Jinpeng Ma

Strategy-Proofness and the Strict Core in a Market with Indivisibilities

We show that, in markets with indivisibilities (typified by the Shapley-Scarf housing market), the strict core mechanism is categorically determined by three assumptions: individual rationality, Pareto optimality and strategy-proofness.

On randomized matching mechanisms

SummaryThis note showed by means of Knuths example that some stable matchings may not be obtained by the random order mechanism.

The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)

We show that in the marriage problem the student-optimal algorithm may in fact generate an equilibrium outcome that is college-optimal and student-pessimal in terms of the true preferences even though it is student-optimal and college-pessimal in terms of the submitted preferences. In the college admissions problem, the student-optimal algorithm generates either a matching that is not stable for the true preferences or a matching that is college-optimal and student-pessimal in terms of the true preferences. Thus, our results show that, in the absence of certain match variations, the newly designed student-optimal algorithm adopted by the NRMP since 1998 either may be bias in favor of hospitals in terms of the true preferences or fails to produce a true stable matching. We also discuss when the core is large and when the core is a singleton at a Nash equilibrium.

Walrasian equilibrium in an exchange economy with indivisibilities

This paper studies an exchange economy with indivisibilities. Our main goal is to see if a price system can function well in an economy (e.g., an economy with complementary preferences) that does not have a Walrasian equilibrium. We study the price adjustment processes governed by the Euler iterative scheme. We show that in an economy that has a Walrasian equilibrium, our price adjustment processes have a common uniform limit that is unique and converges to a Walrasian equilibrium price vector in finite time. Surprisingly, in an economy that does not have a Walrasian equilibrium, our price adjustment processes also have a common uniform limit that is unique and converges to a market equilibrium price vector in finite time. Moreover, market equilibrium prices coincide with Walrasian equilibrium ones in an economy that has a Walrasian equilibrium. Further, there are no prices other than the Walrasian or market equilibrium ones that have such a property of global stability.

Job Matching and Coalition Formation with Utility or Disutility of Co-workers

This paper studies the job matching market in Kelso and Crawford(1982) with one exception that co-workers may generate utility or disutility in the workplace. We provide a simple idea to show how a great number of sufficient condiions for a nonempty core in the literature can be extended to this labor market. We also provide a deterministic and a stochatic recursive dynamic system each of which converges to an efficient core outcome as long as the core is nonempty.

An Alternative Proof of an Equilibrium Existence Theorem in Exchange Economies with Indivisibilities

Abstract Bikhchandani and Mamer (1997, J. Econom. Theory 74 , 385–413) studied an exchange economy with multiple indivisible objects and established a necessary and sufficient condition for the existence of competitive equilibrium by a linear programming approach. This paper provides an alternative proof of their theorem by the core of a coalitional form game. Journal of Economic Literature Classification Number: C71.

Double auction mechanisms on Markovian networks

This paper studies the double auction (DA) mechanism in Ma and Li (2011) for a class of exchange economies. We extend their results to more general cases where sellers and buyers each form a complex time non-homogeneous Markovian chain, as specified in Ram et al. (2009), in the communication of their private information. A numerical example is also provided. Both bubbles and crashes are observed in the example, consistent with results of our theorems. Our example and theoretical results provide new evidence that a DA mechanism, widely utilized in real exchange markets, may contribute to the excess volatility identified in Shiller (1981) and LeRoy and Porter (1981).

Bubbles, Crashes and Efficiency with Double Auction Mechanisms

We provide a quantitative boundary on the stepsizes of bid and ask of a double auction (DA) mechanism to answer two questions, when the DA mechanism is efficient and when it creates bubbles and crashes. The main result is that the ratio of the two stepsizes and their spread are the key factors for the DA mechanism to be efficient. Sentiment that leads to a swing in the spread and the ratio of the two stepsizes can result in prices to deviate from the intrinsic value equilibrium. These results are derived from a theoretical analysis of the DA mechanism built on the incremental subgradient method in Nedic and Bertsekas (2001).

A FIR Filter to Date Post-WWII Recessions

A new FIR filter is designed to date U.S. recessions with the unemployment rate and the Conference Board employment trend index. Our approach is simple but one can see from the curve the dynamic process how the economy moves from one business cycle to the next. We also present a new use of the HP filter and uncover some useful information about the relationships among the yield curve, the Wu-Xia shadow rate, and the unemployment rate. We argue that an assessment of the labor market based on the level of the unemployment rate can be very wrong for the business cycle oriented monetary policy.

Value of hedge and expected returns

We demonstrate how it is possible to generate value for an investor with a hedge attached to the buy-and-hold strategy of an S&P 500 index fund. We study the S&P 500 index portfolio (not including dividends) and the value-weighted S&P 500 index portfolio (including dividends) of the Center for Research in Securities Prices for 1967:01--2011:12, using the capacity utilization and the unemployment rates in real time to determine if a hedge position should be initiated or closed. A hedge is initiated if the capacity utilization, the unemployment rate or a combination of the two signals a contraction in the real economy. The hedge position is closed if it signals otherwise an expansion. We use utility gains (Campbell and Thompson 2008), the manipulation-proof performance measure (MPPM) statistics (Ingersoll et al. 2007) and the P-Sharpe ratio (Bailey and Lopez de Prado 2012) to evaluate the performance of a particular hedge strategy. The empirical results show that there are infinitely many hedges that can generate positive utility gains, higher MPPM statistics and higher P-Sharpe ratios.