# Research

## Work in Progress

Secrecy vs. Patenting in Innovation Races, with Eugen Kovac

This study examines the tradeoff between patenting and secrecy in innovation races, considering a model where two firms simultaneously compete in developing two products that can be substitutes or complements. Patenting ensures a claim on the product but discloses information to rivals, while secrecy may delay immediate profits for future technology leadership. We find that firms have more incentives to patent if they are impatient and if there are no significant technological spillovers. In a scenario where firms are impatient and substantial technological spillovers exist, they exhibit a greater tendency to patent products acting as perfect substitutes rather than perfect complements. These findings are in line with the empirical evidence by Cohen, Nelson, and Walsh (2000), who argue that firms are more likely to keep the innovation secret in "simple" industries, where goods have many potential substitutes, as opposed to "complex" industries, where a new product involves many complementary components.

## Working Papers

Revealing Private Information in a Patent Race (Slides), with Eugen Kovac

In this paper we investigate the role of private information in a patent race. Since firms often do their research in secrecy, the standard assumption in the patent race literature that firms know each other's position in the race is questionable. We analyze how the dynamics of the game changes when a firm's progress is its private information. Further, we address the question whether revealing it might be to a firm's advantage. We find that a firm has an incentive to reveal its breakthrough only if its rival has not done so, and only if research is inefficient.

Boundedly Rational Demand, with Jakub Steiner and Colin Stewart

Evidence suggests that consumers do not perfectly optimize, contrary to a critical assumption of classical consumer theory. We propose a model in which consumer types can vary in both their preferences and their choice behavior. Given data on demand and the distribution of prices, we identify the set of possible values of the consumer surplus based on minimal rationality conditions: every type of consumer must be no worse off than if they either always bought the good or never did. We develop a procedure to narrow the set of surplus values using richer datasets and provide bounds on counterfactual demands.

Endogenous Risk Attitudes, with Nick Netzer, Arthur Robson and Jakub Steiner

In a model inspired by neuroscience, we show that constrained optimal perception encodes lottery rewards using an S-shaped encoding function and over-samples low-probability events. The implications of this perception strategy for behavior depend on the decision-maker's understanding of the risk. The strategy does not distort choice in the limit as perception frictions vanish when the DM fully understands the decision problem. If, however, the DM underrates the complexity of the decision problem, then risk attitudes reflect properties of the perception strategy even for vanishing perception frictions. The model explains adaptive risk attitudes and probability weighting, as in prospect theory and, additionally, predicts that risk attitudes are strengthened by time pressure and attenuated by anticipation of large risks.

Multi-Player Discrete All-pay Auctions

In this paper I study all-pay common-value auctions in which bids are restricted to non-negative integers. I prove that the game has unique symmetric Nash equilibrium in mixed strategies given that there are three or more players. Although players bid on average lower as more players are present, they always randomize on the whole set of bids smaller than the value of the prize, so long as there is sufficiently enough players. Players always receive a positive expected payoff which is bounded by a constant regardless of how large the value of the prize is. Finally, I prove that in limit the equilibrium converges to the equilibrium of a continuous all-pay auction.

## Research in Mathematics

P. Kocourek, W. Takahashi and J. C. Yao (2011), Fixed point theorems and ergodic theorems for nonlinear mappings in Banach spaces, Advances in Mathematical Economics.

W. Takahashi, J.C. Yao, P. Kocourek (2011), Weak and strong convergence theorems for generalized hybrid nonself-mappings in Hilbert spaces, J. Nonlinear Convex Analysis.

P. Kocourek, W. Takahashi and J. C. Yao (2010), Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese Journal of Mathematics.

P. Kocourek (2010), An elementary new proof of the determination of a convex function by its subdifferential, Optimization.