Scalable games

We propose conditions on games of incomplete information, under which solving the game reduces to solving a corresponding game of complete information. These games are referred to as scalable games. After establishing a link between (i) scalable games, (ii) games of complete information and (iii) games with strategy restrictions, we present two distinct applications. The first application demonstrates how scalable games can be used to model complex situations in a tractable manner. For instance we provide a tractable model of an asymmetric private value first price auction with a reserve price and risk averse bidders. The second application shows how certain deterministic all pay auctions with incomplete information are strategically equivalent to stochastic contests with complete information. In particular for the two player case we show that a contest is strategically equivalent to an all-pay auction whenever the relevant contest success function is homogenous of degree 0 and other mild conditions are satisfied. ∗Universidad Carlos III de Madrid, Department of Economics, C/Madrid 126, 28903 Getafe (Madrid), Spain. Email addresses: [email protected], [email protected]. We would like to thank our supervisors Natalia Fabra and Ángel Hernando-Veciana for their support, encouragement and many discussions. We also thank Marco Celentani, Laura Doval, Mikhail Drugov, Alessandro Pavan, Pablo Schenone, Ron Siegel, Asher Wolinsky as well as participants at CEMFI-UC3M Workshop 2013, RES Conference 2014, Stony Brook Festival of Game Theory 2014, EEA Congress 2014, JEI 2014 and seminar participants at Universidad Carlos III, Northwestern University and the University of Mannheim for useful comments and suggestions. .