in game theory terms, I think you're arguing that the founder's assume all parties will act only in their self interests, and if they disclose their financial difficulties, the result will be "Option A", as a result, they choose to go the "Option B" route, where the founder gets off "free" and the employees get screwed.
However, I would argue that "Option C" is possible too, where all parties work together to try to save the ship. I've heard stories of employee's willingly reducing their salaries to extend runway. I personally am in a financial situation to do such a thing and would have. For other reasons, I also could have helped out in a meaningful way with fundraising but wasn't even aware that such a thing was needed until the day I was fired.
Again, this might be naive, but I do think it's possible in situations where there is mutual trust and respect amongst employees. I wouldn't be surprised if there are many stories out there where founders and employees all make sacrifices to extend runway.
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Option A: If A and B each betray the other, each of them serves 2 years in prison
Option B: If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
Option C: If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
Consider the payoff matrix for the employee:
Employee finds a new job, old employer fails: +5
Employee finds a new job, old employer succeeds: +5
Employee stays, old employer fails: +0
Employee stays, old employer succeeds: +6 (+10?, +20?)
I wouldn't say finding a new job is equivalent to "defecting".
A better analogy is if the employer really put together an awesome team, and he hopes to work with them again in the future. In that case, honesty is better. But that's iterated game theory rather than a single game.
If you play Prisoner's Dilemma once with a complete stranger, you could argue that the Nash equilibrium is to defect. When you play with the same people over and over again, then defectors can be punished.
Unfortunately, the modern economy is more like a group of strangers playing with each other for one game. If you defect, you can always find someone else gullible to play with next time.
2. I think you focused on the employee payoff matrix to argue that they'll always pick to defect. but I would argue that humans have "emotions" and sometimes even loyalty. like i said, I personally would have stayed the course and sacrificed some of my "payoff matrix" but never got the chance.
disclaimer: i may have again butchered the theory of prisoner's dilemma, but i think you get my point so hopefully we can avoid arguing the technicalities of prisoner's dilemma.
Lastly, I would argue that in startups, this is a game you do want to play over and over. if you're only hiring expendable, replaceable employees, then you're probably playing the wrong game, with the disclaimer that I definitely don't have all the answers and reserve the right to be wrong.
If you admit that you only have 2 months of runway left, your employees will start shopping around. You'll lose your best employees first.
If you keep it a secret, two things can happen:
1. You raise more money, problem solved! (or market conditions change)
2. In 2 months, you lay off everyone. Sucks to be them, but you got 2 more months to try and raise money.
In a nearly insolvent business, dishonesty is a better strategy, because that maximizes the value of the implied call option if you do turn things around.
There's usually no social penalty for being dishonest. You can always find new employees.