This paper studies n-player games where players beliefs about their opponents behaviour are modelled as non-additive probabilities. The concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibriumnotion of Dowand Werlang (1994) to n-player games in strategic form. Existence of such an equilibrium is demonstrated under usual conditions. For low degrees of ambiguity, equilibria under uncertainty approximate Nash equilibria. At the other extreme, with a low degree of confidence, maximin equilibria appear. Finally, robustness against a lack of confidence may be viewed as a refinement for Nash equilibria.JEL Codes: C72, D81.

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be non-monotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant non-linear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.

We apply Pires's coherence property between unconditional and conditional preferences that admit a CEU representation. In conjunction with consequentialism (only those outcomes on states which are still possible can matter for conditional preference) this implies that the conditional preference may be obtained from the unconditional preference by taking the Full Bayesian Update of the capacity.

In this paper we show that while individuals with non-additive beliefs may display a strict preference for randomisation in an Anscombe Aumann framework, they will not do so in a Savage-style decision theory. Moreover they will be indifferent to randomisation, unless they have strict preferences between two randomising devices with the same probabilities. We argue that this is related to the distinction between one-and two-stage Choquet integrals. We believe our result will have implications for determining a solution concept for games with uncertainty-averse players.

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