“Evolutionary Games and Matching Rules” NEW WORKING PAPER,
Working Paper 2017:11, Department of Economics, Lund University, 2017.
Joint with Martin Kaae Jensen
(Previous versions have been circulated under the title “Evolutionary Games with Group Selection”) (Revisions requested by the International Journal of Game Theory)
This study considers evolutionary models with non-uniformly random matching when interaction occurs in groups of n≥2 individuals. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy and consequently long-run behavior in the population varies with the frequencies of different group types. These frequencies crucially depend on the particular matching process at hand. Two new equilibrium concepts are introduced: Nash equilibrium under a matching rule (NEMR) and evolutionarily stable strategy under a matching rule (ESSMR). When matching is uniformly random, these reduce to Nash equilibrium and evolutionarily stable strategy, respectively. Several results that are known to hold for population games under uniform random matching carry through to our setting. In our most novel contribution, we derive results on the efficiency of the Nash equilibria of population games and show that for any (fixed) payoff structure, there always exists some matching rule leading to average fitness maximization in NEMR. Finally, we provide a series of applications to commonly studied normal-form games.
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.
Other Work in Progress
In markets for credence goods, better-informed sellers can take advantage of less-informed buyers by providing unnecessary services (overtreatment). This paper considers heterogeneously informed customers who can signal their expertise to an expert. We show how the incentive to signal ones expertise depends on the type of language available to buyers. We consider the cases of i) no language (where the customer cannot send any message), ii) hard evidence (where the customer can choose to disclose or hide information he has but cannot try to fake expertise), and iii) full language/cheap talk (where all messages can be sent by all types). Our results show that, under ii) and iii), full efficiency (i.e. no overtreatment) can be achieved in pooling equilibria where informed customers choose to conceal all of their information. Under ii), they can also choose to partially reveal their information, in which case the uninformed customers are the only ones who may be overtreated. Interestingly, in all other cases, partially informed customers are at least weakly better off hiding their information.
“Can social group-formation norms influence behavior?: An experimental Study” [Slides]
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.
“Coordination and Information Acquisition: An Experiment”
Joint with Maxim Goryunov