“A Beauty Contest with Flexible Information Acquisition” [.pdf]
This paper studies beauty-contests with rationally inattentive players. Players are driven by a coordination motive and a fundamental motive. Each player can flexibly acquire information on the fundamental by choosing the probability distribution of her signal while paying a cost linear in the reduction of entropy. A necessary condition is derived for well-behaved equilibria without requiring the fundamental to be normally distributed. Aggregately affine equilibria (AAE) where the average action is an affine function of the fundamental are found to exist only if the fundamental is normally distributed. For a large region of the parameter space, there exists a unique equilibrium within the classes of AAE and equilibria without information acquisition. Interestingly, when the coordination motive is high and for relatively low information costs, there is a multiplicity of equilibria within the classes considered, suggesting that flexible information acquisition technology can be a source of multiple equilibria.
“Evolutionary Games with Group Selection”,
Discussion Papers in Economics 14/09, Department of Economics, University of Leicester, 2014. (Revisions requested by the International Journal of Game Theory)
Joint with Martin Kaae Jensen
This paper introduces two new concepts in evolutionary game theory: Nash equilibrium with Group Selection (NEGS) and Evolutionarily Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, in particular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS and ESSGS are to group selection models (Kerr and Godfrey-Smith, 2002; Bergstrom, 2002) what Nash Equilibrium and ESS are to the standard replicator dynamics: any NEGS is a steady state, any stable steady state is a NEGS, and any ESSGS is asymptotically stable. We also show that all steady states of any haystack/trait-group model (Maynard Smith, 1964; Wilson, 1977; Cooper and Wallace, 2004) are steady states of a group selection model under an appropriately defined matching rule. We proceed to prove what may be called “the second welfare theorem of evolution:” any evolutionary optimum will be a NEGS under some matching rule. Our results are illustrated in a range of Prisoners’ Dilemma games.
Other Work in Progress
“Can social group-formation norms influence behavior?: An experimental Study”
We investigate experimentally the impact of different group formation norms expressed by constant-index-of-assortativity matching rules. We implement a random matching rule as well as an assortative matching rule in a 12-player Hawk-Dove game setting. We test whether the different matching rule implementation affects participant behavior. Our findings suggest that increased assortativity induces lower aggression levels which is consistent with theoretical predictions. More than that, we get evidence of slow convergence towards equilibrium behavior. We also computationally evaluate the predictions of several learning models through simulations.