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.
We analyze a model in which agents make investments and then match into pairs to create a surplus. The agents can make transfers to reallocate their pretransfer ownership claims on the surplus. Mailath, Postlewaite and Samuelson (2013) showed that when investments are unobservable, equilibrium investments are generally ineﬀicient. In this paper we work with a more structured model that is suﬀiciently tractable to analyze the nature of the investment ineﬀiciencies. We provide conditions under which investment is ineﬀiciently high or low and conditions under which changes in the pretransfer ownership claims on the surplus will be Pareto improving, as well as examine how the degree of heterogeneity on either side of the market aﬀects investment eﬀiciency.
“Buy local” arrangements encourage members of a community or group to patronize one another rather than the external economy. They range from formal mechanisms such as local currencies to informal “I’ll buy from you if you buy from me” arrangements, and are often championed on social or environmental grounds. We show that in a monopolistically competitive economy, buy local arrangements can have salutary eﬀects even for selﬁsh agents immune to social or environmental considerations. Buy local arrangements eﬀectively allow ﬁrms to exploit the equilibrium price-cost gap to proﬁtably expand their sales at the going price.
Diﬀerent markets are cleared by diﬀerent types of prices — seller-speciﬁc prices that are uniform across buyers in some markets, and personalized prices tailored to the buyer in others. We examine a setting in which buyers and sellers make investments before matching in a competitive market. We introduce the notion of premuneration values — the values to the transacting agents prior to any transfers — created by a buyer-seller match. Personalized price equilibrium outcomes are independent of premuneration values and exhibit ineﬀiciencies only in the event of “coordination failures,” while uniform-price equilibria depend on premuneration values and in general feature ineﬀicient investments even without coordination failures. There is thus a trade-oﬀ between the costs of personalizing prices and the ineﬀicient investments under uniform prices. We characterize the premuneration values under which uniform-price equilibria similarly exhibit ineﬀiciencies only in the event of coordination failures.
Diﬀerent markets are cleared by diﬀerent types of prices — a universal price for all buyers and sellers in some markets, seller-speciﬁc prices that are uniform across buyers in others, and personalized prices tailored to both the buyer and the seller in yet others. We introduce the notion of premuneration values — the values in the absence of any muneration (payments) — created by the buyer-seller match. We characterize the premuneration values under which uniform-price and personalized-price equilibria agree. In this case, we have eﬀicient allocations, including pre-match investment decisions, without the costs of personalized pricing. We then examine the ineﬀiciencies that arise when the premuneration values preclude the agreement of uniform-price and personalized-price equilibria. We view premuneration values as an important consideration in market design.
Extreme adverse selection arises when private information has unbounded support, and market breakdown occurs when no trade is the only equilibrium outcome. We study extreme adverse selection via the limit behavior of a ﬁnancial market as the support of private information converges to an unbounded support. A necessary and suﬀicient condition for market breakdown is obtained. If the condition fails, then there exists competitive market behavior that converges to positive levels of trade whenever it is ﬁrst best to have trade. When the condition fails, no feasible (competitive or not) market behavior converges to positive levels of trade.
Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public-monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are suﬀicient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.