We offer a detailed examination of a broad class of 2 x 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.
In previous work, the current authors derived a mathematical expression for the optimal (or “saturation”) number of reinsurers for a given number of primary insurers (see Powers and Shubik, 2001). In the current paper, we show analytically that, for large numbers of primary insurers, this mathematical expression provides a “square-root rule”; i.e., the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers. We note further that an analogous “fourth-root rule” applies to markets for retrocession (the reinsurance of reinsurance).
Although short sales make an important contribution to financial markets, this transaction faces legal constraints that do not govern long positions. In evaluating these constraints, other commentators, who are virtually all economists, have not focused rigorously enough on the precise contours of current law. Some short sale constraints are mischaracterized, while others are omitted entirely. Likewise, the existing literature neglects many strategies in which well advised investors circumvent these constraints; this avoidance may reduce the impact of short sale constraints on market prices, but may contribute to social waste in other ways. To fill these gaps in the literature, this paper offers a careful look at current law and draws three conclusions. First, short sales play a valuable role in the financial markets; while there may be plausible reasons to regulate short sales — most notably, concerns about market manipulation and panics — current law is very poorly tailored to these goals. Second, investor self-help can ease some of the harm from this poor tailoring, but at a cost. Third, relatively straightforward reforms can eliminate the need for self-help while accommodating legitimate regulatory goals. In making these points, we focus primarily on a burden that other commentators have neglected: profits from short sales generally are ineligible for the reduced tax rate on long-term capital gains, even if the short sale is in place for more than one year.
Keywords: Short sales, Momentum traders, Value investors
There is a natural tradeoff between the benefits of increasing the number of competitors in an insurance market and the drawback to the weakening of the law of large numbers due to the diminishing of average reserves. In this investigation we consider the possibility for optimal layers of reinsurance and retrocession in the design of the insurance industry. A general question which may be asked of all financial institutions is what factors limit the number of layers of paper which can be constructed?
Keywords: Reinsurance, retrocession, strategic market game
We propose a game-theoretic model to study various effects of scale in an insurance market. After reviewing a simple static model, we present a one-period game in which both the buyers and sellers of insurance make strategic bids, and show that, under reasonably broad conditions, market equilibrium exists. For a special case, we then consider how both the price and quantity of insurance, as well as other quantities of interest to public policy decision makers, are affected by the number of insurance firms, the number of customers, and the total amount of capital provided by investors.