Study suggests a key assumption of economic theory might be wrong
The concept of equilibrium, probably the most central ideas in economics and something of the core assumptions within the majority of economic models, might have serious problems, concludes a study in the Institute for New Economic Thinking in the Oxford Martin School.
The idea of equilibrium may be the foundation of many economic models, including models used by policymakers on issues like monetary policy, climate change, trade policy and the minimum wage. In a paper published today in Science Advances, Marco Pangallo, Dr Torsten Heinrich and Professor Doyne Farmer investigate this in the simple framework of normal form games and reveal that when the game gets complicated this assumption is problematic. If these results carry over from games to economics, this raises deep questions regarding economic models and when they're useful to comprehend the real life.
Professor Doyne Farmer, Director of Complexity Economics in the Institute for New Economic Thinking in the Oxford Martin School explains, “This study shows that even just in the quite simple behavioural models of normal form games, complexity and competition change whether players will use a rational strategy and reach equilibrium. We discover that if player incentives aren’t aligned they're unlikely to find equilibrium when the game gets complicated.
“Many situations in economics are complicated and competitive. This enhances the possibility that lots of important theories in economics might be wrong: When the key behavioural assumption of equilibrium is wrong, then your predictions from the model are most likely wrong too.”
To understand what equilibrium could it be helps you to look at a simple example. Children enjoy playing tic-tac-toe (noughts and crosses), but at around eight years of age they learn that there's a technique for the second player have a tendency to results in a draw. This strategy is what is known as an equilibrium in economics. If all the players in the game are rational they will play an equilibrium strategy. In economics, the word rational means the player can evaluate every possible move and explore its consequences for their endpoint and select the very best move. Once children are old enough to discover the equilibrium of tic-tac-toe they stop playing because the same task always happens and the game becomes boring.
Chess is a much harder game, hard enough that no one can analyse all of the possibilities, and also the usefulness of the idea of equilibrium stops working. This illustrates that whether rationality is really a sensible model of the behaviour of real people depends on the issue they need to solve. If the issue is simple, it is a good behavioural model, however, if the issue is hard, it might break down.
“One way to view this, for that purpose of understanding how people solve problems in games, is that in tic-tac-toe rationality is a great behavioural model for eight-year-olds although not for six-year-olds which is never a good model in chess. In chess, nobody is smart enough to uncover the equilibrium, so the game never gets boring,” says lead author on the paper, Marco Pangallo. “Intuition would suggest that navigating economic forces is more like chess than tic-tac-toe. Yet, theories in economics nearly universally assume equilibrium from the outset.”
To investigate, Pangallo and collaborators studied when equilibrium is a good assumption in games. Rather than games like tic-tac-toe or chess, they studied all possible games of a particular type (called normal form games) and used two simulated players to play them to see what goes on. The simulated players use strategies that do a great job of describing what real people do in psychology experiments. These strategies are simple rules of thumb, look foward to what has worked well in the past or picking the move that is most likely to beat the opponents’ recent moves.
The study indicated that once the game is straightforward enough, rationality is a good behavioural model: players easily find the equilibrium strategy and listen to it. Once the game is more complicated, whether or not the strategies will converge to equilibrium depends on set up game is competitive. If the incentives of the players are lined up they are prone to find the equilibrium strategy, whether or not the game is complicated. But when the incentives from the players aren't lined up and also the game gets complicated, they are unlikely to find the equilibrium. At these times their strategies keep changing over time, usually chaotically, and they never settle down to the equilibrium. In these instances, equilibrium is really a poor behavioural model.
A key insight in the paper is that cycles in the logical structure from the game influence the convergence to equilibrium. The authors analyse what happens when both players are myopic, and play their best response to the last move of the other player. In some cases, this leads to convergence to equilibrium, in which the two players settle on their best move and play it over and over forever. In other cases, the sequence of moves never settles down and instead follows a best reply cycle, in that the players’ moves keep changing but periodically repeat – like “groundhog day” – again and again. When a game has best reply cycles convergence to equilibrium diminishes likely. By using this result the authors are able to derive quantitative formulas for when the players of the game will converge to equilibrium so when they won’t, and show explicitly that in complicated and competitive games cycles are prevalent and convergence to equilibrium is not likely.
Pangallo concluded, “These findings claim that in complex and competitive systems, new approaches to economic modelling are required that explicitly simulate behaviour and look at the proven fact that real individuals are bad at solving complicated problems.”
