Juuso Toikka

Dynamic mechanism design: : a myersonian approach

We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agents equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by “impulse response functions.” The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (“revenue equivalence”). Third, we characterize perfect Bayesian equilibrium‐implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (“bandit auctions”).

Simultaneous Model of Innovation, Secrecy, and Patent Policy

Multiple innovators can and do come up with the same invention independently. A famous case is the telephone: two hours after Alexander Graham Bell filed a patent application for it, another application for the same invention arrived at the patent office. Many scholars, such as Ilkka Rahnasto (2003) and Hal R. Varian et al. (2004), argue that since Bell’s time, simultaneous innovation has become increasingly common. We feel, and our discussions with industry practitioners confirm, that the simultaneous model of innovation characterizes especially network industries such as consumer electronics, the Internet, software, telecommunications, and payment systems, where standardization limits the possible paths for future technologies and so firms concentrate their R&D activities on the same fields. We suggest that simultaneous or independent invention has major implications for intellectual property (IP) policy. In particular, the possibility of simultaneous innovation changes the patenting decision: firms tap patents for a defensive purpose, since the choice is no longer between patenting or resorting to trade secrecy, but between patenting or letting competitors patent. By exploiting the vulnerability of innovative firms to rival innovation, it is possible to design a welfareimproving patent system that induces innovators to patent rather than keep their innovations secret. Taking the simultaneous nature of innovation seriously also changes the way one should think about the relationship between IP and competition policies.

Ironing Without Control

I extend Myersonʼs [R. Myerson, Optimal auction design, Math. Oper. Res. 6 (1981) 58–73] ironing technique to more general objective functions. The approach is based on a generalized notion of virtual surplus which can be maximized pointwise even when the monotonicity constraint implied by incentive compatibility binds. It is applicable to quasilinear principal-agent models where the standard virtual surplus is weakly concave in the allocation or appropriately separable in the allocation and type. No assumptions on allocation rules are required beyond monotonicity.

Value of Persistent Information

We develop a theory of how the value of an agents information advantage depends on the persistence of information. We focus on strategic situations with strict conflict of interest, formalized as stochastic zero‐sum games where only one of the players observes the state that evolves according to a Markov operator. Operator Q is said to be better for the informed player than operator P if the value of the game under Q is higher than under P regardless of the stage game. We show that this defines a convex partial order on the space of ergodic Markov operators. Our main result is a full characterization of this partial order, intepretable as an ordinal notion of persistence relevant for games. The analysis relies on a novel characterization of the value of a stochastic game with incomplete information.