Campaigning: Two candidates, 1 and 2, are running for office. Each has one of th

Question

Campaigning: Two candidates, 1 and 2, are running for office. Each has one of three choices in running his campaign: focus on the positive aspects of one's own platform (call this a positive campaign [P]), focus on the positive aspects of one's own platform while attacking one's opponent's campaign (call this a balanced campaign [5]), or finally focus only on attacking one's opponent (call this a negative campaign [N]). All a candidate cares about is the probability of winning, so assume that if a candidate expects to win with probability pi [0, 1], then his payoff is pi. The probability that a candidate wins depends on his choice of campaign and his opponent's choice. The probabilities of winning are given as follows: If both choose the same campaign then each wins with probability 0.5. If candidate i uses a positive campaign while uses a balanced one then i loses for sure.

Explanation / Answer

a) This is normal game with two players with 3 strategies for each player i.e. Positive, Balanced and Negative. So obviosuly the payoff function of each depends on the other. for e.g. if the 1st player plays the P strategy, and if the j player can anticipate that from before, then the player j has an incentive to play the Negative strategy as his probability of winning is higher.

This game is an extension of a finite case Prisoner's Dilemma. The outcomes of such games is always a negative strategy.

Rest of the answer: http://imgur.com/iBALOjm

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