Investors implement projects based on idiosyncratic signal observations, without knowing how signals and returns are jointly distributed. The following heuristic is studied: investors collect information on previously implemented projects with the same signal realization, and invest if the associated mean return exceeds the cost. The corresponding steady states result in suboptimal investments, due to selection bias and the heterogeneity of signals across investors. When higher signals are associated with higher returns, investors are overoptimistic, resulting in overinvestment. Rational investors increase the overoptimism of sampling investors, thereby illustrating a negative externality imposed by rational investors.

We consider a repeated interaction between a long-run player and a sequence of short-run players, in which the long-run player may either be rational or may be a mechanical type who plays the same (possibly mixed) action in every stage game. We depart from the classical model in assuming that the short-run players make inferences by analogical reasoning, meaning that they correctly identify the average strategy of each type of long-run player, but do not recognize how this play varies across histories. Concentrating on 2 × 2 games, we provide a characterization of equilibrium payoffs, establishing a payoff bound for the rational long-run player that can be strictly larger than the familiar “Stackelberg” bound. We also provide a characterization of equilibrium behavior, showing that play begins with either a reputation-building or a reputation-spending stage (depending on parameters), followed by a reputation-manipulation stage.

When entry is exogenous, strong buyers should be discriminated against weak buyers to maximize revenues (Myerson 1981). When entry is endogenous so that entrants' expected payoffs do not depend on the proposed mechanism, optimal discrimination takes a completely different form. The revenue-maximizing equilibrium requires that there should be no discrimination with respect to entrants irrespective of their ex ante characteristics. Besides, those buyers who always participate should be discriminated against entrants independently of their strength. These predictions are independent of the equilibrium selection when the number of potential entrants grows large. The optimality of first-price auctions is also discussed.

The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex post implementation, which requires that each agent's strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex post implementable in generic mechanism design frameworks with multidimensional signals, interdependent valuations, and transferable utilities are constant functions. In other words, deterministic ex post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex post implementability of a nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions.