Rational herd behavior and informationally efficient security prices have long been considered to be mutually exclusive but for exceptional cases. In this paper we describe the conditions on the underlying information structure that are necessary and sufficient for informational herding and contrarianism. In a standard sequential security trading model, subject to sufficient noise trading, people herd if and only if, loosely, their information is sufficiently dispersed so that they consider extreme outcomes more likely than moderate ones. Likewise, people act as contrarians if and only if their information leads them to concentrate on middle values. Both herding and contrarianism generate more volatile prices, and they lower liquidity. They are also resilient phenomena, although by themselves herding trades are self-enforcing whereas contrarian trades are self-defeating. We complete the characterization by providing conditions for the absence of herding and contrarianism.

This paper examines repeated implementation of a social choice function (SCF) with infinitely lived agents whose preferences are determined randomly in each period. An SCF is repeatedly implementable in Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that its Nash equilibrium set is nonempty and every equilibrium outcome path results in the desired social choice at every possible history of past play and realizations of uncertainty. We show, with minor qualifications, that in the complete information environment an SCF is repeatedly implementable in Nash equilibrium if and only if it is efficient. We also discuss several extensions of our analysis.

Extensive-form market games typically have a large number of noncompetitive equilibria. In this paper, we argue that the complexity of noncompetitive behavior provides a justification for competitive equilibrium in the sense that if rational agents have an aversion to complexity (at the margin), then maximizing behavior will result in simple behavioral rules and hence in a competitive outcome. For this purpose, we use a class of extensive-form dynamic matching and bargaining games with a finite number of agents. In particular, we consider markets with heterogeneous buyers and sellers and deterministic, exogenous, sequential matching rules, although the results can be extended to other matching processes. If the complexity costs of implementing strategies enter players’ preferences lexicographically with the standard payoff, then every equilibrium strategy profile induces a competitive outcome.

We investigate the effect of introducing costs of complexity in the n-person unanimity bargaining game. As is well-known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n-player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.

A common interest game is a game in which there exists a unique pair of payoffs which strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game. We show that if supergame strategies are restricted to be computable within Church's thesis, the only pair of payoffs which survives any computable tremble with sufficiently large support is the Pareto-efficient pair. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future.