My primary research interest is in microeconomic theory, with an emphasis on game theory and decision theory. I have worked on existence of equilibrium in games with payoffs that lack the usual continuity properties, as well as games with imperfect information with neither an a priori order structure nor convexity assumptions on strategy spaces or payoff functions. That work has resulted in several working papers, including a contribution to the fixed point theory of decomposable sets in non-linear analysis. More recently, I have been studying learning and belief formation in an environment in which little information is available to the economic agent and surprises are frequent. I have also been continuously involved in the organization of conferences, workshops, seminars, and minicourses for the Australian National University, many of them multidisciplinary.
On the existence of equilibrium in Bayesian games without complementarities [pdf]
(with Rabee Tourky)
In a recent paper Reny (2011) generalized the results of Athey (2001) and McAdams (2003) on the existence of monotone strategy equilibrium in Bayesian games. Though the generalization is subtle, Reny introduces far-reaching new techniques applying the fixed point theorem of Eilenberg and Montgomery (1946, Theorem 5). This is done by showing that with atomless type spaces the set of monotone functions is an absolute retract and when the values of the best response correspondence are non-empty sub-semilattices of monotone functions, they too are absolute retracts. In this paper we provide an extensive generalization of Reny (2011), McAdams (2003), and Athey (2001). We study the problem of existence of Bayesian equilibrium in pure strategies for a given partially ordered compact subset of strategies. The ordering need not be a semilattice and these strategies need not be monotone. The main innovation is the interplay between the homotopy structures of the order complexes that are the subject of the celebrated work of Quillen (1978), and the hulling of partially ordered sets, an innovation that extends the properties of Reny’s semilattices to the non-lattice setting. We then describe some auctions that illustrate how this framework can be applied to generalize the existing results and extend the class of models for which we can establish existence of equilibrium. As with Reny (2011) our proof utilizes the fixed point theorem in Eilenberg and Montgomery (1946).
Keywords: Bayesian games, monotone strategies, pure-strategy equilibrium, auctions
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 . Motivated by the fixed point problem of Reny  arising in Bayesian games, this paper proves such a theorem.
Keywords: fixed point, decomposable set
- 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.