The Max-Min Group Contest: Weakest-link (Group) All-Pay Auction

Abstract

We investigate a group all-pay auction in which each groups effort is represented by the minimum among the effort levels exerted by the group members and the prize is a group-specific public good. We fully characterize the symmetric equilibria for two groups. There are four types of equilibria: the pure strategy equilibria in which all (active) players exert the same effort; the semi-pure strategy equilibria in which the players in a group play the same pure strategy whereas those in the other group play the same mixed strategy; the nondegenerate mixed strategy equilibria with continuous support; and the nondegenerate mixed strategy equilibria with discontinuous support. We then analyze a general contest with n groups.

The Optimal Defense of Networks of Targets

“…Such best‐shot and weakest‐link complementarities arise in a number of environments. See for example the literature on group contests, for example, Baik (), Baik, Kim, and Na (), Barbieri, Malueg, and Topolyan (), Chowdhury, Lee, and Sheremeta (); Chowdhury, Lee, and Topolyan (), Katz, Nitzan, and Rosenberg (), Kolmar and Rommeswinkel (), Lee (), and Topolyan ().…”

“…Such best-shot and weakest-link complementarities arise in a number of environments. See for example the literature on group contests, for example, Baik (2008), Baik, Kim, and Na (2001), Barbieri, Malueg, and Topolyan (2014), Chowdhury, Lee, and Sheremeta (2013); Chowdhury, Lee, and Topolyan (2016), Katz, Nitzan, and Rosenberg (1990), Kolmar and Rommeswinkel (2013), Lee (2012), and Topolyan (2014). a terrorist "spectacular," we focus on the case in which the defender's objective is to successfully defend all the networks and the attacker's objective is to successfully attack at least one network of targets.…”

On the voluntary provision of “weakest‐link” public goods: The case of private information

“…The weakest-link and the closely related best-shot technologies have recently been explored as alternatives to summation in full-information group contests, for example (Chowdhury, Lee, & Sheremeta, 2013;Chowdhury, Lee, & Topolyan, 2016;Kolmar & Rommeswinkel, the same dimensionality of action and message spaces is important for this result; a natural framework to explore this issue is when possible actions are continuous, but possible messages are finite, as we do.…”

“…The weakest‐link and the closely related best‐shot technologies have recently been explored as alternatives to summation in full‐information group contests, for example (Chowdhury, Lee, & Sheremeta, ; Chowdhury, Lee, & Topolyan, ; Chowdhury & Topolyan, ; Kolmar & Rommeswinkel, ). Therefore, our results may be of help in extending this literature to accommodate private information.…”

The Attack‐and‐defense Group Contests: Best Shot Versus Weakest Link

“…Another stream of research, instead, uses a deterministic (all‐pay auction, à la Baye, Kovenock, and de Vries ) CSF. Among them, Baik, Kim, and Na () and Topolyan () use additive; Chowdhury, Lee, and Topolyan (2013b) use weakest link; Barbieri, Malueg, and Topolyan () use best shot; and Chowdhury and Topolyan () use hybrid IFs.…”