Consider a situation in which there is an employer, E$,$ and a worker, W$.$ E can choose to trust the worker to a high or low level while W can choose either a high or low level of effort. Both are rational and have complete information about the payoffs in this one$-$shot game:

If E chooses high trust, and W chooses high effort, they receive a payoff of $2$ each.

If E chooses high trust, and W chooses low effort, E receives a payoff of $0$ and W receives a payoff of $3.$

If E chooses low trust, and W chooses high effort, E receives a payoff of $3$ and W receives a payoff of $0.$

If E chooses low trust, and W chooses low effort, E receives a payoff of $1$ and W receives a payoff of $1.$

Draw a payoff matrix to show this information as a simultaneous one$-$shot game in which both E and W choose their own action before knowing what the other will do$.$ Player E$$s actions should be given on rows. $(6$ marks$)$

Explain whether either E or W$,$ or both, have a dominant strategy. Show your reasoning in full. $(6$ marks$)$

Identify and explain the Nash equilibrium in this game. Explain whether it is also a Pareto optimal outcome. $(6$ marks$)$

Explain in full why, if E and W play the game repeatedly, outcomes may depend on whether repetitions are known by them to be finite. $(7$ marks$)$