Single Play Games

Single Play Games.

Game 1.The Prisoner’s Dilemma

Preference Ranking: A. 1. (Ad: Bc): 2.(Ac, Bc); 3. (Ad, Bd); 4 (Ac, Bd)

Preference Ranking: B. 1. (Ac: Bd): 2.(Ac, Bc); 3. (Ad, Bd); 4 (Ad, Bc)

Suppose B cooperates. The best strategy is to defect. (Bottom right)

Suppose B defects. The best strategy is to defect. (Bottom left)

One strategy is dominant: Defection or Non-cooperation.

Game 2. The High Risk Bargain

Preference Ranking: A. 1. (Ak: Bk): 2.(Ab, Bk); 3. (Ab, Bb); 4 (Ak, Bb)

Preference Ranking: B. 1. (Ak: Bk): 2.(Ak, Bb); 3. (Ab, Bb); 4 (Ab, Bk)

Suppose B keeps his promise. The best strategy is for A to keep his.

Suppose B breaks his promise. It is slightly better for B to break his than to keep it.

This is a high risk strategy, since in playing for the optimal outcome, both A and B risk getting the worst.

There is no dominant strategy.

Game 3.The Moral High Ground

Preference Ranking: A. 1. (Ak: Bk): 2.(Ak, Bb); 3. (Ab, Bk); 4 (Ab, Bb)

Preference Ranking: B. 1. (Ak: Bk): 2.(Ab, Bk); 3. (Ak, Bb); 4 (Ab, Bb)

This is a very low risk game, since by keeping one’s promise one gets the best outcomes.

Suppose B keeps her promise. The best strategy is for A to keep his.

Suppose B breaks her promise. The best strategy is for A to keep his.

The dominant strategy is to keep one’s promisies

Game 4.Morality first, then Treachery.

Preference Ranking: A. 1. (Ak: Bk): 2.(Ak, Bb); 3. (Ab, Bk); 4 (Ab, Bb)

Preference Ranking: B. 1. (Ak: Bk): 2.(Ab, Bk); 3. (Ak, Bb); 4 (Ab, Bb)

Also a relatively low risk strategy.

Suppose B keeps her promise. The best strategy is for A to keep his.

Suppose B breaks his promise. It is better for A to keep his than to break it.

Here there is no dominant strategy.

So which game represents the everyday situation of Hobbesian inhabitants of the state of nature, assuming that every one of these is of the same psychological type.

Hobbes’ third Law of Nature is:

That men performe their Covenants made, Lev 15.

“The Foole hath sayd in his heart, there is no such thing as Justice; and sometimes also with his tongue; seriously alleaging, that every mans conservation, and contentment, being committed to his own care, there could be no reason, why everyman might not do what he thought conduced thereunto; and therefore also to make or not make; keep or not keep Covenants, was not against Reason, when it conduces to one’s benefit.” Lev 15.

“For the question is not one of promises mutuall, where there is no security of performance on either side; as when there is no Civill Power erected over the parties promising; for such promises are no Covenants; But either where one of the parties has performed already; or where there is a Power to make him performe; there is the question whether it be against reason, that is against the benefit of the other person to performe, or not. And I say it is not against reason.Lev 15.

So according to Hobbes.

1. It is not against reason to keep one’s promises in civil society, where the power of the sovereign can make it in one’s interests to do so. (In game theoretic terms the Sovereign can do this by penalising defection or promise breaking.)
2. It is not against reason to keep one’s promises in the state of nature where one person has already performed their side of the bargain.

Why is this? The answer is that building trust is instrumentally necessary for the formation of confederacies which can bring about mutual advantages.

“In a condition of Warre, wherein every man to every man for want of a common Power to keep them all in awe, is an Enemy, there is no man can hope by his own strength, or wit, to defend himselfe from destruction, without the help of Confederates; where every one expects the same defence by the Confederation, that any one else does; and therefore he which declares he thinks it reason to deceive those that help him, can in reason expect no other menas of safety, than what can be had from his own single Power.” Lev 15.

All this seems to rule out decisively that the state of nature gives rise to Prisoner’s dilemma situations.

Maybe this is too quick.

The inhabitant of the state of nature might make expected utility calculations, in order to determine what to do.

EU calculations show that:

1. If the probability that alter will defect is high, then B should other things being also defect.

On the one hand If the harm, suffered by A if she cooperates and B defects is high enough, (as in Game 2. The High risk Bargain) then A should defect even if the probability of B defecting is low.

On the other hand, if the harm suffered by A if B defects is relatively low, (as in Games 3. and 4.), it might still be rational for A to cooperate.

Is the state of nature therefore a pretty nice place where contracts are nearly always completed and promises kept. In which case the state of Warre is not something that is to be greatly feared.

In which case what is the motivation and justification for Covenanting with each other to erect a Sovereign and to enter into civil society? Hobbes’ rather drastic cure, will be worse than the disease.