The effect of uncertainty on interactive behaviour

The effect of uncertainty in single-agent optimisation models has been widely studied. In contrast, the implications of common uncertainty on the equilibrium outcome of a multi-agent interaction have hardly been analysed. In this paper we focus on a general class of simple non-cooperative games with common uncertainty, in which the players have two argument utility functions. In such games with homogeneous players, under plausible normality conditions, the effect of increased uncertainty on the equilibrium strategies is very similar to its effect on the optimal strategy of a single agent. In games with heterogeneous players, significant differences can arise relative to single-agent situations. We conclude with some remarks on further possible research. One interesting question is the effect of increased uncertainty on the expected utility of the players in the game. For a risk-averse single agent there are two effects; the direct effect of uncertainty holding fixed the agent's choice, and the indirect effect due to the change in the optimal choice as a result of increased uncertainty. In the situations usually considered in the uncertainty literature, both effects lower the agent's utility. In a game, the equilibrium outcome need not be efficient, and therefore the change in equilibrium resulting from increased uncertainty may increase rather than decrease utility due to the indirect effect. This could then dominate a negative direct effect, in which case an increase in uncertainty would lead to an overall increase in utility. When the Nash equilibrium is inefficient, increased uncertainty affects optimal choices and utilities as well as those at equilibrium, and the effect of uncertainty on the gap between optimal and equilibrium values is another important question. For example, in an oligopoly context the gap between equilibrium profits and the maximal level of joint profits is a natural measure of the intensity of firms' incentives to collude. The gap... [ABSTRACT FROM AUTHOR]