In his classic work, Knight (1921) pointed out an important difference between uncertainty and risk, where risk is characterized by randomness that can be measured precisely. Ellsberg (1961) proposed a more precise definition of uncertainty, in which an event is uncertain or ambiguous if it has unknown probability. Ellsberg’s paradox illustrates important consequences of this distinction by showing that individuals may prefer gambles with precise probabilities to gambles with unknown odds.
Uncertainty and risk are distinct characteristics of random environments, and this distinction has been shown to affect individual decision making. The observation that behavior is often inconsistent with the expected utility model has inspired a significant amount of recent research in economics. In particular, since uncertainty can exert a significant influence on individual behavior, it can also be a significant determinant of equilibrium outcomes.
In this paper, we explore the implications of the presence of uncertainty in games with private information, and study how the introduction of such uncertainty can affect mechanism design problems. The source of uncertainty in the mind of each agent is what other players know. Following Harsanyi (1967), the beliefs of each agent are condensed into the definition of a player’s type. Thus the set of all players’ conceivable types determines a player’s state space. We consider games in which the distinction between uncertainty and risk is formalized by assuming that players may have incomplete preferences over state-contingent payoffs, as in Bewley (1986).
Without completeness, individual decision-making depends on a set of probability distributions over the state space. A state contingent payoff is preferred to another if and only if it yields a larger expected utility for all probability distributions in this set. When preferences are complete this set is a singleton, and the model reduces to the standard Bayesian framework. Since incompleteness of preferences induces multiple probabilities, this approach provides a way of formalizing the distinction between risk and uncertainty which also highlights a connection between the incompleteness of preferences and the perception of uncertainty.
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Uncertainity in Mechanism Design
