Evolutionary Game Theory

(5 marks) Two politicians, Alice and Barbara, are running against one another for the

same position. They are the only candidates in the running, so one of the two will win the election. Each

candidate chooses (simultaneously) to run their campaign ads in one of three ways. The candidates can

(i) focus ads on positive aspects of the candidates' own platform (P), (ii) focus ads on negative aspects

of their opponents' platform (N), or (iii) choose a balanced approach that combines both positive and

negative campaign ads (B). The probability that a candidate wins depends on her choice of ads as well

as her opponent's choice. The probabilities of winning for each combination of outcomes are given as

follows:

If both choose the same type of campaign then each wins with probability 0.5.

If candidate i uses a positive campaign while j uses a balanced campaign, then j wins with

probability 1.

If candidate i uses a positive campaign while j uses a negative campaign, then i wins with

probability 0.3.

If candidate i uses a balance campaign while j uses a negative campaign, then i wins with

probability 0.4.

(a) (1 mark) Can we set payoff to each player under each outcome to be the probability that they

win the election? Why or why not?

(b) (2 marks) Set up a payoff matrix for the game.

(c) (2 marks) Reduce the game by eliminating dominated strategies. Is there a dominant strategy

equilibrium?