The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty.
We study the “ex post equivalence” question: when is interim implementation on all possible type spaces equivalent to requiring ex post implementation on the space of payoff types? We show that ex post equivalence holds when the social choice correspondence is a function and in simple quasi-linear environments. When ex post equivalence holds, we identify how large the type space must be to obtain the equivalence. We also show that ex post equivalence fails in general, including in quasi-linear environments with budget balance.
For quasi-linear environments, we provide an exact characterization of when interim implementation is possible in rich type spaces. In this environment, the planner can fully extract players’ belief types, so the incentive constraints reduce to conditions distinguishing types with the same beliefs about others’ types but different payoff types.
The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces, with more higher order uncertainty.
We study the “ex post equivalence” question: when is interim implementation on all possible type spaces equivalent to requiring ex post implementation on the space of payoff types? We show that ex post equivalence holds when the social choice correspondence is a function and in simple quasi-linear environments. When ex post equivalence holds, we identify how large the type space must be to obtain the equivalence. We also show that ex post equivalence fails in general, including in quasi-linear environments with budget balance.
For quasi-linear environments, we provide an exact characterization of when interim implementation is possible in rich type spaces. In this environment, the planner can fully extract players’ belief types, so the incentive constraints reduce to conditions distinguishing types with the same beliefs about others’ types but different payoff types.
Keywords: Mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex-post equilibrium, Dominant strategies
We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.
We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.
Keywords: Dynamic competition, Marginal contribution, Markov perfect equilibrium, Common agency
We consider the provision of venture capital in a dynamic model with multiple research stages, where time and investment needed to meet each benchmark are unknown. The allocation of funds is subject moral hazard. The optimal contract provides for incentive payments linked to attaining the next benchmark, which must be increasing in the funding horizon of each stage. Benchmarking reduces agency costs, directly by shortening the agent’s guaranteed funding horizon, and indirectly via an implicit incentive effect of information rents in future financing rounds.
The ex ante need to provide incentives and the venture capitalist’s desire to cut information rents ex post create a hold-up conflict, which can be overcome by providing all funds in every stage in a single up-front payment. Empirical patterns of the evolution of financing rounds and research intensity over the lifetime of a project are explained as optimal choices: the optimal capital allocated and the funding horizon are increasing from one stage to the next. This emphasizes the notion that early stages are the riskiest in an innovative venture.
A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.
A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.
Keywords: Optimal Auction, Private Values, Information Structures, Partitions
This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion.
The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices.
The robustness of these results with respect to different model specifications is discussed.
This paper considers the financing of a research project under uncertainty about the time of completion and the probability of eventual success. We distinguish between two financing modes, namely relationship financing, where the allocation decision of the entrepreneur is observable, and arm’s length financing, where it is unobservable.
We find that equilibrium funding stops altogether too early relative to the efficient stopping time in both financing modes. The rate at which funding is released becomes tighter over time under relationship financing, and looser under arm’s length financing. The trade-off in the choice of financing modes is between lack of commitment with relationship financing and information rents with arm’s length financing.
This paper considers the financing of a research project under uncertainty about the time of completion and the probability of eventual success. The uncertainty about future success gradually diminishes with the arrival of addtional funding. The entrepreneur controls the funds and can divert them. We distinguish between relationship financing, meaning that the entrepreneur’s allocation of the funds is observable, and arm’s length financing, where it is unobservable.
We find that equilibrium funding stops altogether too early relative to the efficient stopping time in both financing modes. We characterize the optimal contracts and equilibrium funding decisions. The financial constraints will typically become tighter over time under relationship finance, and looser under arm’s length financing. The trade-off is that while relationship financing may require smaller information rents, arm’s length financing amounts to an implicit commitment to a finite funding horizon. The lack of such a commitment under relationship financing implies that the sustainable release of funds eventually slows down. We obtain the surprising result that arm’s length contracts are preferable in a Pareto sense.
This paper considers the financing of a research project under uncertainty about the time of completion and the probability of eventual success. The uncertainty about future success gradually diminishes with the arrival of addtional funding. The entrepreneur controls the funds and can divert them. We distinguish between relationship financing, meaning that the entrepreneur’s allocation of the funds is observable, and arm’s length financing, where it is unobservable.
We find that equilibrium funding stops altogether too early relative to the efficient stopping time in both financing modes. We characterize the optimal contracts and equilibrium funding decisions. The financial constraints will typically become tighter over time under relationship finance, and looser under arm’s length financing. The trade-off is that while relationship financing may require smaller information rents, arm’s length financing amounts to an implicit commitment to a finite funding horizon. The lack of such a commitment under relationship financing implies that the sustainable release of funds eventually slows down. We obtain the surprising result that arm’s length contracts are preferable in a Pareto sense.
This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion.
The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices.
The robustness of these results with respect to different model specifications is discussed.