Unique equilibrium in rent-seeking contests with a continuum of types

Abstract

h i g h l i g h t s• Considered are rent-seeking contests with continuous and independent types. • Contestants may be ex-ante asymmetric.• It is shown that there exists a unique pure-strategy Nash equilibrium. a b s t r a c tIt is shown that rent-seeking contests with continuous and independent type distributions possess a unique pure-strategy Nash equilibrium.

Contests between groups of unknown size

“…Ryvkin (2010) extended the analysis to contests with more than two players, general cost distributions, and a more general class of contest success functions. More recent work has further demonstrated the existence and, in some cases, uniqueness, of pure strategy Bayesian equilibrium for individual contests (see, e.g., Wasser, 2013a,b;Ewerhart, 2014;Einy et al, 2015;Ewerhart and Quartieri, 2016), and for group contests with incomplete information (Brookins and Ryvkin, 2016;Barbieri and Malueg, 2016). Existing results suggest that private information can sometimes reduce and sometimes increase aggregate equilibrium investment compared to the full information case (Wasser, 2013a).…”

Voluntary Disclosure in Unfair Contests

“…This can be seen by normalizing payo¤ functions in the agent-normal form of the Bayesian contest game. Further, we conjecture that our results extend to the case of continuous type spaces (Fey, 2008;Ryvkin, 2010;Wasser, 2013aWasser, , 2013bEwerhart, 2014), yet we also suspect that the technical complications necessary would not be rewarded by additional insights.…”

Bayesian Nash equilibrium existence in (almost continuous) contests

“…A natural approach is to consider "limits" of BNE strategy pro…les that exist in constrained contests G(m); as the positive lower bound m on e¤orts tends to 0; and to check whether such a limit is a genuine BNE in G; the contest without constraints, in which a deviating player's e¤ort may be arbitrarily small, or zero. This direction has been fruitfully explored in some recent results on BNE existence in contests (see Einy et al (2013), Ewerhart (2014), and Ewerhart and Quartieri (2020)). We will show that the limit approach works also in our very general framework.…”

“…tests with incomplete information have seen rather limited BNE existence results. The earlier works on incomplete information Tullock contests in which BNE existence was shown considered uncertainty only on some parameters and assumed speci…c forms of information endowments, such as one-sided incomplete information on continuously distributed valuation (Hurley and Shogren (1998a)), discrete valuations (Hurley and Shogren (1998b), Malueg and Yates (2004) and Schoonbeek and Winkel (2006)), a continuously distributed common valuation (Harstad (1995), Wärneryd (2012) and Rentschler (2009)), and continuously and independently distributed marginal costs (Fey (2008), Ryvkin (2010), Wasser (2013) and Ewerhart (2014)). 4 Two later works that addressed BNE existence, Einy et al (2015) and Ewerhart and Quartieri (2020), admitted all modes of incomplete information on both the valuations and the costs, but restricted the cardinality of type sets.…”

“…It turns out that a BNE can be arrived at by an extension of the method that has been employed in Einy et al (2013), Ewerhart (2014), and Ewerhart and Quartieri (2020) in their treatment of simpler cases. The method consists of approximating the contest by a sequence of "constrained" contests, where all e¤orts are required to be above a small positive constant.…”