A principal has private information that directly affects her agent's payoff (i.e., "common values" obtains). The authors analyze their relationship as a three-stage game: (1) the principal proposes a contract; (2) the agent accepts or rejects; and (3) the contract is executed. They show that the equilibrium outcomes are the allocations that weakly Pareto dominate the allocation maximizing the payoff of each "type" of the principal within the class of incentive-compatible allocations ensuring the agent his reservation utility irrespective of his beliefs about the principal's type. The authors also characterize the equilibria that are immune to renegotiation.

The authors analyze the principal-agent relationship when the principal has private information as a three-stage game: contract proposal, acceptance/refusal, and contract execution. They assume that the information does not directly affect the agent's payoff (private values). Equilibrium exists and is generically locally unique. Moreover, it is Pareto optimal for the different types of principal. The principal generically does strictly better than when the agent knows her information. Equilibrium allocations are the Walrasian equilibria of an "economy" where the traders are different types of principal and "exchange" the slack on the agent's individual rationality and incentive compatibility constraints.

The authors introduce a class of alternating-move, infinite-horizon models of duopoly. The timing captures the presence of short-run commitment s. They apply this framework to a natural monopoly in which costs are so large that at most one firm can make a profit. The firms install short-run capacity. In the unique symmetric Markov perfect equilibriu m, only one firm is active and practices the quantity analogue of lim it pricing. For commitments of brief duration, the market is almost c ontestable. The authors conclude with a discussion of more general mo dels where the alternating timing is derived rather than imposed.

The authors provide game theoretic foundations for the classic kinke d demand curve and Edgeworth cycle. In their alternating-move model, there are multiple Markov perfect equilibria of both the kinked deman d curve and Edgeworth cycle variety. In any Markov perfect equilibria , profit is bounded away from the Bertrand equilibria level. A kinked demand curve at the monopoly price is the unique symmetric "renegot iation proof" equilibrium when there is little discounting. The auth ors then endogenize the timing by allowing firms to move at any time. They find that firms end up alternating, thus vindicating the fixed timing assumption of the simpler model.

[This paper shows how a number of questions about dominant strategy mechanisms in models with public goods can be conveniently formulated as systems of partial differential equations. The question of the existence of dominant strategy mechanisms with given desirable properties becomes equivalent to the integrability of these equations.]

When either there are only two players or a full dimensionality condition holds, any individually rational payoff vector of a one-shot game of complete information can arise in a equilibrium of the infinitely-repeated game if players are sufficiently patient. In contrast to earlier work, mixed strategies are allowed in determining the individually rational payoffs (even when only realized actions are observable). Any individually rational payoffs of a one-shot game can be approximated by sequential equilibrium payoffs of a long but finite game of incomplete information, where players' payoffs are almost certainly as in the one-shot game. THAT STRATEGIC RIVALRY in a long-term relationship may differ from that of a one-shot game is by now quite a familiar idea. Repeated play allows players to respond to each other's actions, and so each player must consider the reactions of his opponents in making his decision. The fear of retaliation may thus lead to outcomes that otherwise would not occur. The most dramatic expression of this phenomenon is the celebrated for repeated games. An outcome that Pareto dominates the minimax point is called individually rational. The Folk Theorem asserts that any individually rational outcome can arise as a equilibrium in infinitely repeated games with sufficiently little discounting. As Aumann and Shapley [3] and Rubinstein [20] have shown, the same result is true when we replace the word Nash by (subgame) perfect and assume no discounting at all. Because the Aumann-Shapley/Rubinstein result supposes literally no discounting, one may wonder whether the exact counterpart of the Folk Theorem holds for equilibrium, i.e., whether as the discount factor tends to one, the set of equilibrium outcomes converges to the individually rational set. After all, agents in most games of economic interest are not completely patient; the no discounting case is of interest as an approximation. It turns out that this counterpart is false. There can be a discontinuity (formally, a failure of lower hemicontinuity) where the discount factor, 8, equals one, as we show in Example 3. Nonetheless the games in which discontinuities occur are quite degenerate, and, in the end, we can give a qualified yes (Theorem 2) to the question of whether the Folk Theorem holds with discounting. In particular, it always holds in two-player games (Theorem 1). This last result contrasts with the recent work of Radner-Myerson-Maskin [18] showing that, even in two-player games, the equilibrium set may not be continuous at 8 = 1 in

[We characterize a seller's optimal scheme for the sale of an indivisible good to one of n risk averse buyers. We also compare certain commonly used schemes, such as the high bid and second bid auctions, under the hypothesis of risk aversion.]

The authors study repeated games in which players observe a public outcome that imperfectly signals the actions played. They provide conditions guaranteeing that any feasible, individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting. The central condition requires that there exist action profiles with the property that, for any two players, no two deviations--one by either player--give rise to the same probability distribution over public outcomes. The results apply to principal-agent, partnership, oligopoly, and mechanism-design models, and to one-shot games with transferable utilities.