Beliefs form perfect bayesian nash equilibrium

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Reference no: EM131099396

Gal is expecting a proposal from Guy. She is unsure whether Guy is a Deadbeat with little wealth and/or earning capacity, or is a Keeper with lots of wealth and/or earning capacity-this is the asymmetry in information in this problem. Gal preferences are such that she would prefer to Accept a proposal from a Keeper and to Reject a proposal from a Deadbeat. Her mom says that she can safely infer that Guy is a Keeper if his proposal is accompanied by a Big Rock, and that he is a Deadbeat if it is accompanied by NoRock. Having been certified as a game theorist (because she got a B+ in 373),Gal's problem in evaluating this motherly advice is to figure out whether or in what circumstances there is PBNE that separates the Deadbeat from the Keeper of the following sort: Gal's Actions: Accept proposal if a Big Rock is offered, and reject proposal if No Rock is offered. Gal's Beliefs: Guy is a Keeper if a Big Rock is offered, and a Deadbeat if No Rock is offered. Guy's Actions: O§er a Big Rock if he is a Keeper, and offer No Rock if he is a Deadbeat. Guy's Beliefs: Gal will Accept proposal if a Big Rock is offered, and Reject proposal if No Rock is offered. If he buys a Big Rock, Guy suffers a payoff loss of CBR (cost of the Big Rock),and if he does not buy one, there is no loss. If Deadbeat's proposal is accepted, he gets a short term utility payoff of ST (where ST > 0) its short term because when Gal discovers he is a Deadbeat, she kicks him out. If Keeper's proposal is accepted, he gets a long term utility payoff of LT (where LT > 0) it's long term because he doesn't get kicked out. If a proposal is rejected, Guy's payoff is 0,regardless of whether he is a Keeper or a Deadbeat. If she Accepts Guy's proposal, Gal's payoff depends only on whether Guy is a Keeper or a Deadbeat, if he is a Keeper her payoff is K > 0, and if he is a Deadbeat it is DB 0. If she Rejects the proposal, Gal's payoff is 0. Find values for the payoff parameters CBR; ST; LT, K; and BB such that the above strategies form a PBNE. More generally, find restrictions on payoff parameters such that the above strategies and beliefs form a Perfect Bayesian Nash equilibrium.

Reference no: EM131099396

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