Bellow are abstracts of my articles on game theory, rationality, learning, and social epistemology. You can find downloadable drafts of the full articles at my academia.edu profile.
The cultural red king hypothesis predicts that differentials in groups size may lead to inequitable outcomes for minority groups even in the absence of explicit or implicit bias. We test this prediction in an experimental context where subjects divided into groups engage in repeated play of a simplified Nash demand game. We run 14 trials involving a total of 112 participants. The results of the experiments are significant and suggestive: individuals in minority groups do indeed end up making low demands more frequently than those in majority groups, and so receive lower payoffs.
News reporting provides us with information essential in forming beliefs regarding matters of public import. These beliefs drive the ways we vote and act. Yet reporting is subject to characteristic distortions. Only sufficiently unusual or extreme events tend to be reported. Events which are reported tend be exaggerated in intensity. Norms of ‘fair-and-balanced’ reporting may give equal weight to positions with asymmetric evidential support. These distortions interact with the individual tendency to differentially accept (reject) news congenial (uncongenial) to prior beliefs. We examine how characteristic distortions in reporting in tandem with confirmation bias can lead to distortions in public belief.
Typically, public discussions of questions of social import exhibit two important properties: (1) they are influenced by conformity bias, and (2) the influence of conformity is expressed via social networks. We examine how social learning on networks proceeds under the influence of conformity bias. In our model, heterogeneous agents express public opinions where those expressions are driven by the competing priorities of accuracy and of conformity to one’s peers. Agents learn, by Bayesian conditionalization, from private evidence from nature, and from the public declarations of other agents. Our key findings are that networks that produce configurations of social relationships that sustain a diversity of opinions empower honest communication and reliable acquisition of true beliefs, and that the networks that do this best turn out to be those which are both less centralized and less connected.
A perennial open question in the theory of games is the extent and conditions under which we can expect rational agents to play the Nash equilibria of games. In “Rational Agents Learn to Play Nash Equilibrium”  Kalai and Lehrer show that Bayesian rational agents whose priors satisfy the ‘absolute continuity’ condition learn to play the Nash equilibria of games. In response to this result, Foster and Young, in “The Impossibility of Prediction the Behavior of Rational Agents,”  provide an impossibility theorem demonstrating the ‘non-robustness’ of Bayesian learning—they show that, in games containing near-zero-sum subgames, agents cannot be simultaneously rational and also learn to accurately predict the strategies of other players, and so cannot play the Nash equilibria of these games. We explain the relation between the two results, and demonstrate that, with natural extensions of Foster & Young’s assumptions, rational agents may once again learn to play Nash. We demonstrate that Bayesian learning provides a more robust justification of the rationality of Nash than Foster & Young suggest.
We consider how an epistemic network might self-assemble from the ritualization of the decisions of individual inquirers with varying abilities. In such evolved social networks, the heterogeneous agents may be significantly more successful than they could be investigating nature on their own. The evolved networks may also dramatically lower the epistemic risk faced by even the most talented inquirers. We consider networks that self-assemble in the context of both perfect and imperfect communication and compare the evolved behavior of inquirers in each.
The replicator dynamics and Moran process are the main deterministic and stochastic models of evolutionary game theory. These models are connected by a mean-field relationship—the former describes the expected behavior of the latter. However, there are conditions under which their predictions diverge. I demonstrate that the divergence between their predictions is a function of standard techniques used in their analysis, and of differences in the idealizations involved in each. My analysis reveals problems for stochastic stability analysis in a broad class of games. I also demonstrate a novel domain of agreement between the dynamics, and draw a broader methodological moral for evolutionary modeling.
Within the framework of evolutionary game theory, equilibrium concepts adapted from rational choice game theory are employed to identify the probable outcomes of evolutionary processes. Over the last several decades results have emerged in the literature demonstrating limitations to each of the proposed equilibrium concepts. These results rely on an undefined notion of evolutionary significance. We explicitly define evolutionary significance for evolutionary games. This definition enables an analysis of the success of equilibrium concepts across different models of evolution. We demonstrate that even under favorable assumptions as to the underlying dynamics and stability concept—the replicator dynamics and asymptotic stability—each equilibrium concept makes errors of both omission and commission.