A Game Theoretic View of Our Savings Glut December 20, 2011
Posted by Sina in : Main , trackbackI try to convince my economist (and non-economist) friends all the time that the world’s current deep economic slump is a simple demand problem. We just don’t have enough demand. Or in other words, we just have way too much saving. You can talk about debt, you can talk about structural changes, you can talk about demographics, you can talk about all these things, and they may be valid, but these are all things that market economies can deal with as long as the macro picture is stable. What we desperately need right now is more spending and less saving.
I know, it sounds paradoxical, but it’s true. Trust me.
But the question is, why then don’t we just spend more and make all our problems go away? Good question. Let’s play a quick and dirty game that demonstrates why we’re stuck where we are.
Suppose we have three equal-size players: Government (G), People (P), and Business (B). And each of these players has the option of two strategies: More Spending (↑) or Less Spending (↓).
Now the payoffs for these strategies work as follows:
If a player decides to spend, the cost of that spending to the player is exactly 1.
The total payoff of that spending will depend on how many other players decide to spend as well (because of economic multipliers), and the resulting total payoff is then equally distributed among all players no matter which players do the spending.
If 1 player spends, the payoff is a total of 3, and therefore amounts to 1 for each player.
If 2 players spend, the payoff is a total of 9, and amounts to 3 for each player.
If all 3 players spend, the payoff is a total of 18, and amounts to 6 for each player.
Taking those payoffs and subtracting costs, we can construct a payoff matrix with every possible scenario. With three players, the payoff matrix is three dimensional. Here it is as two 2D matrices:
You can work through this and find that the game has two Nash equilibria:
(1) everyone spends more at (↑,↑,↑) and payoffs are (5,5,5).
(2) everyone spends less at (↓,↓,↓) and payoffs are (0,0,0).
The scenario at (↑,↑,↑) is also the optimal outcome for all players, equilibrium or not, so that’s the scenario we ideally want.
The world is today stuck at (↓,↓,↓). No one is spending even though we would all be better off if we did. There is just no incentive for any player to unilaterally change their strategy.
And so there you go, that’s why we’re stuck where we are.
Okay fine, this is a very simplified game that doesn’t reflect all the contraints that people, businesses and governments face in the real world. Debt, for example, doesn’t play a part in the game at all. But I do think this game is still very insightful, especially if you keep in mind that all we want to do is to get more spending.
And what’s particularly interesting about this game is the flow of scenarios. I’ve drawn in red arrows in the payoff matrix to demonstrate how each player would adjust their strategy under each scenario. If you follow the arrow directions you will see that, except for the equilibrium at (↓,↓,↓) where no one spends, all other scenarios will flow or gravitate to the (↑,↑,↑) equilibrium. So given that the world is right now at (↓,↓,↓), this tells us that all we need is for only one player to unilaterally move to More Spending, and all other players will eventually move to More Spending as well in response. That’s the insight of this game: we just need someone to start spending and we’ll all be better off.
Then why aren’t they spending?! Why aren’t People (P) or Business (B) or Government (G) unilaterally initiating the spending to get things rolling? They should know that it will eventually make them better off, afterall, once the other players increase their spending as well. You are a smart reader for pointing this out.
Well first of all, do the players actually know this dynamic? People probably don’t. Businesses might. Governments should. But even more importantly, in the real world, who is actually able to spend more unilaterally? You have to look at the political economy of it.
Consider People (P). People are scattered. They can’t get together in a room and unilaterally decide as a group to spend more. They can only respond individually, and so they will sit tight and do nothing until their individual incentives change. The same is true for Business (B).
But Government (G) can! Disregarding the fact that there are many governments, the government can sit down in a boardroom by itself and unilaterally decide to spend more — now I would advocate more infrastructure spending if I was in that boardroom, but what the money is spent on is besides the point. This unilateral government spending would actually make everyone better off (including the government itself!), as both people and businesses respond by spending more as well. The government just needs the will to do it.
So then why aren’t governments spending more?! I have no idea.
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