In game theory, separating
equilibrium is a scenario wherein each player is forced to reveal his or her
private information. In normal circumstances agents send out different signals
for different contexts. The recipient would be served best if he or she are
able to decode the true self of the messenger and the mess. Often, the hiding
of private information and preferences by the agents is to enable them to
counter posit the strategy of the rivals. Ideally, any strategy must be aimed
to garner the private information and preferences of the agent. Implied is the
true self of the agent must be revealed. For example to an insurance company
the firm must be in a position to get the exact status of health information of
the person doing the policy. The agent knowing a great deal of their health would
obviously have incentives in hiding the information from the insurance company.
For the firm, the ideal scenario is wherein, the agent has to reveal his or her
true health status. The equilibrium arise out of self-selection.
Substantial literature
in economics, strategy and game theory dealing with separating equilibrium
exists, yet it is quite interesting to note the concept was not unusual in
ancient times. Though the vocabulary might be new, many instances from
mythology do point out our ancient ancestors were well versed with the concept
of separating equilibrium. To them, it was the objective, talent and skill to
make the agent reveal himself his true selves, preferences, information etc.
Few examples from mythology would be in order to comprehend the same.
It was in
Odysseus’ destiny to lead Greeks to victory in the Trojan War. Odysseus had
been warned by an oracle that if he were to join Trojan War, he would be away
from his family for many years. Knowing the pitfalls, he had decided to avoid
going to the War. Yet there was a promise to be kept to King Agammemon of
joining hands with him to rescue Helen of Troy. When Helen had chosen
Agammemon, other kings and princes had promised to support Agammemon in case someone
harms or attempted to harm Helen of Troy. So Odysseus had to keep his promise
but only if he was sane. So Odysseus started to behave as a mad person when the
messenger came asking him to betake himself to the war. He started ploughing at
random times including at night and at random places. He began to sow salt
instead of seed. So the messenger Palmedes had to test whether Odysseus was genuinely
insane or pretending to be one. So a separating equilibrium scenario was needed
and it was a month old son of Odysseus named Telemachus who proved to be one.
Odysseus was emotionally bound to his son and so when Palmedes placed
Telemachus in front of the plough, Odysseus did not plough over his son but
skirted it. It would not be possible if it was genuine insane action therefore,
the separating equilibrium saw Odysseus reveal his true self. Odysseus had to
join the war.
Indian mythology
too is replete with instances of separating equilibrium. Both Ramayana and
Mahabharata provide instances of the same. The analysis will proceed on the
swayamwara of both Sita and Draupadi. Rather just dispelling myths of
patriarchy etc. the swayamwara show the freedom of choice of women in choosing
their life partners as also scheme designed to create and nurture a separating equilibrium.
Sita’s
swayamvara was designed to get Rama marry her. The bow was designed in such a
way that only Rama could have lifted the bow and strung it. More interesting
would be the swayamwara of Draupadi. After her father Draupada had been
humiliated by Drona, he had conducted a yagna wherein he had prayed for a
daughter who would marry Arjuna and son who would kill Drona. Post
Khandavaprastha, it was believed Pandavas had been burnt alive. So, next
alternative was someone equivalent to Arjuna. So the target and the method of
hitting the target was chosen keeping Arjuna or his equivalent in mind. Only an
archer of Arjuna’s calibre would be able to look the image of the target in
plate of oil and shoot the bull’s eye. Arjuna along with other Pandavas had
been present in the swayamwara disguised as Brahmins. After Kshatriyas failed,
Brahmins were invited and Arjuna accepted the invitation and succeeded. Arjuna
and Pandavas were re-discovered to be alive and what made that possible was
Arjuna’s mastery and devotion to archery made him the bull’s eye without any
trouble. Nothing better illustrates the same than this.
Bheema’s killing
of Bakasura too would have revealed the true self of Pandavas yet they had an
occasion to escape but Draupadi’s swayamwara was situation where escape was
impossible. Killing Bakasura was subconscious separating equilibrium. The attempts
by Kauravas was to created multiple separating equilibrium attempts to bring
true selves of Pandavas during Agyantvasa or period of disguise. Keechaka’s
killing was signal towards the same so was the battle with Arjuna and Uttara
Kumar. The Kauravas’ argument was they had managed to make Pandavas reveal
themselves but the situation was not conclusive fool proof revelation. The dispute
over this ended with Pandava victory in the Kurukshetra War.
While the
nomenclature and mathematical treatment might be new, the application has been
enshrined in strategy and practice for thousands of years. The illustrations
from mythology reinforce the same. In a universe of asymmetric information,
each agent through signals sends out certain contextual messages and the recipient
strategy would be to make the sender reveal the true preference or self.
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