6) Consider the following signaling game:20, 50,010, -10-10,0LeftLeftRightRightPlayer 2Player 21-aUpUpNaturePlayer 1-APlayer 1-BТуре А — 50%Туре В — 50%DownDownPlayer 21-BPlayer 2LeftRightLeftRight10,50,05, -100,0Let's see if it has a pooling equilibrium. Follow the following steps:a. Specify strategies of a possible pooling equilibriumb. Determine player 2’s on-path beliefs for the belief probabilities a and ß asappropriate. You can infer these beliefs from what we know about beliefs inpooling equilibria, and do not havefully calculate them.c. Check whether either player wants to deviate. Is there a pooling equilibrium?d. Determine the off-path beliefs that make the equilibrium hold.

For the Above signaling game following steps are taken : Player 1 is chosen by nature to make first decision . Where player 1 can be of type A & B and either ways has two strategies to choose from {Up, Down } . Based on player 1's chosen strategy player two chooses his own strategy . But the type for player 1 is unknown to player 2 . Game ends Pooling Strategies Player 1 : If type A : He chooses {Up} (As the all over payoffs in choosing Up (20& 0) are better than choosing down(10 &0) ) (α) being the probability of choosing (Up) when player 1 is type A . Hence , ( α) = 1 & Therefore (β) = 0 If type B : He chooses {Up} with probability (1 - α ) => 0 He chooses {Down } with probability (1 -β ) => 1 Hence , player 1 chooses strategy {Up} when he is of type (A) and chooses strategy { Down } when he is of type (B). Player 2 Beliefs : If player 1 chooses {Up } , Probability of him being type (A) = 1 If player 1 chooses {Down } , Probability of him being type (A) = 0 Vice - versa for being type (B). Strategies available are { Left , Right } , which he chooses after observing player 1 . If player 1 chooses {Up } => Then player 2 get to know that player (1) is type (A) So , he will choose strategy {Left } , as payoff (5 >0) If player 1 chooses {Down } => Then player 2 gets to know that player (1) is type (B). So , he will choose strategy {Right } , as payoff ( 0> -10 ). Hence the equilibrium strategies are : ( Up , Left ) & (Down , Right ) *As per our guidelines we are only allowed to solve only 1 question with 3 maximum sub parts at a time. *