Nikhil and Swati are playing a game designed to model labor relations called the "gift exchange game." In this game, Swati takes the role of an "employer" and Nikhil takes the role of an "employee."

The employer's moves are to pay a "high wage" or a "low wage." The employee chooses to exert "high effort" or "low effort" in their job.

The high wage (paid by the employer to the employee) is $3. The low wage is $1.

Exerting high effort costs the employee $1. Exerting low effort costs the employee $0.

If the employee exerts high effort, the employer will earn $6 of revenue.

If the employee exerts low effort, the employer will earn $3 of revenue.

Note: These dollar amounts are revenue, not profit. The only cost the employer has to pay is the wage paid to the employee.

The game can be played as either a simultaneous move game or a sequential move game.

For the simultaneous move version of the game, set up the game in normal form (i.e. the payoff matrix), and find the pure strategy Nash Equilibrium or equilibria. Explain how you arrive at your solution.

b) For the sequential move version of the game, set up the game in extensive form (i.e., as a game tree), and find the subgame perfect equilibrium (SPE). Explain how you arrive at your solution.

c) When the sequential move version of the game has been played in experiments for real money, 64% of employers have chosen to pay the high wage, and when paid the high wage, 76% of employees have chosen to exert high effort.

Imagine there are two types of people:

- those who believe in reciprocity, i.e. rewarding people who have treated them well and punishing people who have treated them poorly.

- those who are rational and self-interested.

Given the experimental findings described above, should employers who play this game in the future choose to pay the high wage or the low wage? To answer this question, show which wage maximizes the employer's expected payoff.