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Adapting to the entirely unpredictable, and other aspects of dynamic behaviour: beyond von Neumann's standard paradigm in games and economics


Much of social science models multi-person decision problems as non-cooperative games in "strategic form", where each player commits to a single optimal strategy covering all possible eventualities. Von Neumann presumes that this captures all relevant aspects of a general dynamic game. In one-player games, this paradigm entails what moral philosophers call "consequentialism", requiring behaviour to be explicable as the choice of consequences. My previous work shows that this hypothesis implies many properties treated as axioms in orthodox decision theory. Game theorists already relax this "standard paradigm" by, for example, requiring players to respond credibly when others deviate former expected behaviour.

But more drastic relaxation is needed, because in many realistic decision problems or games, the range of all possible uncertain future eventualities must expand over time to include actual events that ex ante had been entirely unpredictable, or at least outside the bounds of any practical model. Then the best current action may no longer be the one with the best pattern of uncertain consequences in the usual sense; instead, the relevant consequence patterns emerge in stages from an evolving retrospective analysis applied to an adapting decision model.

Such evolving consequences can be fitted mathematically within a coherent probabilistic framework embodying all possible relevant results of applying retrospective analysis to a sequence of increasingly detailed models. Apart from new theory, modifying the standard paradigm like this has major implications for models often used to discuss policy. As just one economic example, unforeseen crises could (and did) render unenforceable the Eurozone's original strict Maastricht treaty limits on member states budget deficits. In the end any rigid rule must be expected to break down when faced with unlikely extreme events, outside any practical model, which call for a discretionary policy response.

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