Social Welfare in Search Games with Asymmetric Information

Bavly, Gilad and Heller, Yuval and Schreiber, Amnon (2020): Social Welfare in Search Games with Asymmetric Information.

Abstract

We consider games in which players search for a hidden prize, and they have asymmetric information about the prize's location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an equilibrium that yields the first-best payoff (i.e., the highest social payoff under any strategy profile), and we characterize the first-best payoff. The results have interesting implications for innovation contests and R&D races.

• Item Type: MPRA Paper
• Language: English
• Keywords: search duplication, decentralized research, social welfare, incomplete information
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

References

Adamczyk, Sabrina, Bullinger, Angelika C, & Möslein, Kathrin M. 2012. Innovation contests: A review, classification and outlook. Creativity and Innovation Management, 21(4), 335–360.

Akcigit, Ufuk, & Liu, Qingmin. 2015. The role of information in innovation and competition.Journal of the European Economic Association, 14(4), 828–870.

Aumann, Robert J. 1976. Agreeing to disagree. The Annals of Statistics, 4(6), 1236–1239.

Ben-Zwi, Oren. 2017. Walrasian’s characterization and a universal ascending auction. Games and Economic Behavior, 104, 456–467.

Berman, Abraham, & Plemmons, Robert J. 1994. Nonnegative Matrices in the Mathematical Sciences. Vol. 9. SIAM.

Birkhoff, Garrett. 1946. Tres observaciones sobre el algebra lineal. Universidad Nacional de Tucumán, 5, 147–154.

Blonski, Matthias. 2005. The women of cairo: Equilibria in large anonymous games. Journal of Mathematical Economics, 41(3), 253–264.

Bronfman, Slava, Alon, Noga, Hassidim, Avinatan, & Romm, Assaf. 2018. Redesigning the israeli medical internship match. ACM Transactions on Economics and Computation, 6(3–4), 1–18.

Bryan, Kevin A, & Lemus, Jorge. 2017. The direction of innovation. Journal of Economic Theory, 172, 247–272.

Budish, Eric, Che, Yeon-Koo, Kojima, Fuhito, & Milgrom, Paul. 2013. Designing random allocation mechanisms: Theory and applications. American Economic Review, 103(2), 585–623.

Chatterjee, Kalyan, & Evans, Robert. 2004. Rivals’ search for buried treasure: Competition and duplication in r&d. RAND Journal of Economics, 35(1), 160–183.

Che, Yeon-Koo, & Gale, Ian. 2003. Optimal design of research contests. American Economic Review, 93(3), 646–671.

Chen, Yiling, Nissim, Kobbi, & Waggoner, Bo. 2015. Fair information sharing for treasure hunting. Pages 851–857 of: Twenty-Ninth AAAI Conference on Artificial Intelligence.

Cormen, Thomas H, Leiserson, Charles E, Rivest, Ronald L, & Stein, Clifford. 2009. Introduction to Algorithms. MIT Press: Cambridge, MA.

Erat, Sanjiv, & Krishnan, Vish. 2012. Managing delegated search over design spaces. Management Science, 58(3), 606–623.

Fershtman, Chaim, & Rubinstein, Ariel. 1997. A simple model of equilibrium in search procedures. Journal of Economic Theory, 72(2), 432–441.

Ford, LR, & Fulkerson, DR. 1956. Maximal flow through a network. Canadian Journal of Mathematics, 8, 399–404.

Hall, P. 1935. On representatives of subsets. Journal of the London Mathematical Society, 1(1), 26–30.

Kleinberg, Jon, & Oren, Sigal. 2011. Mechanisms for (mis)allocating scientific credit. Pages 529–538 of: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing.

Konrad, Kai A. 2014. Search duplication in research and design spaces: Exploring the role of local competition. International Journal of Industrial Organization, 37, 222–228.

Letina, Igor. 2016. The road not taken: competition and the r&d portfolio. The RAND Journal of Economics, 47(2), 433–460.

Letina, Igor, & Schmutzler, Armin. 2019. Inducing variety: A theory of innovation contests. International Economic Review, 60(4), 1757–1780.

Liu, Qingmin, & Wong, Yu Fu. 2019. Strategic exploration. mimeo.

Loch, Christoph H, Terwiesch, Christian, & Thomke, Stefan. 2001. Parallel and sequential testing of design alternatives. Management Science, 47(5), 663–678.

Loury, Glenn C, et al. 1979. Market structure and innovation. Quarterly Journal of Economics, 93(3), 395–410.

Mihm, Jürgen, & Schlapp, Jochen. 2019. Sourcing innovation: On feedback in contests. Management science, 65(2), 559–576.

Milchtaich, Igal. 1996. Congestion games with player-specific payoff functions. Games and Economic Behavior, 13(1), 111–124.

Monderer, Dov, & Shapley, Lloyd S. 1996. Potential games. Games and Economic Behavior, 14, 124–143.

Selten, R. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4(1), 25–55.

Tierney, Ryan. 2019. The problem of multiple commons: A market design approach. Games and Economic Behavior, 114, 1–27.

Von Neumann, John. 1953. A certain zero-sum two-person game equivalent to the optimal assignment problem. Contributions to the Theory of Games, 2(0), 5–12