Learning under floating-point genetic algorithms, with an application to insurance markets.

摘要

This work begins by discussing previous applications of genetic algorithms (GAs). It then moves on to explore the differences between binary and floating-point GAs, focusing on the implications of each as a learning framework for applications in economics. It shows that binary GAs have undesirable properties as learning algorithms whenever the underlying objects being learned are real numbers. In particular, under both the standard binary encoding and the Gray encoding of binary numbers, the mutations induced by binary GAs do not have smooth densities, they are often biased, and their variances often depend on the point being mutated. These properties seem at odds with reasonable methods of trial and error on the part of economic actors. As an alternative, a floating-point GA is developed.; The work then applies such a floating-point GA to an insurance model in which the principals who underwrite insurance contracts cannot observe the risk characteristics of the agents who sign those contracts. Under perfect rationality, the equilibria of this model are analogous to those in the 1976 paper by Rothschild and Stiglitz. The learning version of the model exhibits interesting transition dynamics as well as novel outcomes. When the learning model converges to the equilibrium from the model with perfect rationality, pooling contracts break down over time and the set of contracts bifurcates, with one group of principals serving high-risk agents and another group serving low-risk agents. When there are relatively few low-risk agents in the market, the economy converges to contracts that provide full insurance for high-risk agents, while low-risk agents do not get served at all. When there are relatively few high-risk agents in the market, some types of pooling contracts are sustainable. These last two results are at odds with the outcomes that obtain under models of perfect rationality.