Suppose two agents play a game, each using a computable algorithm to decide what to do, these algorithms being common knowledge. The author shows that it is possible to act rationally provided he limits his attention to a natural subset of solvable games and to opponents who use rational algorithms; the outcome is a Nash equilibrium. Going further, the author shows that rationality is possible on many domains of games and opposing algorithms but each domain requires a particular solution algorithm; no one algorithm is rational on all possible domains. Copyright 1992 by The Econometric Society.

In a recent paper, Acemoglu and Johnson (2007) argue that the large increases in population health witnessed in the 20th century may have lowered income levels. We argue that this result depends crucially on their assumption that initial health and income do not affect subsequent economic growth. Using their data we reject this assumption in favor of a model of conditional convergence, with income adjusting to its steady state over time. We show that, allowing for conditional convergence, exogenous improvements in health due to technical advances associated with the epidemiological transition appear to have increased income levels.