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Consider the following Bayesian game: player 1 can be of two types (determined by "Nature") -Reliable (R) with probability "x" or Unreliable (U) with probability "1-x". These probabilities areknown to both players. Player 2 does not know player 1's type.Player 1 has no actions. Player 2 has two actions - to hire player 1 to work in a project (H) or not hireplayer 2 (N).Payoffs: if player 2 does not hire player 1 both get 0 utility because the project does not get done. Ifplayer 2 hires the R type of player 1, both players get +3 units of utility. If player 2 hires the U type ofplayer 1, player 2 gets -3 units of utility (i.e, loses 3 units) while player 1 gets +3 units of utility.
a) Carefully draw the extensive form of the (Bayesian) Game. Make sure to label all actions andpayoffs.
b) Assuming x = 0.2, solve for all pure-strategy Bayesian Nash Equilibria of this game.
c) For what values of x will the pure-strategy Bayesian equilibrium involve player 2 hiring player1? Show your calculations
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Find out what they are, how they work, and post your findings here. Be sure to review the posts of your classmates as well and comment on their discoveries.
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