My recent research focuses on exploring how sensitive are the conceptual frameworks, mathematical methods and tools that economists use to conduct research against contingencies. This idea has led me to work on the mathematical and statistical foundations of Decision Theory and Game Theory, resulting in a range of projects that cover a fairly extensive variety of seemingly unrelated topics in Economics. One of my first projects investigated minimal conditions for existence of equilibrium in games with payoffs that lack the usual continuity properties. I have also described the existence of equilibria in games with imperfect information with neither an *a priori* order structure nor convexity assumptions on strategy spaces or payoff functions. That work resulted in several working papers, which required a contribution to the fixed point theory of decomposable sets in non-linear analysis. I have studied how sensitive the conclusions of an experiment are with respect to the characteristics of the benchmark model of beliefs used by the analyst. More recently, I also have been drawn to the study of consistency properties of belief formation in an environment in which little if any information is available.

### Working papers

**Learning under unawareness [pdf]**

(with Simon Grant and Rabee Tourky)

This paper proposes a model of learning when experimentation is possible, but unawareness and ambiguity matter. In this model, complete lack of information regarding the underlying data generating process is expressed as a (maximal) family of priors. These priors yield posterior inferences that become more precise as more information is available. As information accumulates, the decision maker’s level of awareness as encoded in the state space expands. Newly learned states are initially seen as ambiguous, but as evidence accumulates there is a gradual reduction of ambiguity.

**Keywords:** learning, ambiguity, unawareness

**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

### Publications

- Grant, S., Kline, J., Meneghel, I., Quiggin, J., and Tourky, R. (2016). “A theory of robust experiments for choice under uncertainty.”
*Journal of Economic Theory*, 165, pp. 124-151. - Grant, S., Meneghel, I., and Tourky, R. (2016). “Savage games.”
*Theoretical Economics*, 1 (2), pp. 641-682. - Barelli, P. and Meneghel, I. (2013). “A note on the equilibrium existence problem in discontinuous games.”
*Econometrica*, 81 (2), pp. 813-824.