{"id":1610,"date":"2023-07-02T22:41:29","date_gmt":"2023-07-02T13:41:29","guid":{"rendered":"https:\/\/saraheee.com\/?p=1610"},"modified":"2023-07-02T22:51:42","modified_gmt":"2023-07-02T13:51:42","slug":"game-theory-semi-separating-equilibrium","status":"publish","type":"post","link":"https:\/\/saraheee.com\/ko\/2023\/07\/game-theory-semi-separating-equilibrium\/","title":{"rendered":"Game Theory : Semi-Separating \/ Partially-Pooling Equilibrium"},"content":{"rendered":"

Topics: Semi-Separating Equilibrium, Partially-Pooling Equilibrium
(semi-separating is the more common label)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

It was a terrorist group as Robust with probability .4 and Vulnerable with probability .6 the group<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

then chooses whether to commit an attack or not if the group attacks
then player 2 who is the target chooses whether to resist or ignore payoffs are as follows<\/p>\n\n\n\n

If player 1 does not attack everyone receives a status quo outcome of 0
If player 1 attacks and player 2 ignores then player 1 gets a point for a successful attack and player 2 loses a point for the same reason<\/p>\n\n\n\n

The key difference between the types is what happens following resistance the vulnerable group will completely fall apart<\/p>\n\n\n\n

Robust Type<\/h4>\n\n\n\n

Let’s get to solving this we begin by noting that the Robust type clearly must attack it receives either 3 or 1 by doing so in contrast it receives 0 by not attacking
Thus no matter how player 2 acts the Robust type finds attacking more profitable<\/p>\n\n\n\n

Vulnerable Type<\/h4>\n\n\n\n

Now let’s see if we can describe the vulnerable types action using the types of equilibria
we have covered previously suppose the vulnerable type separates by not attacking
then conditional on observing an attack player 2 knows it is facing the Robust type it chooses to ignore and receive -1 instead resisting and receiving -3 given this does the vulnerable type have a profitable deviation indeed it does bluffing is just too attractive<\/p>\n\n\n\n

* Bluffing: a strategical method of demonstrating one\u2019s unpredictability<\/p>\n\n\n\n

Separating?<\/h4>\n\n\n\n

If it were to attack player 2 would ignore under the False assumption that player 1 is Robust
This allows the Vulnerable type to receive one which is better than the 0 it earns by maintaining its strategy<\/p>\n\n\n\n

Pooling?<\/h4>\n\n\n\n
\"\"<\/figure>\n\n\n\n

u(resist) = .4(-3) + .6(2) = 0
u(ignore) = .4(-1) + .6(-1) = -1<\/mark><\/strong><\/p>\n\n\n\n

for a total payoff of 0 if she ignores she receives negative one regardless of the opposing type
Because 0 is greater than -1 she chooses to resist given this does the vulnerable type have a profitable deviation<\/p>\n\n\n\n

It does once more now the vulnerable types Bluff backfires it earns negative two for sticking with its strategy whereas it can secure zero by not attacking as such we cannot find any equilibria given our current tools<\/p>\n\n\n\n

Semi-Separating Equilibrium<\/h3>\n\n\n\n