Waging Simple Wars: A Complete Characterization of Two Battlefield Blotto Equilibria

Abstract: We analyze the strategic allocation of resources across two contests as in the canonical Colonel Blotto game. Such environments were among the first to be studied in game theory. In the games we study, two players simultaneously allocate their forces across two fields of battle. The larger force on each front wins that battle, and the payoff to a player is the sum of the values of fronts won. We completely characterize the set of Nash equilibria of all two battlefield Blotto games and provide the unique equilibrium payoffs. Our characterization extends to cover previously unstudied games with nonlinear resource constraints.

Read the full article here (pdf)

A Statistical Test for Partisan Gerrymandering

Abstract: Is redistricting the result of partisan gerrymandering or apolitical considerations? I develop a statistical test for partisan gerrymandering and apply it to the U.S. Congressional Districting plan chosen by the Republican legislature in Pennsylvania in 2001. First, I formally model the optimization problem faced by a strategic Republican redistricter and characterize the theoretically optimal solution. I then estimate the likelihood a district is represented by a Republican, conditional on district demographics. This estimate allows me to determine the value of the gerrymanderer’s objective function under any districting plan. Next, I use a geographic representation of the state to randomly generate a large sample of legally valid plans. Finally, I calculate the estimated value of a strategic Republican redistricter’s objective function under each of the sample plans and under the actual plan chosen by Republicans. When controlling for incumbency the formal test shows that the Republicans’ plan was a partisan gerrymander.

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(Updated 11/21/2011)

Rendering Gerrymandering Impotent: A Simple Redistricting Reform

Abstract: I introduce a new and novel electoral reform that continues to allow redistricting but changes the incentives to do so. This reform ensures that parties earn seats proportional to their performance at the polls without substantially changing the electoral system in the U.S. In order to evaluate the reform’s impacts, I model and solve a game that incorporates the redistricting decision, candidate choice, state legislative elections, and policy choice. Unsurprisingly, strategic redistricting biases policy in favor of the redistricting party. In the environments studied, the new reform never increases policy bias, and often reduces it.

Read a (Very) Preliminary Draft Here (pdf)

What is a Congressional Seat Worth? Estimating the Value Using Auction Theory

Abstract: This paper models campaign expenditures as bids in an asymmetric all-pay auction. It predicts intuitive mixed Nash expenditure strategies and electoral outcome probabilities. As district demographics, such as partisan voter registration statistics, favor a candidate more heavily, the mixed expenditure strategies converge pointwise to the classic Median Voter Model.  The parameter of the model is then estimated based on the predicted moments of the expenditure distribution.  We use the district level voter registration statistics and observed campaign expenditure behavior to estimate the value of a Congressional House seat to be about $4.5 million.

Read the full article here (pdf)

Choosing When to Pay Capital-Gains Taxes

Abstract: Capital gains tax rates in the U.S. change frequently. However, most theoretical work assumes that capital earnings are taxed every period at a constant rate. How does the variation in capital gains taxes over time affect investment behavior? Additionally, the answer to this question has significant implications for how capital gains tax rate changes affect tax revenues.

Read the full article here (pdf)