In my class blog (to which we do not allow public access for reasons of student privacy), we have been discussing Iman Anabtawi's paper on shareholder power, which Iman will be presented in the seminar today. One of my students made an interesting observation, which prompted a discussion as to what is the appropriate game theory game for modeling shareholder interactions. Is it the Prisoner's Dilemma, as my student argues, or something else?
Student Post:
Anabtawi notes that shareholders could engage in collective action for disciplining managers, an assumption crucial to shareholder primacists, but such coordination is impractical given the wide fragmentation of ownership. At the individual level, a rational shareholder would internalize the costs of disciplining management only if its proportionate share is more than its expected costs. At the collective level, it would be desirable for a shareholder to discipline managers if the expected collective benefits exceed their expected costs. The result is that there is no collective action, given that the substantial discipline costs outweigh the expected benefits. As Anabtawi notes, increasing shareholder power in this context is unlikely to generate more shareholder action, given the substantial costs and modest expected benefits. This result is similar to the Tragedy of the Commons, a phrase used to describe a situation where the exercise of individual interests leads to the deterioration of the common good, given that individuals do not have strong incentives to collectively invest or work towards a particular common interest. Here, shareholders’ expected benefits, either individual or collective, do not exceed the expected costs of disciplining management, so individual shareholders would rather pursue other interests other than this “common good”. As Anabtawi notes, increasing shareholder power may actually lead shareowners to underdiscipline management when promoting their private interests at the expense of the general shareholder interests.
Anabtawi’s account of shareholders’ divergent interests is parallel to the classic example of the Prisoner’s Dilemma in game theory, where two separate prisoners must decide separately whether to confess to a crime: if a prisoner confesses, she will get a lighter sentence and her accomplice will get a heavier one, but if neither confesses, sentences will be lighter than if both confess. In the absence of shareholder collusion for a common interest i.e. collective action to discipline management, shareholders instead will compete amongst each other in an attempt to further their own private interests e.g. short-term vs. long-term interests. Such competition will lead to a decrease in overall shareholder value, given that some private interests conflict with the interests of shareholders in general. In other words, even though shareowners are better off collectively by cooperating with each other, their self-interest will deal them to compete with each other, disregarding the negative effects that such competition may have on other shareholders.
To which I responded:
The difficulty I have with using the Prisoner's dilemma to model the shareholder situation is the number of players involved. In a classic prisoner's dilemma, the dilemma arises where the game is played a single time. Where the game is played in multiple iterations, however, a tit-for-tat strategy has been shown to induce the players to reach the collective best outcome. Although the shareholder-shareholder interaction is a repeate game with no finite terminus, which should be ideal for tit-for-tat strategies, the number of players involved would seem to preclude that solution.
To which the student responded:
In regards to your comment, professor, at first I hesitated in using the prisoner's dilemma as an example of shareholder vs. shareholder interactions. It's true that this dilemma is typically used for 2 players where the game is only played once. But I think that if we assume that a large shareowner of a major corporation represents player A, and the remaining shareholders are minor and fragmented in a way that altogether can be categorized as player B, and the game is repeated infinitely, then we may end up with Nash equilibrium where player A would pursue its own self-interests given what player B does, and vice versa. Player A’s actions would likely be designed to benefit its own private interests, while Player B’s actions may be designed to benefit shareholders overall. Or Player A may just engage in a dominant strategy where it will pursue its own interests, no matter what Player B does over time. Of course, the collusion of small shareholders as Player B is an assumption that Anabtawi’s article challenges, thereby suggesting that Player A would eventually win if more shareholder power is granted. This may be a stretch of game theory as applied to shareholder primacy, but it doesn’t hurt to try (I hope).
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