To ensure that individual actors take certain actions, community enforcement may be required. This can present a rules-versus-discretion dilemma: it can become impossible to employ discretion based on information that is not widely held, because the wider community is unable to verify how the information was used. Instead, actions may need to conform to simple and widely verifiable rules. We study when discretion in the form of exceptions to a simple rule can be implemented, if the information is shared by the action taker and a second party, who is able to verify for the larger group that an exception is warranted. In particular, we compare protocols where the second party excuses the action taker from taking the action ex ante with protocols where the second party instead forgives a rule-breaking actor ex post.

Imagine that one player, the “incumbent” competes with several “entrants”. Each entrant competes only with the incumbent, but observes play in all contests. Previous work shows that, as more and more entrants are added, the incumbent's reputation may dominate play of the game, if the entrants are faced in sequence. We identify conditions under which similar results obtain when the entrants are faced simultaneously, and we find specifications in which adding more simultaneous entrants has a dramatically different effect. We also show that, with either sequential or simultaneous play, incumbents need not prefer the situation in which their reputations can and do dominate play to the “informationally isolated” case in which each entrant observes only play in its own contest.

[We propose a new criterion for equilibria of extensive games, in the spirit of Selten's perfectness criteria. This criterion requires that players' strategies be sequentially rational: Every decision must be part of an optimal strategy for the remainder of the game. This entails specification of players' beliefs concerning how the game has evolved for each information set, including informaiton sets off the equilibrium path. The properties of sequential equilibria are developed; in particular, we study the topological structure of the set of sequential equilibria. The connections with Selten's trembling-hand perfect equilibria are given.]

I. Introduction, 323.—II. Formulation, 325.—III. An example, 326.—IV. Consistent price schemes, 328.—V. Back to the example, 332.—VI. Relaxing the assumptions, 333.—VII. Concluding remarks, 334.

This paper studies the set of equilibrium payoffs in repeated games with long- and short-run players and little discounting. Because the short-run players are unconcerned about the future, each equilibrium outcome is constrained to lie on their static reaction (best-response) curves. The natural extension of the folk theorem to games of this sort would simply include this constraint in the definitions of the feasible payoffs and minmax values. In fact, this extension does obtain under the assumption that each player's choice of a mixed strategy for the stage game is publicly observable but, in contrast to standard repeated games, the set of equilibrium payoffs is different if players can observe only their opponents' realized actions.

It is sometimes asserted that rational speculative activity must result in more stable prices because speculators buy when prices are low and sell when they are high. This is incorrect. Speculators buy when the chances of price appreciation are high, selling when the chances are low. Speculative activity in an economy in which all agents are rational, have identical priors, and have access to identical information may destabilize prices, under any reasonable definition of destabilization. It takes extremely strong conditions to ensure that speculative activity (of the commodity storage variety) "stabilizes" price, even in a very weak sense.