The main result of this paper is that the multiple equilibrium problem in mechanism design can be avoided in private-value models if agents do not use weakly dominated strategies in equilibrium. We show that in such settings, any incentive-compatible allocation rule can be made the unique equilibrium outcome to a mechanism. We derive a general necessary condition for unique implementation that implies that the positive result for private-value models applies with considerably less generality to common-value settings.
A Cournot model of oligopoly in which otherwise identical firms have private differential information about the common cost of production and a shared (but unknown) demand curve is examined. A Bayesian equilibrium of the corresponding game of incomplete information is solved for explicitly and analysed. In the symmetric equilibrium, different firms produce at different output levels because they have different information. Because the information individual firms have is random, total output and hence market price is also random for any finite number of firms. The main result of the paper relates to the asymptotic properties of the equilibrium, when the number of firms becomes large. Under fairly general conditions on the joint distribution of demand and individual firms' information about demand, the random equilibrium price converges almost surely to a constant in the limit. More importantly, this price equals the perfectly competitive price. In other words, in large markets, even if no firm knows the true market demand curve and firms are not price-takers and do not use price as a signal to improve their information, the competitive price will prevail with certainty. In the limit, aggregate outcomes are as if all firms shared their private information with each other.
This paper examines spatial equilibrium in political competition when established parties choose their platforms competitively while rationally anticipating entry of a vote-maximizing third party. The resulting equilibrium is substantially different from the Hotelling "median" equilibrium. Established parties are spatially separated and third parties will generally lose the election. This provides one theoretical explanation for the stability of two-party systems. Namely that non-cooperative behavior between established parties can effectively prevent third parties from winning.
We report the results of voluntary contributions experiments where subjects are randomly assigned different rates of return from their private consumption. These random assignments are changed round to round, enabling the measurement of individual player contribution rates as a function of that player's investment cost. We directly test these response functions for the presence of warm-glow and/or altruism effects. We find significant evidence for heterogeneous warm-glow effects that are, on average, low in magnitude. We statistically reject the presence of an altruism effect.
This paper analyzes bundling decisions of a rnultiproduct monopolist facing uncertain demand. The monopolist sells his products using an auction mechanism and the market is analyzed as a game with incomplete information in which the buyers as well as the seller are strategic agents. With a small number of buyers, a profit maximizing seller will bundle all his output. This makes buyers uniformly worse off compared to the case where the same monopolist does not bundle, in the sense that any buyer is worse off regardless of his demand for the monopolist's outputs. With a larger number of buyers, the seller will have a tendency to unbundle his output and "high-demand" buyers are worse off than they would be if the monopolist bundled his output. "Low-demand" buyers. on the other hand. are always better off when the monopolist unbundles his output, regardless of the number of competing buyers. Despite the fact that "high demand" buyers are the typical purchasers of the monopolist's output, the net effect of increasing the number of buyers is greater market efficiency since bundling creates market inefficiencies both ex post and ex ante.
We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts.
In this paper, we analyze the problem of designing incentive compatible mechanisms in pure exchange economic environments when agents have incomplete information. The equilibrium concept employed is Bayesian Nash equilibrium and the notion of implemantation is full implementation, which is stronger than the more commonly employed notion of truthful implementation. An allocation rule is truthfully implementable if there exists a direct mechanism to which truth telling is an equilibrium and which yields the allocation rule as its truthful equilibrium outcome. An allocation rule is fully implementable if there exists mechanism which yields the allocation rule as its unique equilibrium outcome. More generally, a set of allocation rules, or a social choice set, is fully implementable if there exist a mechanism whose equilibrium outcomes coincide with the set. This stronger notion of implemention avoids the well known problems of multiple equilibria which arise in direct revelation games. We develop a condition, termed Bayesian monotonicity, which we show is necessary for full implementation. An incentive compatibility condition is also necessary. We prove that Bayesian monotonicity and a slightly stronger incentive compatibility condition are sufficient for full implementation when there are at least three agents. We present several examples of allocation rules which do and do not satisfy our condition. One example is that of an allocation rule which is fully inplementable by an indirect mechanism, but for which every equivalent direct mechanism has multiple equilibrium outcomes.
In this paper, we consider the following classical public goods problem. A group of individuals must decide on a level of public good that is produced according to constant returns to scale up to some capacity constraint. In addition to deciding the level of public good, the group must decide how to tax the individuals in the group in order to cover the cost. The distribution of the burden of taxation is important because different individuals have different marginal rates of substitution between the private good (taxes) and the public good, and may have different incomes as well. These individual marginal rates of substitution are private information; that is, each individual knows his or her own marginal rate of substitution, but not those of the other members of the group. Adopting a Bayesian mechanism design framework, we assume that the distribution of marginal rates of substitution is common knowledge.
The authors report the results of voluntary contributions experiments where subjects are randomly assigned different rates of return from their private consumption. These random assignments are changed round to round, enabling the measurement of individual player contribution rates as a function of that player's investment cost. The authors directly test these response functions for the presence of warm-glow and/or altruism effects. They find significant evidence for heterogeneous warm-glow effects that are, on average, low in magnitude. The authors statistically reject the presence of an altruism effect.