The commenters who referred you to the prisoner's dilemma are exactly correct, but I wanted to give a more detailed explanation because I find game theory quite interesting.
The Dilemma
The prisoner's dilemma is a classic scenario in game theory where even though it's in the best interests of two or more players to cooperate, they fail to do so. Wikipedia has a simple example using prisoners, but I'll use a simple example using Fidel and Charles, who are fund managers at Fidelity and Charles Schwab, respectively.
To make the table shorter, I abbreviated a bit: INC = increase fees, KEEP=keep fees the same, DEC=decrease fees. Here is the dilemma itself, in the table that shows the resulting market shares if each fund manager follows the course of action in question.
| Charles INC (cooperates) | Charles DEC (betrays)
-----------------------------------------------------------------------------------
Fidel INC (cooperates) | Fidel (50%) / Charles (50%) | Fidel (25%) / Charles (75%)
Fidel DEC (betrays) | Fidel (75%) / Charles (25%) | Fidel (50%) / Charles (50%)
While this example isn't mathematically rigorous because I completely fabricated the numbers, it makes a good example. The most profitable course of action would be both fund managers agreeing to increase their fees, which would keep their market shares the same but increase their profits as they earn more fees. However, this won't happen for several reasons.
- Regulators in most industries normally frown on such collusion agreements because they're not competitive, and in the case of investment funds, regulators can normally enforce anti-collusion measures. In other industries such enforcement isn't as easy.
- Since regulatory pressure might prevent the use of a formal contract, why not a gentleman's agreement? As the table shows, Fidel could choose to decrease his fees while Charles maintains the agreement. Fidel reaps greater profits in the short run when his market share increases, until eventually (hopefully soon, if Charles is wise), Charles decreases his fees to match those of Fidel's fund, thus returning the market to an equilibrium.
Assumptions
Because economies of scale exist in the market for investment funds, it's reasonable to assume in a simple example that as funds grow larger, their costs decrease, so even though a fund manager decreases his fees (betraying the other players), this decrease won't be enough to reduce their profits. In fact, the increased market share resulting from such a decrease may well dominate the decreased fees and lead to higher profits.
The prisoner's dilemma is highly applicable to markets such as these because they exist as oligopolies, i.e. markets where a relatively small number of established sellers possess considerable market power.
Complications
If you actually wanted to model the market for donor-advised funds using game theory, you need to take a few more things into account.
Obviously there are more than two firms. It's probably a valid assumption that the market is an oligopoly with significant economies of scale, but I haven't researched this extensively.
There is more than one time period, so some form of the iterated prisoner's dilemma is needed.
The market for donor-advised funds is also complicated by the fact that these are philanthropic funds. This may introduce tax implications or the problem of goodwill and institutional opinion of these funds. Although both funds increasing their fees may increase their profits in theory, institutional investors may look on this as a pure profit-seeking and take their funds elsewhere. For example, they may choose to invest in smaller funds with higher fees but better reputations. While reputation is important for any company, it might make more of a difference when the fund/investment vehicle is philanthropic in nature.
I am by no means an expert on game theory, so I'm sure there are other nuances to the situation that I'm unaware of.
