China's zombie companies are playing chicken

Earlier this month, Andrew Batson wrote an interesting blog article about China's zombie companies:

One of the more interesting developments in official Chinese discussions about the economy has been the appearance of the term “zombie companies”... money-losing companies that seem to stay alive far longer than economic fundamentals warrant. This problem is particularly acute in the commodity sectors: a global supply glut has driven down prices of iron ore and coal to multi-year lows, levels where China’s relatively low-quality and high-cost mines have difficulty being competitive. And yet they continue operating despite losing money, because it is easier to keep producing than to completely shut down.

In ECON100 we no longer cover cost curves in detail, so we also don't talk about the section of the firm's marginal cost curve where it makes losses but prefers to continue trading because the losses from trading are smaller than the losses from shutting down. However, this is exactly the situation for China's zombie firms. As Batson notes:

An excellent story this week in the China Economic Times on the woes of the coal heartland of Shanxi quoted one executive saying, “If we produce a ton of coal, we lose a hundred yuan. If we don’t produce, we lose even more.”

Another aspect of the reluctance of China's zombie companies to shut down is strategic, and in this case it may be that the zombie companies continue to operate even if their losses would be smaller by shutting down. What the zombie companies are doing is playing a form of the 'chicken game'. In the classic version of the game of chicken, the two players are driving cars and line up at each end of the street. They accelerate towards each other, and if one of the drivers swerves out of the way, the other wins. If they both swerve, neither wins, and if neither of them swerve then both die horribly in a fiery car accident.

Now consider the game for zombie companies, as expressed in the payoff table below (assuming for simplicity that there are only two zombie firms, A and B). If either firm shuts down, they incur a small loss (including if both firms shut down). However, if either firm continues operating while the other firm shuts down, the remaining firm is able to survive and return to profitability. Finally, if both firms continue operating, both incur a big loss.

Where are the Nash equilibriums in this game? To identify them, we can use the 'best response' method. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium).

For our game outlined above:

1. If Zombie Company A continues operating, Zombie Company B's best response is to shut down (since a small loss is better than a big loss) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Zombie Company A shuts down, Zombie Company B's best response is to continue operating (since survival and profits is better than a small loss);
3. If Zombie Company B continues operating, Zombie Company A's best response is to shut down (since a small loss is better than a big loss); and
4. If Zombie Company B shuts down, Zombie Company A's best response is to continue operating (since survival and profits is better than a small loss).

Note that there are two Nash equilibriums, where one of the companies shuts down, and the other continues operating. However, both firms want to be the firm that continues operating. This is a type of coordination game, and it is likely that both firms will try to continue operating, in the hopes of being the only one left (but leading both to incur big losses in the meantime!).

What's the solution? To avoid the social costs of the zombie companies continuing to operate and generating large losses, the government probably needs to intervene. Or, as noted at the bottom of the Batson blog article, mergers of these firms will remove (or mitigate) the strategic element, which is the real problem in this case.