Skewing the Odds: Taking Risks for Rank-Based Rewards

Mean Field Contest with Singularity

“…Remark 5.3. A discussion related to Theorem 5.1 can be found in the work [17] on n-player capacity-constrained contests, which can be related to the present game via Skorokhod embedding. (Some results of the preprint [17] were later published as [18].)…”

“…A discussion related to Theorem 5.1 can be found in the work [17] on n-player capacity-constrained contests, which can be related to the present game via Skorokhod embedding. (Some results of the preprint [17] were later published as [18].) Namely, [17,Proposition 9] studies the effect of scaling the n-player contest by multiplying the number of participants while dividing the reward at each rank.…”

“…(Some results of the preprint [17] were later published as [18].) Namely, [17,Proposition 9] studies the effect of scaling the n-player contest by multiplying the number of participants while dividing the reward at each rank. This basically corresponds to taking lim n F * n , if only for the particular case where R is a step function.…”

Gambling in Risk-Taking Contests: Experimental Evidence

“…In such settings contest incentives are liable to induce excessive risk taking as first explored in a theoretical model by Hvide (2002). The subsequent theoretical literature has identified two robust predictions about behaviour in a general class of contests in which agents can influence the risk: (i) excessive risk-taking is pervasive (for example, Fang and Noe, 2016;Strack, 2016;Fang, Noe, and Strack, 2020) and (ii) the potential losses for the principal are highest if additional risk comes at a moderate expected loss (for example, Seel and Strack, 2013). This paper investigates experimentally these two predictions by implementing a novel experimental stopping task: each subject privately observes a stochastic process over time-a random walk with drift, which could, for example, be thought of as representing the value of a fund manager's risky assets.…”

“…In this case, the expected value of the stopped process is quasi-convex in the drift, i.e., highest losses occur for moderately negative expectations. While the model of Seel and Strack (2013) is deliberately simple and highly stylized, the recent literature has shown that many qualitative predictions, such as the excessive risk-taking, extend if one allows for more general stochastic processes (Feng and Hobson, 2015), asymmetric bankruptcy constraints (Seel, 2015), incomplete information about the endowment (Feng and Hobson, 2016a;Fang and Noe, 2018), flow costs of research (Seel and Strack, 2016), multiple prizes with an arbitrary structure (Fang and Noe, 2016;Strack, 2016), partial observability and a Black-Scholes model rather than a simple stopping problem (Strack, 2016).…”