Evolutionary Game Theory
(5 marks) Two politicians, Alice and Barbara, are running against one another for the
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
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
If candidate i uses a positive campaign while j uses a negative campaign, then i wins with
If candidate i uses a balance campaign while j uses a negative campaign, then i wins with
(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