We present a dynamic model of venture capital financing, described as a sequential investment problem with uncertain outcome. Each venture has a critical, but unknown threshold beyond which it cannot progress. If the threshold is reached before the completion of the project, then the project fails, otherwise it succeeds. The investors decide sequentially about the speed of the investment and the optimal path of staged investments. We derive the dynamically optimal funding policy in response to the arrival of information during the development of the venture. We develop three types of predictions from our theoretical model and test these predictions in a large sample of venture capital investments in the U.S. for the period of 1987-2002.
First, the investment flow starts low if the failure risk is high and accelerates as the projects mature. Second, the investment flow reacts positively to information that arrives while the project is developed. We find that the investment decisions are more sensitive to the information received during the development than to the information held prior to the project launch. Third, investors distribute their investments over more funding rounds if the failure risk is larger.
We analyze sequential investment decisions in an innovative project that depend on the investor’s information about the project failure risk and its potential final value. We consider the feedback effects between learning about the project parameters and the continuous adjustment of the investment strategy. Investors decide sequentially about the speed of investment and the optimal degree of involvement. We develop three types of predictions from our theoretical model and test these predictions in a large sample of venture capital investment in the U.S. for the period of 1987-2002.
First, the investment flow starts cautiously if the failure risk is high and accelerates as the projects mature. Second, the investment flow reacts positively to information that arrives while the project is developed. We find that interim information is more significant for investment decisions than the information prior to the project launch. Third, investors distribute their investments over more funding rounds if the failure risk is larger.
We present a dynamic model of venture capital financing, described as a sequential investment problem with uncertain outcome. Each venture has a critical, but unknown threshold beyond which it cannot progress. If the threshold is reached before the completion of the project, then the project fails, otherwise it succeeds. The investors decide sequentially about the speed of the investment and the optimal path of staged investments. We derive the dynamically optimal funding policy in response to the arrival of information during the development of the venture. We develop three types of predictions from our theoretical model and test these predictions in a large sample of venture capital investments in the U.S. for the period of 1987-2002.
First, the investment flow starts low if the failure risk is high and accelerates as the projects mature. Second, the investment flow reacts positively to information that arrives while the project is developed. We find that the investment decisions are more sensitive to the information received during the development than to the information held prior to the project launch. Third, investors distribute their investments over more funding rounds if the failure risk is larger.
We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions.
We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. We show that the dynamic pivot mechanism is equivalent to a modified second price auction.
We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions.
We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. The dynamic pivot mechanism here is equivalent to a modified second price auction.
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.
Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.
Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.
We consider the role of the common prior for robust implementation in an environment with interdependent values. Specifically, we investigate a model of public good provision which allows for negative and positive informational externalities. In the corresponding direct mechanism, the agents’ reporting strategies are strategic complements with negative informational externalities and strategic substitutes with positive informational externalities.
We derive the necessary and sufficient conditions for robust implementation in common prior type spaces and contrast this with our earlier results without the common prior. In the case of strategic complements the necessary and sufficient conditions for robust implementation do not depend on the existence of a common prior. In contrast, with strategic substitutes, the implementation conditions are much weaker under the common prior assumption.
We consider the problem of pricing a single object when the seller has only minimal information about the true valuation of the buyer. Specifically, the seller only knows the support of the possible valuations and has no further distributional information.
The seller is solving this choice problem under uncertainty by minimizing her regret. The pricing policy hedges against uncertainty by randomizing over a range of prices. The support of the pricing policy is bounded away from zero. Buyers with low valuations cannot generate substantial regret and are priced out of the market. We generalize the pricing policy without priors to encompass many buyers and many qualities.
We consider the following belief free solution concepts for games with incomplete information: (i) incomplete information rationalizability, (ii) incomplete information correlated equilibrium and (iii) ex post equilibrium. We present epistemic foundations for these solution concepts and establish relationships between them. The properties of these solution concepts are further developed in supermodular games and potential games.
We consider the role of the common prior for robust implementation in an environment with interdependent values. Specifically, we investigate a model of public good provision which allows for negative and positive informational externalities. In the corresponding direct mechanism, the agents’ reporting strategies are strategic complements with negative informational externalities and strategic substitutes with positive informational externalities.
We derive the necessary and sufficient conditions for robust implementation in common prior type spaces and contrast this with our earlier results without the common prior. In the case of strategic complements the necessary and sufficient conditions for robust implementation do not depend on the existence of a common prior. In contrast, with strategic substitutes, the implementation conditions are much weaker under the common prior assumption.
Keywords: Common prior, Correlated equilibrium, Ex post equilibrium, Mechanism design, Robust implementation, Rationalizability, Strategic complements, Strategic substitutes, Uniqueness