Subgame consistent economic optimization under uncertainty

Abstract

In many economic problems, uncertainty prevails. An essential characteristic of time—and hence decision making over time—is that though the individual may, through the expenditure of resources, gather past and present information, the future is inherently unknown and therefore (in the mathematical sense) uncertain. There is no escape from this fact, regardless of what resources the individual should choose to devote to obtaining data, information, and to forecasting. An empirically meaningful theory must therefore incorporate time-uncertainty in an appropriate manner. This development establishes a framework or paradigm for modeling game-theoretic situations with stochastic dynamics and uncertain environments over time. Again, the noncooperative stochastic differential games discussed in Chap. 2 fail to reflect all the facets of optimal behavior in n-person market games. Therefore cooperative optimization will generally lead to improved outcomes. Moreover, similar to cooperative differential game solutions, dynamically stable solutions of cooperative stochastic differential games have to be consistent over time. In the presence of stochastic elements, a very stringent condition—that of subgame consistency—is required for a credible cooperative solution. In particular, the optimality principle agreed upon at the outset must remain effective in any subgame starting at a later time with a realizable state brought about by prior optimal behavior.