We offer an approach to cooperation in repeated games of private monitoring in which players construct models of their opponents' behavior by observing the frequencies of play in a record of past plays of the game in which actions but not signals are recorded. Players construct models of their opponent's behavior by grouping the histories in the record into a relatively small number of analogy classes for which they estimate probabilities of cooperation. The incomplete record and the limited number of analogy classes lead to misspecified models that provide the incentives to cooperate. We provide conditions for the existence of equilibria supporting cooperation and equilibria supporting high payoffs for some nontrivial analogy partitions.
We examine the evolutionary selection of attitudes toward aggregate risk in an age structured population. Aggregate shocks perturb the population's consumption possibilities. Consumption is converted to fertility via a technology that exhibits first increasing and then decreasing returns to scale, captured in the simplest case by a fertility threshold. We show that evolution will select preferences that exhibit arbitrarily high aversion to aggregate risks with even very small probabilities of sufficiently low outcomes. These findings complement the familiar result that evolution will select for greater aversion to aggregate than idiosyncratic risks by identifying circumstances under which the difference can be extreme.
Decision theory can be used to test the logic of decision making---one may ask whether a given set of decisions can be justified by a decision-theoretic model. Indeed, in principal-agent settings, such justifications may be required---a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain-act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the the Fundamental Theorem of Finance (for the special case of a Bayesian agent) and revealed-preference results.
People reason about uncertainty with deliberately incomplete models, including only the most relevant variables. How do people hampered by diﬀerent, incomplete views of the world learn from each other? We introduce a model of “model-based inference.” Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. We nd that unless the diﬀerences in agents’ models are trivial, interactions will often not lead agents to have common beliefs, and indeed the correct-model belief will typically lie outside the convex hull of the agents’ beliefs. However, if the agents’ models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit some bizarre idiosyncrasies and their information is widely dispersed.
“Crowds” are often regarded as “wiser” than individuals, and prediction markets are often regarded as eﬀective methods for harnessing this wisdom. If the agents in prediction markets are Bayesians who share a common model and prior belief, then the no-trade theorem implies that we should see no trade in the market. But if the agents in the market are not Bayesians who share a common model and prior belief, then it is no longer obvious that the market outcome aggregates or conveys information. In this paper, we examine a stylized prediction market comprised of Bayesian agents whose inferences are based on diﬀerent models of the underlying environment. We explore a basic tension—the diﬀerences in models that give rise to the possibility of trade generally preclude the possibility of perfect information aggregation.
(Contributing editors: Bo Honoré, Ariel Pakes, Monika Piazzesi, Serena Ng, Jesse M. Shapiro, Ulrich K. Müller, Mark W. Watson, Harald Uhlig, Dirk Krueger, Kurt Mitman, Fabrizio Peeri, Johannes Brumm, Felix Kubler, Simon Scheidegger, Jakub Kastl, Ivan A. Canay, Azeem M. Shaikh, Kate Ho, Adam M. Rosen)
This is the second of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montreal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics. The book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their ﬁelds. The second volume addresses topics such as big data, macroeconomics, ﬁnancial markets, and partially identiﬁed models.
(Contributing editors: Bo Honoré, Ariel Pakes, Monika Piazzesi, Alessandro Pavan, Johannes Hörner, Andrzej Skrzypacz, Igal Hendel, Bernard Salanie, Fuhito Kojima, Parag A. Pathak, Sanjeev Goyal, Áureo de Paula, Rachel E. Kranton)
This is the ﬁrst of two volumes containing papers and commentaries presented at the Eleventh World Congress of the Econometric Society, held in Montreal, Canada in August 2015. These papers provide state-of-the-art guides to the most important recent research in economics. The book includes surveys and interpretations of key developments in economics and econometrics, and discussion of future directions for a wide variety of topics, covering both theory and application. These volumes provide a unique, accessible survey of progress on the discipline, written by leading specialists in their ﬁelds. The ﬁrst volume includes theoretical and applied papers addressing topics such as dynamic mechanism design, agency problems, and networks.