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Game Theory and Congressional Gridlock

https://www.theatlantic.com/politics/archive/2013/01/how-game-theory-explains-washingtons-horrible-gridlock/267142/

In class we have discussed quite a bit about game theory in general and Nash equilibrium specifically. One of the more interesting takeaways is how often that the benefit to two players in a Nash equilibrium situation often enjoy less collective benefit than if they had found a way to coordinate their efforts and agree to cooperate, such as with the simple prisoners dilemma. The article provides some commentary on this type of situation in negotiations between the two parties in congress but this commentary  can easily be far more formalized.

Specifically each representative has two moves that they can make: cooperating with their party or defecting to vote with the other party. Lets say we have party A and party B and that party B has just proposed legislation of some sorts intended to improve an issue faced by the country. If we consider the options of some senator from party A, they receive high payoff if either they defect and the legislation has positive effect or if they cooperate and the legislation has negative effects. They receive negative payoff if they defect and the legislation has negative effect or if they cooperate and the legislation has positive effect.  If they defect and the legislation has negative effect, the negative payoff will be great as voters and politicians from party A will put this politician in the spotlight and place significant blame on them resulting in terrible publicity and a lower chance of reelection. In the other case of negative payoff most of part A will share the negative payoff resulting in minimal penalty specific to this senator. Bringing all this together: the situation a senator wants to avoid is defecting and the legislation having negative effect. Therefore it is a Nash equilibrium to have partisan votes in congress where it may be optimal overall for every senator to vote for or against the legislation.

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