Can you help me with this please? Worker'sabilityHighLowDemanding5XY2Firm's jobUndemanding3424There is a 50% chance the worker is of high ability. Which of the following alternatives is correct?(a) Assume Y > 2, then for any X < 4 the worker reports truly (cheap talk works)(b) Assume Y > 2, then if 4 < X < 5 the worker reports truly (cheap talk works)(c) Assume cheap talk fails, then for any Y > 4 the firm offers the undemanding job(d) The firm always offers the undemanding job when cheap talk fails

Cheap Talk is defined as a commination between players in game theory which does not have any direct effect on the pay-offs of the game Given, Two Players or Categories : Worker's Ability and Firm's job Worker's Ability has two types : High and Low Firm's Jobs are of two types : Demanding and Undemanding. The game matrix is given as follows :Assume Y>2, then for any X<4, the worker reports truly (cheap talk works) The game is now given as : Firm's Job Worker's Ability Demanding Undemanding High 5, 3 3, 2 Low 2, 2 4, 4 We now calculate Nash Equilibrium, For Worker's Ability : When Firm's Job is Demanding, Workers Ability is High When Firm's Job is Undemanding, Workers Ability is Low For Firm's Job : When Worker's Ability is High, Firms Job is Demanding When Workers Ability is Low, Firms Job is Undemanding. Therefore Nash Equilibrium is obtained at (High, Demanding) and (Low, Undemanding), i.e. (5, 3) and (4, 4). Cheap talk works as if both there is communication between both players, then both will choose (Low, Undemanding) jobs, i.e. with equal pay-off of (4, 4) Assume Y>2, then if 4<X<5 the worker reports truly (cheap talk works) The game is now given as : Firm's Job Worker's Ability Demanding Undemanding High 5, 3 3, 2 Low 4.5, 2 4, 4 We now calculate Nash Equilibrium, For Worker's Ability : When Firm's Job is Demanding, Workers Ability is High When Firm's Job is Undemanding, Workers Ability is Low For Firm's Job : When Worker's Ability is High, Firms Job is Demanding When Workers Ability is Low, Firms Job is Undemanding. Therefore Nash Equilibrium is obtained at (High, Demanding) and (Low, Undemanding), i.e. (5, 3) and (4, 4). Cheap talk works as if both there is communication between both players, then both will choose (Low, Undemanding) jobs, i.e. with equal pay-off of (4, 4) Assume cheap talk fails, then for any Y>4, the firm offers undemanding job The game is now given as : Firm's Job Worker's Ability Demanding Undemanding High 5, 6 3, 2 Low 2, 2 4, 4 We now calculate Nash Equilibrium, For Worker's Ability : When Firm's Job is Demanding, Workers Ability is High When Firm's Job is Undemanding, Workers Ability is Low For Firm's Job : When Worker's Ability is High, Firms Job is Demanding When Workers Ability is Low, Firms Job is Undemanding. Therefore Nash Equilibrium is obtained at (High, Demanding) and (Low, Undemanding), i.e. (5, 6) and (4, 4). Since Cheap talk Fails, If Firms jobs are demanding, they will want the workers ability to be high. Therefore, there will not be any unison. The Workers Ability pay-off will be higher than the Firms Jobs pay-off. Therefore, they will be wanting the Demanding jobs.The Firm does not offer the undemanding job when the cheap talk fails since the pay-off of workers ability is higher and the firms job is more demanding. Therefore, when the cheap talk does not work, firm will want workers with higher ability to do the more demanding jobs. Therefore, Options (a) and (b) are the correct alternatives.