In the run-up to the 2021 local government elections, two Councillors are interacting to try get donations from constituent citizens in their neighbourhood. Each Councillor has to decide whether they want to run a campaign that promotes themselves or which smears their opponent. Their interaction is represented by the game in normal form below, where payoffs represent thousands of Rands of funds raised.

		Councillor 2
		Promote Self	Smear Opponent
Councillor 1	Promote Self	670, 670	125, 750
	Smear Opponent	750, 125	325, 325

1. Solve for the Nash Equilibrium/Equilibria and Nash Equilibrium Outcome(s) of the game above. [2 marks]

2. Represent the game above graphically, with Councillor 1s payoff on the horizontal axis and Councillor 2s payoff on the vertical axis. [5 marks]

3. What is the socially optimal cell in the game above? In this cell, what is the total payoff to society? [2 marks]

4. What type of game does this represent? Justify your answer. [4 marks]

Imagine now that if a Councillor chooses to run a self-promoting campaign instead of smearing their opponent, a multinational business has offered to partner with the Councillor and make a large donation to their campaign. The donation from the multinational company is of size X.

5. Redraw the game table including the new payoffs after the donation from the company is taken into account. [4 marks]

In the run-up to the 2021 local government elections, two Councillors are interacting to try get donations from constituent citizens in their neighbourhood. Each Councillor has to decide whether they want to run a campaign that promotes themselves or which smears their opponent. Their interaction is represented by the game in normal form below, where payoffs represent thousands of Rands of funds raised.

Councillor 2

Promote Self

Smear Opponent

Councillor 1

Promote Self

670, 670

125, 750

Smear Opponent

750, 125

325, 325

Solve for the Nash Equilibrium/Equilibria and Nash Equilibrium Outcome(s) of the game above. [2 marks]

Represent the game above graphically, with Councillor 1s payoff on the horizontal axis and Councillor 2s payoff on the vertical axis. [5 marks]

What is the socially optimal cell in the game above? In this cell, what is the total payoff to society? [2 marks]

What type of game does this represent? Justify your answer. [4 marks]

Imagine now that if a Councillor chooses to run a self-promoting campaign instead of smearing their opponent, a multinational business has offered to partner with the Councillor and make a large donation to their campaign. The donation from the multinational company is of size X.

Redraw the game table including the new payoffs after the donation from the company is taken into account. [4 marks]

How large must the donation be in order to make the unique Nash Equilibrium of this game one where the Councillors only promote themselves in the campaign? Show your working. [3 marks]

6. How large must the donation be in order to make the unique Nash Equilibrium of this game one where the Councillors only promote themselves in the campaign? Show your working. [3 marks]