The concept of balance is one of the most central ideas in economics. This is one of the fundamental assumptions of the vast majority of economic models, including the models used by policymakers on issues ranging from monetary policy to climate change, to trade policy and minimum wage. But is this a good hypothesis? In a near Progress of science The paper, Marco Pangallo, Torsten Heinrich and Doyne Farmer examine this question in the context of games and show that when the game becomes complicated, this hypothesis is problematic. If these results echo games on the economy, it raises deep questions about when economic models are useful for understanding the real world.
Kids love to play tic-tac-toe, but when they are around 8 years old, they learn that there is a strategy for the second player that always ends in a draw. This strategy is what is called a balance in economics. If all the players in the game are rational, they will play a balance strategy. In economics, the rational word means that the player can evaluate each possible move and explore the consequences until their end point and choose the best move. Once the children are old enough to discover the tic-tac-toe balance, they stop playing because the same thing always happens and the game is really boring. One way to look at this is that, in order to understand how kids 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 model of behavior. The problem is that chess is a much more difficult game, hard enough so that no one can analyze all the possibilities, and the utility of the concept of balance will collapse. In chess, no one is smart enough to discover balance and the game never becomes boring. This shows that the fact that rationality is or not a reasonable 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 it is difficult, it can collapse.
Theories in economics almost universally presuppose equilibrium from the beginning. But is it still a reasonable thing to do? To better understand this question, Pangallo and his collaborators study when equilibrium is a good hypothesis in games. They do not just study games like tic-tac-toe or chess, but instead study all possible games of a certain type (called normal-form games). They literally make up random games and are played by two simulated players to see what happens. Simulated players use strategies that describe what real people do in psychology experiments. These strategies are simple rules of thumb, such as doing what worked well in the past or picking the shot that is most likely to beat the opponent's recent moves.
Pangallo and his colleagues demonstrate that the intuition between tic-tac-toe and chess holds up in general, but with a new twist. When the game is fairly simple, rationality is a good behavior model: players easily find the balance strategy and play it. When the game is more complicated, the convergence of strategies to balance depends on whether the game is competitive or not. If the players are well motivated, they will probably find the strategy of balance, even if the game is complicated. But when the players' motives are not aligned and the game gets complicated, it is unlikely that they find the balance. When this happens, their strategies constantly change over time, usually in a chaotic manner, and they never settle in equilibrium. In these cases, balance is a poor behavioral model.
One of the key elements of this article is that the cycles of the logical structure of the game influence the convergence towards equilibrium. The authors analyze what happens when both players are short-sighted and play their best response at the last shot of the other player. In some cases, this results in a convergence to balance, where both players determine their best shot and replay it forever. However, in other cases, the movement sequence never stops and follows a cycle of best response, in which the movements of the players change but recur periodically – such as "a day of ground hunting". , again and again. When a game has the best response cycles, convergence to balance becomes less likely. Using this result, authors can derive quantitative formulas indicating when gamers will converge on equilibrium and when they will not, and explicitly show that in complicated and competitive games, cycles are common and that convergence towards equilibrium is unlikely. Many of the problems faced by economic actors are too complicated to be modeled easily with the help of a normal form game. Nevertheless, 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 are flawed: if the key behavioral assumption of equilibrium is false, the predictions of the model are probably also false. In this case, new approaches are needed to explicitly simulate the behavior of players and take into account the fact that real people are not good at solving complicated problems.
The reason we lose games
"Better response structure and equilibrium convergence in generic games" Progress of science (2019). advance.sciencemag.org/content/5/2/eaat1328