A game-theory take on ponzi schemes

Game theory is a branch of mathematics that studies strategic interactions among rational agents.

Let’s compare two very different casino games: roulette and poker.

Roulette vs. Poker

In roulette, the outcome of any given bet is entirely a matter of probability. The outcome of a specific bet (e.g. black or evens) is not knowable, but two players that each make the same bet a thousand times are likely to wind up in very much the same place.

Game theory doesn’t really apply to roulette, because (with apologies to wishful thinkers) there is no betting strategy that will produce a long-term win at the roulette table. Eventually, the house always wins, and players can make their own decisions without considering the decisions of other players.

Poker is categorically different. While the distribution of cards in a given hand is just as random as the fall of a roulette ball, each player then makes critical decisions after the cards are dealt. Of course a competent poker player takes probability into account… but a winning poker player also accounts for the state of mind of the other players at the table.

Poker strategy is recursive: my decisions depend on what I believe you believe I believe about the cards the cards in your hand, and so on. It also has a memory: if you display a pattern in your betting, I might profitably take it into account… unless your pattern is a deliberate attempt to influence my decisions!

The Prisoner’s Dilemma

The Prisoner’s Dilemma is a classic example of game theory in action.

Gang members Andy and Bob are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain.

Here are the choices available to Andy and Bob, along with their consequences:

Andy’s Choice	Bob’s Choice	Andy’s Outcome	Bob’s Outcome
silence	silence	1 year	1 year
silence	betrayal	3 years	freedom
betrayal	silence	freedom	3 years
betrayal	betrayal	2 years	2 years

Assume there will be no further consequences beyond prison time, and no more opportunities to make a deal. In a prisoner’s shoes, which would you choose?

If Andy is confident Bob will remain silent, Andy’s best option is to betray him. If Bob expects Andy to betray him, Bob’s best option is betray Andy as well. But if both remain silent, then neither will suffer the worst outcome.

In practice, there is no certainty about another person’s state of mind. And if Andy and Bob are arrested again, another factor comes into play: memory.

Iteration Strategies

Say Andy betrays Bob the first time around, while Bob remains silent. Shortly after Bob is released from prison, both are arrested again and offered the same deal.

Will Bob retaliate against Andy’s betrayal by betraying Andy in turn? If so, Bob’s silence is not an option, and Andy should betray Bob again and accept a two-year sentence instead of three. Freedom for Andy is no longer on the table.

But if Bob and Andy both remain silent—in other words, both decide to play nice—they can both get off with a single year.

There’s a great deal of depth here. Add more prisoners, more options, and more iterations, and the outcomes quickly get bewilderingly complex, and apparently random…

But not actually random! Remember, there are no dice here, no roulette wheels, no shuffled cards. Just the complexity generated by a recursive theory of mind.

The ponziFarm Connection

A quick reminder of how ponziFarm operates (click here for a deeper dive):

• Players deposit money into the game for a fixed lockup period.

• Every deposit increases the game balance, extending the life of the game in the short term.

• Every deposit also creates an obligation that depletes the game balance in the future.

• When the game balance drops to zero, the game ends and all outstanding deposits are lost.

If many players make short-term deposits with low returns, then the game balance will rise slowly and be depleted slowly. An aggressive player can take advantage of this to make a large, long-term, very profitable deposit… and confidently expect it to mature before the game ends. The resulting withdrawal at maturity will leave many short-term depositors high and dry.

But if many other players seize this opportunity to make slightly shorter-term, slightly less profitable deposits, then the most aggressive player’s strategy will fail and the game will crash before he can execute his withdrawal.

If a few players make long-term deposits with high returns, then the game balance will rise quickly and remain stable for a long time before suddenly crashing. A cautious player can take advantage of this to make short-term, low-profit deposits, confidently expecting to collect his profits before the game ends. Enough of these will offset the large depositors’ contributions, leaving many of them high and dry before their deposits expire.

But if other players seize this opportunity to make slightly less conservative, slightly more profitable deposits, then these players will profit at the expense of many of the more conservative players!

There is no question that EVERY ponziFarm game has a winning strategy. But the specifics of every winning strategy are completely dependent on what every other player thinks is the winning strategy!

The net result of all this recursion looks a great deal like a classic random walk… except that none of it is random. It is merely so complex that it is impossible for humans to tell the difference.

An actual ponziFarm game in progress.

So as games go, ponziFarm is a great deal more like the Prisoner’s Dilemma—and more like poker—than it resembles a game of pure chance like roulette.

There is no source of randomness in ponziFarm. Instead, there is complexity, generated by the collective and recursive estimation, on the part of every player, of the state of mind of every other player in the game.

Winning at ponziFarm

Winning at ponziFarm is mechanically simple but operationally complex.

Mechanically: make deposits that mature before the game crashes. But how?

Operationally, the best way to know another player’s state of mind is to influence it. Game theory offers two strategies:

• Collaborate with other players! Create a pattern of deposits that generates enough confidence in new depositors to extend the game long enough for your deposits to mature.

• Betray your collaborators! Make deposits that are slightly more aggressive than theirs—or less, depending on your strategy—so you can cash out at their expense.

Sound horrible? Maybe. But those are the only active strategies on the table.

If the Prisoner’s Dilemma and other recursive games teach us anything, it is this: strategy is amoral.

A poker player who never bluffs will not be a poker player for long. And while playing nice is absolutely a valid ponziFarm strategy, it is by no means the only one.

Now get out there and win!

from Hacker News https://ift.tt/xRbhYEL