A Game Theorist's View of How Billionaires Might React to Twitter's Anti-Musk Poison Pill

The Twitter Preferred Stock Rights Agreement of April 15, 2022 is a poison pill meant to stop Elon Musk from acquiring the company. It says that if any Person or Group of persons acquires over 15% of the shares of Twitter stock, the *other* shareholders each get a huge payout from the company. Delaware courts long ago said that such poison pills were legal, despite how they discriminate against a minority shareholder.

But imagine the following story. Elon Musk has bought 14% of Twitter shares. Under current management, his purchase will be unprofitable, but if he gets to fire the management, it will be profitable. Three other people, Andreessen, Buffett, and Carlos, can afford to buy 14% each, but will only do so if it is profitable. If there were no poison pill, Musk could buy 60% himself, or Musk, Andreessen, Buffett, and Carlos could agree to buy 60% jointly (let's ignore what *would* happen as a result of competition among them). But the poison pill makes this unprofitable.

So suppose instead that Andreessen says publicly:

"If I thought Buffett and Carlos would buy 14% each, I would buy 14% too, and then we'd all want to vote with Musk to fire the current management. I am not making any sort of promise by saying this. I am not committing myself legally or morally. I am just saying this is what it would be in my best interest to do in that situation."

And suppose Buffett issues a similar statement, and then Carlos does. After these statements, which are "cheap talk", not contracts. and not agreements to act. but rather statements of personal self-interest, Andreessen would be willing to buy 14%, knowing that Buffett will then buy 14% because Buffett will know that Carlos will then buy 14%.

It is crucial, for the law, that these statements are non-binding; they do not commit anyone to anything. In the terminology of game theory, they are like Warnings as opposed to Threats, or Predictions as opposed to Promises. They are perhaps even less meaningful, since we are not assuming that there is any punishment for lying (I will not get into the game-theory/Wittgenstein problems of whether "I am hot" might mean "I am cold" in equilibrium, or whether the small cost of the effort to make a statement matters as in “forward induction”).

Would the statements even be necessary? Not if there is perfect information. This is like a ranked coordination game, but it is stretched out over time. Each of the three players would like to buy 14% if he thinks the other two will buy 14%. Each of them would prefer NOT to buy if the other two will not buy. Thus, there are two Nash equilibria in the simultaneous-move game--- All Buy, and None Buy--- even though all three players prefer All Buy. In the sequential game, though, suppose that each had the expectation that the other two would Not Buy. Andreessen, moving first, could choose BUY and change the expectation of the other two. They would say, "I thought it was impossible that Andreessen would buy, so I have to take that as a fact even if he did it by mistake or something." Then Buffett could also choose BUY, and Carlos would think to himself,"I didn't think Andreessen or Buffett would buy, but they did, so now I am safe in buying 14% myself." Foreseeing this, Andreessen and Buffett would buy.

If there were imperfect information, though, the statements would be helpful, at least if there is even a very small cost in making them. Suppose Andreessen, Buffett, and Carlos did not know that each other were able to come up with the cash to buy 14%. In that case, it would be risky for Andreessen to buy first, because Buffett and Carlos might not be able to follow. If Buffett and Carlos makes statements that they have the cash, though, Andreessen is safe to take the lead. (Note that it is only necessary for two of the three to make statements; the third can then act as leader safely.)

Is there some reason from corporate law why this would not work? One thing I have omitted is what exactly happens when the people who want to fire the current management get 51% of the shares. Twitter has a staggered board, I have heard, so it would take some years to vote in a majority on the board of directors. It probably has similar institutions to thwart shareholder majorities from controlling the company. I don't know the corporate and securities law of how a majority of shareholders would go about taking the company private or selling it to another corporation or revising the charter without electing a majority of directors first.