Reverse AGT Workshop: "Competition in Selection Markets"
About this series:
At the Reverse AGT Workshop local economists will present an area of economic study for an algorithmic game theory (AGT) audience. The presentations will include a brief introduction to the area and several current research topics. The schedule includes ample time for discussion to make connections to related research in AGT and to highlight research questions that methods from AGT might help to answer. This series is organized by Glen Weyl, Brendan Lucier, and Jason Hartline.
In many markets, especially for insurance and financial products, the value of a sale depends on the identity of the customer, as this determines the chance of their, e.g., getting sick or defaulting on a loan. Competition between firms (e.g., insurance companies, banks) for customers may lead to inefficiencies, even complete market collapse, in such markets as firms are not sensitive to the costs their actions have on other firms. For example, a firm may design products to selectively attract ("cream-skim") the safe customers, which worsens the pool of remaining customers. This can cause the market to unravel.
Economists have taken two contrasting, but complementary, approaches to studying these issues. The first, dominant from the 1970's through the mid-2000's, assumed customers differed only along a single dimension like health risk and studied equilibrium when firms perfectly compete and offer arbitrarily complicated mechanisms. Nathan Hendren will present some classic results from this "game theoretic" approach. In the last decade, economists have been interested in a "price theoretic" approach where firms use very simple strategies, like offering a single, standard insurance contract, but where they compete in a more realistic environment where they have market power or when customers differ along multiple dimensions such as their income as well as their health. Glen Weyl will present this approach. Eduardo Azevedo will present his joint work with Daniel Gottlieb, which tries to bridge these approaches with a new perfectly competitive solution concept that exists generally, applies in settings with multiple dimensions of consumer heterogeneity but allows for a rich range of contracts to be traded.
1:45: Coffee and cookies
2:00: Nathaniel Hendren: Unraveling and Equilibrium in Insurance Markets
2:30: Q/A and discussion
2:45: Glen Weyl: The Price Theory of Selection Markets
3:15: Q/A and discussion
3:30: Eduardo M. Azevedo: Perfect Competition in Markets with Adverse Selection
4:00: Q/A and discussion
4:15: Coffee and cookies
4:45: Summary discussion and closing comments
Unraveling and Equilibrium in Insurance Markets
Nathaniel Hendren (Harvard, Economics)
The talk will discuss issues arising in competition in selection markets, with a focus on binary insurance environments. In these contexts, classic papers by Akerlof (1970) and Rothschild and Stiglitz (1976) show that insurance markets may “unravel”. I clarify the distinction between these two notions of unraveling. We show that the two concepts are mutually exclusive occurrences. Moreover, we provide a regularity condition under which the two concepts are exhaustive of the set of possible occurrences in the model. Akerlof unraveling characterizes when there are no gains to trade; Rothschild and Stiglitz unraveling shows that the standard notion of competition (pure strategy Nash equilibrium) is inadequate to describe the workings of insurance markets when there are gains to trade. I discuss other equilibrium concepts that have arisen in the past 40 years to deal with the Rothschild and Stiglitz non-existence problem.
The Price Theory of Selection Markets
E. Glen Weyl (Microsoft Research)
I will discuss recent advances in studying selection markets, ones where the value of a sale to a firm depends on the identity of the customer it sells to, based on a price theoretic approach pioneered by Einav, Finkelstein and Levin. The first generations of work on selection considered simple environments (a binary loss, single-dimensional heterogeneity and perfect competition) and derived surprising conclusions about market unravelling and equilibrium non-existence when firms and offer arbitrary mechanisms to consumers. The price theoretic approach investigates the robustness and empirical magnitude of these insights in richer environments by restricting firms to offer simple "realistic" contracts differing only in their prices and/or another tightly parameterized characteristic. Results from this literature often contrast with pre-existing conventional wisdom, suggesting that multidimensional heterogeneity may lessen selection in some cases and that imperfect competition may be, and may make selection, beneficial.
Perfect Competition in Markets with Adverse Selection
Eduardo M. Azevedo (U. Penn, Wharton)
Policy makers and economists consider adverse selection an important problem. Governments typically respond with complicated regulations, which include mandates, community rating, subsidies, risk adjustment, and regulation of contract characteristics. This paper proposes a perfectly competitive model of adverse selection. Most existing models are particular cases, but I will consider a solution concept where prices are determined by firms making no profits, and the set of transacted contracts is determined by entry into new contracts being unprofitable. Crucially for the applications, contract characteristics are determined endogenously, equilibria always exist, and consumers can differ across more than one dimension. We apply the model to show that mandates can increase efficiency, but may have unintended consequences, getting more consumers to purchase insurance but potentially increasing adverse selection between different levels of coverage. Joint work with Daniel Gottlieb.