is competitive or not. If the players’ incentives are lined up, they will likely find the equilibrium strategy, even if the game is complicated. But when the incentives from the players are not lined up and the game becomes complicated, they are unlikely to find the balance. When this happens, the strategies continue to change in time, usually chaotic, and they never come down to equilibrium. In these cases, equilibrium is a poor behavior model.

An important insight from the paper is that cycles in the game’s logical structure affect the convergence towards equilibrium. The authors analyze what happens when both players are myopic and play their best response to the other player’s last move. In some cases, this leads to convergence towards equilibrium, where the two players solve their best moves and play it again and again forever. In other cases, however, the sequence of movements does not go down and instead follows a best response cycle, where the player’s movements continue to change but is repeated regularly &#821

1; as “green pig day” over and over again. When a game has the best response cycles, convergence towards equilibrium is less likely. Using this result, the authors can derive quantitative formulas for when the players in the game will converge to equilibrium and when they do not, and clearly show that in complex and competitive games, cycles are common and convergence towards equilibrium is unlikely. Many of the economic operators’ problems are too complicated to easily model with a regular game. Nevertheless, this work suggests a potentially serious problem. Many situations in the economy are complicated and competitive. This gives rise to the possibility that many important theories in the economy can be incorrect: If the most important behavioral absorption of equilibrium is wrong, it is also likely that the model’s predictions are incorrect. In this case, new methods 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 stake

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

Journal reference:
Science Advances

Provided by:
Oxford University

Share
Published by
Faela