Kelsey, David: Games of Complete and Perfect Information with Knightian Uncertainty
World Conference Econometric Society, 2000, Seattle

David Kelsey, University of Birmingham
Games of Complete and Perfect Information with Knightian Uncertainty
Session: C-6-6  Sunday 13 August 2000  by Kelsey, David
We study extensive form games with non-additive beliefs, which we interpret as representing Knightian uncertainty. Dow and Werlang, (JET 1994) defined equilibrium for normal form games with non- additive beliefs. We extend this to a class of extensive form games. The extension is non-trivial since it is necessary to model how beliefs are updated as information is received in the course of play. We use the Dempster-Shafer rule to model this. Updating beliefs potentially creates a dynamic consistency problem. However we are able to prove existence and dynamic consistency of equilibria with non-additive beliefs. Dynamic consistency is a less severe constraint in an extensive form game, since the decision tree is fixed. For games of complete and perfect information we show that a pure equilibrium exists with Knightian uncertainty. We also show that a modified version of backward induction can be applied. Backward induction vastly reduces the complexity of finding an equilibria and hence may prove to be a useful tool.
As an application, we consider problems of entry deterrence. Knight (1921)argued that uncertainty is important for investment decisions. We argue that entering a new industry, is the kind of investment most likely to be affected by uncertainty. In the model, a firm has to decide whether or not to enter an industry with an incumbent monopolist who may respond either by accommodating or fighting entry. Fighting will result in losses to both firms. Thus fighting entry is a non-credible threat. We find a new type of equilibrium. In this the monopolist does not fight. However entry does not occur because the entrant is uncertainty-averse. We provide an alternative argument for eliminating equilibria, in which the monopolist fights, by arguing that they are not robust to the introduction of small amounts of uncertainty.

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