A brilliant idea!

Is Game Theory a new definition of Love?

(και λέω Love γιατί στα αγγλικά δεν διαχωρίζεται ο Έρωτας –που έχει ως γνωστόν 98 οκτάνια-, από την Αγάπη που είναι, ας πούμε, η απλή αμόλυβδη -φθηνότερη και δε σε κάνει turbo).

Λοιπόν διαβάστε για να μάθετε πέντε πράγματα και να εντυπωσιάζετε στα dates -και στο κομμωτήριο.

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.

In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. The practical and general implication is that when players also act in the interests of the group, then they are better off than if they acted in their individual interests alone.

Μετάφραση σε απλά ερωτικά: «Α zero sum game», θα πει όταν π.χ. έχεις περάσει ένα ολόκληρο Σαββατοκύριακο να τσακώνεσαι με τον άλλον, να μην έχει υπερισχύσει η γνώμη κανενός από τους δύο και στο τέλος να ΜΗΝ έχεις κάνει make-up sex. Αν κάνεις make-up sex την Κυριακή το βράδυ, χαλάει το Nash equilibrium που διαβάζουμε στην δεύτερη παράγραφο. Τώρα, αν υπάρχει τρίτο πρόσωπο, («the interests of the group» όπως λέει), έχουμε Nash equilibrium, αλλά με απαραίτητη και ικανή συνθήκη, να έχεις κάνει sneak out το απόγευμα της Κυριακής –πως πας σε μια θεία σου- και να κάνεις σεξ ΚΑΙ με το τρίτο πρόσωπο. (Αλλά να του αρέσει και αυτού, του τρίτου δηλαδή –αλλιώς χαλάς το equilibrium –και καλύτερα να μην το μάθει ο Nash, ούτε ο νόμιμος partner). Πάμε παρακάτω.

Pareto efficiency.
In a Pareto efficient economic system no allocation of given goods can be made without making at least one individual worse off. Given an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement. An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made.
Λοιπόν το θέμα Pareto efficiency έχει πιο πολύ να κάνει με τα ψώνια, και λιγότερο με τον έρωτα per se. Δηλαδή, τι λέει ο Pareto?
Αν είναι να κάνετε ακριβά και αβάσιμα, για τη χρονική στιγμή, ψώνια, καλύτερα να πετάξετε τις αποδείξεις και να τα χώσετε στην ντουλάπα σας ενώσω το άλλο άτομο κοιμάται. «It makes one individual better off, without making any other individual worse off». Εκτός βέβαια αν του έχετε πάρει την πιστωτική κάρτα –οπότε δεν υπάρχει Pareto efficiency –ειδικά όταν έρθει ο λογαριασμός. Αν προλάβετε και τον σκίσετε πριν τον δει, τότε έχουμε «Pareto optimal». Απλά μαθηματικά. 

Και η επιτομή όλων: The prisoner’s dilemma

The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992). A classic example of the prisoner's dilemma (PD) is presented as follows:

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal—if one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?

If it is supposed here that each player is only concerned with lessening his time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. In the game, the sole worry of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the logical decision leads each to betray the other, even though their individual ‘prize’ would be greater if they cooperated.

In the regular version of this game, collaboration is dominated by betrayal, and as a result, the only possible outcome of the game is for both prisoners to betray the other. Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other. Because betrayal is always more beneficial than cooperation, all objective prisoners would seemingly betray the other.

Εδώ κανονικά, δεν έχω να προσθέσω τίποτα. Είναι η απόλυτη αλληγορία του Γάμου!

Δηλαδή και οι δύο σώζονται, αν αποφασίσουν να σώσει ο ένας τον άλλον. Όμως, όπως λέει και ο Sartre : «L’ enfer c’ est les autres» (η Κόλαση είναι οι άλλοι), και κανείς δεν σώζει κανέναν και να κοιτάτε την πάρτη σας, πράγμα γνωστό τόσο στη ζωή, όσο και στο κομμωτήριο.