Commitment - Restrictions for Improved Reward

Wow. What an oxymoron. We had briefly heard about this in game theory in Economics way back in Q1 and now it's coming up again in Q3 in finance.

First in game theory and dominant strategies. Look at the following example of the prisoner's dilemma:

So in the typical fashion, the dominant strategies for both players show that they will end up in the lower right corner with a return of 3 each. This is unfortunate, as there is a potential to get 5 each if they could only credibly commit to Strategy A each. But because of the conditions of the prisoner's dilemma, it's impossible.

To change the parameters of the game, what if it was possible for Player 1 and 2 to commit to impairing their own return matrix? For instance, what if Players 1 and 2 could reduce their returns in the cells AB and BA to 4 instead of 7 (as shown below)? Suddenly, the dominant strategy changes and the end game to a return of 5 each rather than 3.
We achieve a counter intuitive result. By placing restrictions on their own returns, both players can achieve a higher return.

In our finance class today, we talked about a different scenario with similar characteristics. First, an overly simplified example. Because equity holders are only liable for capital at risk (what money they put in), with the effects of leverage, they can increase their upside with a bottom of bankruptcy. This will encourage them to take on projects even if they have a stand-alone negative NPV (but a positive NPV with regards to the equity holder's return and relationship in bankruptcy - equity holders don't lose more money then they put in).

However, the debt holders will require a larger return on their debt to compensate them (make them whole) and offset the risk. This in turn can make projects unattractive and become prohibitive.
However, shareholders can introduce debt covenants in order to restrict the their own flexibility (preventing them from taking on too much risk and inflating their upside) to secure financing and ensure debt holders that they won't have to bear the dead weight loss of projects which fail.
Again, a counter intuitive result: You can do better by restricting your choices.