Dimer algebras, ghor algebras, and cyclic contractions

A ghor algebra is the path algebra of a dimer quiver on a surface, modulo relations that come from the perfect matchings of its quiver. Such algebras arise from abelian quiver gauge theories in physics. We show that a ghor algebra $\Lambda$ on a torus is a dimer algebra (a quiver with potential) if and only if it is noetherian, and otherwise $\Lambda$ is the quotient of a dimer algebra by homotopy relations. Furthermore, we classify the simple $\Lambda$-modules of maximal dimension and give an explicit description of the center of $\Lambda$ using a special subset of perfect matchings. In our proofs we introduce formalized notions of Higgsing and the mesonic chiral ring from quiver gauge theory.Comment: 39 pages. I am reorganizing and expanding arXiv:1412.1750 into four shorter papers; this paper is the first of the fou

Bargaining power and supply base diversification

In this paper, the authors examine a supply base diversification problem faced by a buyer who periodically holds auctions to award short term supply contracts among a cohort of suppliers (i.e., the supply base). To mitigate significant cost shocks to procurement, the buyer can diversify her supply base by selecting suppliers from different regions. The authors find that the optimal degree of supply base diversification depends on the buyer’s bargaining power, i.e., the buyer’s ability to choose the auction mechanism. At one extreme, when the buyer has full bargaining power and thus can dictatorially implement the optimal mechanism, she prefers to fully diversify. At the other extreme, when the buyer uses a reverse English auction with no reserve price due to her lack of bargaining power, she may consider protecting herself against potential price escalation from cost-advantaged suppliers by using a less diversified supply base. The authors find that in general the more bargaining power the buyer has to control price escalation from cost-advantaged suppliers the more she prefers a diversified supply base. This insight is shown to be robust to correlation between regional costs, asymmetry across regions, and intermediate levels of bargaining power.supply base diversification; supplier; buyer; procurement; bargaining