I am currently working on a variety of projects centered around the question of existence of equilibrium in the presence of incomplete information. I started studying sufficient conditions for existence of Bayesian equilibria in games without neither an *a priori* order structure nor convexity assumptions on strategy spaces or payoff functions. That work resulted in several working papers, including a contribution to the fixed point theory of decomposable sets in non-linear analysis. I would be delighted to receive comments on any of my current projects.

# Working papers

### A fixed point theorem for closed-graphed decomposable-valued correspondences [pdf]

with Rabee Tourky

Extending the fixed-point theorem of Cellina–Fryszkowski [1, 7], which is for functions on decomposable sets, to decomposable-set-valued correspondences has been an unresolved challenge since the early attempt of Cellina, Colombo, and Fonda [2]. Motivated by the fixed point problem of Reny [12] arising in Bayesian games, this paper proves such a theorem.

Keywords:fixed point, decomposable set

### A theory of robust experiments for choice under uncertainty [pdf]

with Simon Grant, Jeff Kline, John Quiggin and Rabee Tourky

Thought experiments are commonly used in the theory of behavior in the presence of risk and uncertainty to test the plausibility of proposed axiomatic postulates. The prototypical examples of the former are the Allais experiments and of the latter are the Ellsberg experiments. Although the lotteries from the former have objectively specified probabilities, the participants in both kinds of experiments may be susceptible to small deviations in their subjective beliefs. These may result from a variety of factors that are difficult to check in an experimental setting: including deviations in the understanding and trust regarding the experiment, its instructions and its method. Intuitively, an experiment is robust if it is tolerant to small deviations in subjective beliefs in models that are in an appropriate way close to the modeler’s model. The contribution of this paper lies in the formalization of these ideas.

Keywords:Ellsberg experiment, Allais experiment, subjective belief

# Publications

Barelli, P. and Meneghel, I. (2013). A note on the equilibrium existence problem in discontinuous games. Econometrica, 81 (2), pp. 813-824.

Grant, S., Meneghel, I. and Tourky, R. (2015). Savage games. Theoretical Economics, forthcoming.