** Project: "Odd, Enter; Even, Out: A Peculiarity of Political Rivalry, Buyout, Blackmail, Extortion, and Nuisance Suit Games."**
Suppose the incumbent leader faces possible entry and attack by a sequence of rivals in a very simple game. For plausible parameters, no rivals enter in the unique equilibrium when the number of rivals is even and exactly one enters when the number is odd. The prospect of later rivalry can have other peculiar effects. Though the incumbent never wishes to weaken only himself, he may wish to reduce the incumbency advantage or reduce the entry cost, and an entrant may wish to weaken himself.

** "Law, Coercion, and Expression: A Review Essay on Frederick Schauer's The Force of Law and Richard McAdams's The Expressive Powers of Law." **What is law and why do people obey it? Two books published in 2015, Frederick Schauer's

** "Requirements Contracts and Transactions Costs.'' ** Requirements contract ensure reliable supply at a pre-arranged price without having to
resort to efficient breach if the buyer is
unsure of his future demand and the seller must invest in capacity or specialization. Transaction costs are key; without them a better
outcome can be obtained with a fixed-quantity contract.

** Project: "Understanding Shrinkage Estimators: From Zero to Oracle to James-Stein."**
Constructing an estimator by shrinking the sample mean results in a biased estimator, with an expected value less than the population mean. On the other hand, shrinkage reduces the estimator's variance and mean squared error. This paper tries to explain how that works. I start with estimating a single mean using the zero estimator and the oracle estimator, which is allowed to use in an ancillary role the very parameter being estimated. I continue with the unrelated-average estimator and the James-Stein estimator.

**Project: "What Does It Mean To Be a Liberal? An Objective Approach.'' ** with J. Mark Ramseyer. How does one define what it means to be a liberal? We suggest a measure based on what the average person thinks it means, regressing a person's self-reported liberalism on his characteristics and answers to political survey questions. This method allows one to test whether people think of liberalism as social identity (``I'm an unmarried black female, so I must be liberal'') or political belief (``I'm pro-abortion, so I must be a liberal'').

** Project: ``Why Immigration Is Different from Free Trade.'' **
Can immigration hurt the welfare of a country? Yes, if there are decreasing returns to the factor, or if the dilution of ownership of public capital is even moderately important. Free trade is different because it has no direct effect on domestic marginal productivity. Capital inflow is different because it does not convey ownership of public capital.
http://www.rasmusen.org/papers/immigration-rasmusen.pdf.

** Project: "Machiavelli:
The Han Fei of Italy?"** (with Dan Zhao). 1,700 years before Machiavelli, Han Fei also put aside morality and emphasized maintaining order in a world where intrigues could not be prevented by education in virtue. Both were vilified over the centuries, but nonetheless had immense influence.

** "Quasi-Concavity versus Concavity,'' ** with Christopher Connell. We show that if and only if a real-valued function f is strictly quasi-concave except possibly for a flat interval at its maximum, and furthermore belongs to an explicitly determined regularity class, does there exist a strictly monotonically increasing function g such that g of f is concave. We prove this sharp characterization of quasi-concavity for functions whose domain is any Euclidean space or even any arbitrary geodesic metric space. http://www.rasmusen.org/papers/quasi-connell-rasmusen.pdf.

** "Exclusive Dealing: Before, Bork, and Beyond," **
with
J. Mark Ramseyer. * Journal of Law and Economics * (2015). Antitrust scholars have come to accept the basic ideas about exclusive dealing that Bork articulated in The Antitrust Paradox. Indeed, they have even extended his list of reasons why exclusive dealing can promote economic efficiency. Yet they have also taken up his challenge to explain how exclusive dealing could possibly cause harm, and have modelled a variety of special cases where it does. Some (albeit not all) of these are sufficiently plausible to be useful to prosecutors and judges.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2308218.

** "Lowering the Bar to Raise Up the Bar: Licensing Difficulty and Attorney Quality in Japan," ** * Journal of Japanese Studies* (2015) with J. Mark Ramseyer. A relaxation in licensing standards can increase the quality of those who enter the industry. The effect turns on the opportunity cost of preparing for licensing. Making the test easier can increase the quality of those passing by increasing the number willing to take the test. We explore the theoretical circumstances under which this can occur and the actual effect in Japan from 1992 to 2011.
http://rasmusen.org/papers/barpass-ram-ras.pdf.

** "How Useful Is a Product Umbrella for Reputation?'' ** forthcoming, * Journal of Economics and Management Strategy.* A firm with a reputation for high quality in one product may usefully extend that reputation to other products. I look at how that works in a moral hazard model of product quality. http://www.rasmusen.org/papers/umbrella.pdf.

** The Economics of Regulation.** I have notes for an undergraduate textbook on regulation. I start with 4 chapters of theory (supply-and-demand, market failure, government failure, discounting and life valuation) and have just 2 chapters of antitrust, with 6 more chapters on other topics. My aim, if I do end up trying to publish this, is to write a relatively short book (350 pages) with lots of photos and stories, skipping many topics and being interesting enough for someone to read for recreation. http://rasmusen.org/g406/chapters/.

** "The Concealment Argument: Why No Proof for God’s Existence Will Be Found,"** Logic and Biblical evidence suggest that God wishes that some but not all humans become convinced of His existence and desires. If so, this suggests that attempts to either prove or disprove such things as God's existence, past miracles, or present supernatural intervention are doomed to failure, because God could and would take care to evade any such efforts. http://rasmusen.org/papers/conceal-rasmusen.pdf.

**"Project: Hilbert's Side-Angle-Side Axiom in Proposition I-4 of Euclid's Elements".** I search for a better axiom with which to fix up Euclid's flawed proposition that two triangles are the same if two of their sides and the angle created by them are the same.