Game theory is a useful tool for examining problems where there are two or more players and each player takes into consideration the reaction of the others. I see three possible scenarios over the next 2.5 weeks before we hit President Trump's deadline for Congressional action.
1) Congress passes a bipartisan bill on border security with protection for dreamers and over $5.7b in spending for border security. The language on barriers is kept sufficiently vague so that Democrats can say fence and Trump can say wall. Trump vetos the bill because he fears the loss of support from his core supporters (no wall and amnesty, all in one package).
2) Congress is unable to pass a bill. Trump shuts down the government again.
3) Congress is unable to pass a bill. Trump declares a national emergency so he can reallocate funds to start work on a wall.
From a game theory perspective there are two players: Congress and Trump. The obstacles of getting a bipartisan bill through a Democratic House and a Republican Senate (with 60 votes needed to bust a filibuster) are massive. Assuming time-consistent behavior by Trump (he has already turned down the wall-for-dreamers trade multiple times), there will be little incentive to reach an agreement and vote in favor of it. So I put the odds of a bipartisan bill being passed as extremely low.
With no bill, Trump has to decide whether to go through another shutdown. Well five weeks of shutdown did not work, so does Trump really think another 5+ weeks will? Despite Trump's apparent issues with impulse control, I have trouble seeing this happening as well. As my fellow-Kentuckian Mitch McConnell said, there is no education in the second kick of a mule.
But the emergency is the perfect solution for both sides. Not a single brick or girder will be put in place between now and the 2020 election because the emergency wall declaration will be tied up in the court system. Trump looks decisive to his base and can blame the Democrats in Congress and Obama judges for his failure to deliver. Democrats are happy because (1) Trump will lose some support from his Republican base for ignoring the Constitution and (2) there won't be a wall before the election.
You can take my advice and monetize it on the betting markets.
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