http://www.foxbusiness.com/markets/industries/government/article/games-played-vote_482985_18.html

This Fox Business article discusses how game theoretic strategies might be applied to voting for a president. In particular, it cites Wisconsin as being a state where voters are allowed to vote for any of the candidates in the primaries, regardless of party affiliation. The article points out that this means a Republican can choose to vote for the Democratic candidate he or she deems to be less of a threat in the ultimate presidential election. Since this can essentially be treated as a multi-step game, it may indeed be more beneficial to not vote for one’s favorite candidate in the hopes of providing less competition in the next stage of voting. This illustrates the complexities of playing a multi-stage game compared to the one-shot game examples shown in class, as the greatest payoff may arise from having different strategies at the different rounds.

The article proceeds to describe an example where a similar scenario was attempted in the past. Lincoln deduced that in the election of 1856, if Buchanan failed to win Illinois in the presidential election, then no candidate would have enough electoral votes to win, in which case the matter would be brought to the House of Representatives. Lincoln persuaded supporters of Fillmore to vote for his favorite candidate Fremont in order to join forces against Buchanan in Illinois, explaining that it would be the only chance of Fillmore’s success. Assuming Lincoln’s deductions were correct and not simply a means of trying to steal votes for his favorite candidate, this illustrates that attempting to locally maximize your own payoff (by voting for your favorite choice) may not be the best way to get the desired outcome. This is somewhat analogous to the Prisoner’s Dilemma, in which following your dominant strategy (i.e. confess) may lead to a worse payoff than some other possible outcome (i.e. no one confesses), but the better outcome would require collaboration to effectively work.

Thus it is not always the case in a multi-stage voting scheme to vote for your favorite candidate at each round, demonstrating some possibly counter-intuitive intricacies of a multi-stage game.