## Game Theory of the Presidential Campaigns

With the election for president coming up this November, both Mitt Romney and Barack Obama are turning up the campaign trail intensity. As time goes on, the candidates and their supporters seem to become even more polarized against each other. Romney, Obama, and their supporters use campaign tactics that become even more ruthless. However, do these techniques actually work? Are mud-slinging campaign techniques effective? The choice to use negative campaign ads can be modeled as a two person game. The two players are Romney and Obama, and they both have the option to produce positive campaign ads about themselves or negative ads about their opponent. For the sake of the exercise, we’ll assume that these options are mutually exclusive.

Romney\Obama |
Positive |
Negative |

Positive |
0, 0 |
-1, 1 |

Negative |
1, -1 |
0, 0 |

If both candidates run positive ads, they both have equal chances of winning the election (based on only the ads of course). If one of them runs a negative ad, they have a natural advantage and are more likely to win the race. However, if they both run negative ads, they are effectively on the same playing field, leaving each with an equal payoff. So what strategy should each candidate use for their campaign ads? Well, assuming they both start off in the top left square, with both candidates running positive ads, Romney has a motivation to go negative because it will increase his payoff from zero to one. The same applies to Obama because of the symmetry of the game. However, once one of the candidates runs a negative ad, the other is motivated to also run a negative ad to even the playing field and increase their payoff. So what is the dominant strategy for the candidates? Due to the symmetry of the game, it should be the same for both candidates. If Romney runs a positive ad, Obama will have a higher payoff if he runs a negative ad. If Romney runs a negative ad, Obama will have a more even playing field by also going negative. So the dominant strategy for both candidates is to run negative campaign ads. The most recent ad by president Obama features quotes from Romney on how he views the forty-seven percent of Americans that he assumes will be voting for Obama. The ad doesn’t even feature any information at all about Obama or his platforms. The focus of the ad is on the negative influence Romney would have on hardworking Americans. The only words actually spoken by Obama are in the beginning of the ad clarifying that he approves the following message. Because of the dominant strategies of both candidates, it’s unlikely that Obama or Romney’s campaign will abandon their negative strategies.

– Castor Troy