w133 - Are You A Prisoner of Your Trust?




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PAPER ABSTRACT:

 

We will define a game.

 

2 players (P1 and P2), each with one move called [C] and [D]

 

Payoff is 100 > 50 > 25 > 0.

 

Objective is to maximize your payoff.

 

 

 

If C and C, then both players earn 50. Game ends in a draw.

 

If D and D, then both players earn 25. Game ends in a draw.

 

If P1[C] and P2[D], then P1 = 0 and P2 = 100. P2 wins.

 

If P1[D] and P2[C], then P1 = 100 and P2 = 0. P1 wins.

 

 

Strict rationality says that you should always play D

 

If you play D, then you will win either 100 or 25

If you play C, then you will win either 50 or 0

 

Because each player sees the same playoff, each play D, and earn 25.

Game ends in a draw.

 

But had each player played C, they could have earned 50 each

 

Even had the players agreed ahead of time to play C-C, there is no enforcement mechanism for a play of C-C so each player plays D

 

This problem is known as the Prisoner’s Dilemma.

 

Please see   Prisoner's dilemma at Wikipedia  for full details

 

END OF ABSTRACT

 

 

 

 

This problem is very interesting because a line of perfectly correct logic ends in a result that is not logical where logical means to maximize your return.

 

Strict logic dictates that each player play D, but that play is not a maximum return and as a consequence the logic which dictates a game of D-D is deficient and illogical because the maximum return is lost. A game of C-C dominates a game of D-D, yet there is no way for the players to adopt that strategy.

 

The analysis of this problem breaks quite sharply between a single play game and an iterative series of games. This has fostered a whole industry of analysis and experimentation. I would recommend a study in depth of this problem, but this paper does not concern itself with iterative games. Or does it?

 

We here are strictly looking at a single game between players which will never be repeated and the players will never meet again.

 

Player 2 (P2) sees the following game structure with regards to plays and outcomes:

 

 

If P1 plays C, then you (P2) can earn either 50 or 100. A 100 is better than 50, so P2 chooses to play D.

If P1 plays D, then you (P2) can earn either 0 or 25. A 25 is better than 0, so P2 chooses to play D.

 

 

Player 1 (P1) sees exactly the same situation. Both players are isomorphic to each other, that is, they are plug replaceable, they see the same situation from their POVs, (Point of View).

 

 

 

If P2 plays C, then you (P1) can earn either 50 or 100. A 100 is better than 50, so P1 chooses to play D.

If P2 plays D, then you (P1) can earn either 0 or 25. A 25 is better than 0, so P1 chooses to play D.

 

 

Even should both players have the ability to meet before the game and agree to both choose C, there is no enforcement against cheating or breaking your word so neither player can trust the other, and  both play D.

In real world situations, even with a signed contract, there is still the breaking of that contract which has kept lawyers and judges in business since the dawn of time,

 

The situation is stark and very human.

 

From each player’s POV, the logic of the game requires that they play D to maximize their return, and yet a game of D-D is not optimum, and not rational because C-C has a better return.

 

The stark situation requires a third POV which is yours, the reader of this paper and not a player. You clearly see that C-C is the best overall return because you are looking at both sides of the game. Each player can see what you are seeing, but they are trapped as players because they cannot trust the other player to do the right thing and play C-C.

 

This is also a very human thing.

 

Why do you perform a kindness to a complete stranger who you will never see again?  Why do you participate in a system of etiquette or manners which require you to pay a cost, however slight, for the stranger who will not ever repay that cost? This is pertinent to the parable of the Good Samaritan who pays a considerable cost in helping the other person.

 

Human beings actually do Play C to help the other person even when they know full well that it will cost them to do so because the other person will play D. In those sorts of situations, such a person is actually giving  to the other person with no expectation of any return.

 

This sort of attitude is used by scammers who telemarket knowing that the person on the line will usually be too polite to simply hang up. It’s used by aggressive individuals who know that the other person will be too polite to reject or say no. There are no end to angles that individuals use to force another human being to give them something simply because the scamee is following a level of social trust in a stranger.

 

 

So why do we do it?

 

Usually it is like the Good Samaritan, what we give is a free gift, and we do no look for a return. We are basically giving alms to the poor.

 

If the cost of a C-D play is sustainable for the giver (The Good Samaritan), then that individual usually does not even consider any of this.

 

In the game as it is laid out above, the rewards are just numbers with no context. There is no way to understand sustainability within the game. So if these are just numbers like Monopoly money, you might play C-D always and not care about winning the game. The objective is to win the game and you do that by playing D-D.  C-C and D-D are actually a draw because the reward is equal so there can be no winner with the rules above, but the overall outcome is greater for C-C at a total of 100 than D-D at a total of 50. One of the players would have to decide to lose the game and allow the other player to win the game. Alms to the poor, a free gift from you to a complete stranger. Or you might allow a complete stranger to win a game simply out of polite courtesy to a stranger, but once again, a free gift.

 

And most human beings have a limit to free gifts, “Give everything to the poor and come follow me.” may sound nice on the preacher’s tongue, but even he does not follow that command as it is literally written in the holy book. Hypocrisy or human failings?

 

 

One explanation that might be true, is that we see all human interaction, as a potential relationship, and a free gift is something of an invitation to relate, something like Buber’s I-Thou, because you never know when a “stranger in a strange land” might turn out to become a friend and an ally.

 

No prediction  for the future is perfect, and one never knows for sure, what will happen.

 

Or perhaps the person you help, helps someone else, who happens to be a business partner, who is encouraged by kindness to be considerate of you, and so the free gift to a stranger earned interest and returned to you in exponential quantity paying many dividends.

 

Everything which is imaginary and real is strangely interconnected.

 

So according to a higher logic, perhaps the so-called losing strategy of C-D in a non-iterative Prisoner’s Dilemma does end up being an overall winning one at the last analysis with the realization that everything is iterative eventually, and that the problem as stated above is impossible as mathematical formalism.

 

 

The chains that bind you are many. Are you a prisoner of your trust?

 

 

 

 

 

 

 

 

 







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