Best-shot versus weakest-link in political lobbying: an application of group all-pay auction

We analyze a group political lobbying all-pay auction with a group specific public good prize, in which one group follows a weakest-link and the other group follows a best-shot impact function. We completely characterize all semi-symmetric equilibria. There are two types of equilibria: (1) each player in the best-shot group puts mass at the upper bound of the support, whereas each player in the other group puts mass at the lower bound of the support; (2) players in the best-shot group put masses at both the lower and the upper bounds, while the other group randomizes without a mass point. An earlier and longer version of this study was circulated under the title “The Group All-pay Auction with Heterogeneous Impact Functions.” We appreciate the comments of an Associate Editor and two anonymous referees, Kyung Hwan Baik, Walter Enders, Matt Van Essen, Paan Jindapon, David Malueg, Paul Pecorino, Seth Streitmatter, Ted Turocy, the participants at the 2015 conference of ‘Contest: Theory and Evidence’ at the University of East Anglia, and the seminar participants at the University of Alabama and Korea University. Iryna Topolyan gratefully acknowledges the support from the Charles Phelps Taft Research Center. Any remaining errors are our own

Group Contests with Internal Conflict and Power Asymmetry

We investigate simultaneous inter- and intra-group conflict in the shadow of within-group power asymmetry and complementarity in members' group-conflict efforts. A more symmetric group faces a higher degree of internal conflict, and might expend more effort in external conflict when the group-conflict effort technology is highly complementary. Depending on the degree of complementarity, the stronger player's relative contribution to external conflict might be higher in a more asymmetric group and, as a result, it is possible for the weaker player to earn a higher payoff. In the absence of any complementarity, the rent-dissipation is non-monotonic with the within-group power asymmetry

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

We investigate a group all-pay auction in which each group's 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

On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms

A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasiconvex, nor strictly concave. On the other hand, a DFD density need, in general, be neither unimodal nor logconcave. Regarding smoothness, we show that a compactly supported DFD density cannot be analytic and will often exhibit a kink even if its components are smooth. The analysis highlights the risks for model consistency resulting from the strategy widely adopted in the economics literature of imposing assumptions directly on a difference of noise terms rather than on its components

Contests with Linear Externality in Prizes

This study examines contests in which prizes are affected linearly by aggregate effort. In particular, this research analyzes a contest among individuals as a benchmark to scrutinize the effects of prize externality and sharing-rule information on rent-dissipation rate and social welfare. Thereafter, the current study investigates two types of group contest with linear prize externality: one with private information on intra-group sharing rules and the other with public information on intra-group sharing rules. Results indicate as follows. (1) An increase in prize externality increases rent-dissipation rate but has no effect on social welfare. (2) The group contest with private information on sharing rules yields higher social welfare and lower rent-dissipation rate than the one with public information on sharing rules

The Optimal Defense of Networks of Targets

This paper examines a game-theoretic model of attack and defense of multiple networks of targets in which there exist intra-network strategic complementarities among targets. The defender’s objective is to successfully defend all of the networks and the attacker’s objective is to successfully attack at least one network of targets. Although there are multiple equilibria, we characterize correlation structures in the allocations of forces across targets that arise in all equilibria. For example, in all equilibria the attacker utilizes a stochastic ‘guerrilla warfare’ strategy in which a single random network is attacked

Essays on Microeconomic Theory.

The present work collects three essays on microeconomic theory. In the first essay, I study a model in which a finite number of men and women look for future spouses via random meetings. I ask whether equilibrium marriage outcomes are stable matchings when search frictions are small. The answer is they can but need not be. For any stable matching there is an equilibrium leading to it almost surely. However unstable---even Pareto-dominated---matchings may still arise with positive probability. In addition, inefficiency due to delay may remain significant despite vanishing search frictions. Finally, a condition is identified under which all equilibria are outcome equivalent, stable, and efficient. In the second essay, a joint work Kfir Eliaz, we model a competition between two teams as an all-pay auction with incomplete information. The teams may differ in size and individuals exert effort to increase the performance of one's own team via an additively separable aggregation function. The team with a higher performance wins, and its members enjoy the prize as a public good. The value of the prize is identical to members of the same team but is unknown to the other team. We show that there exists a unique monotone equilibrium in which everyone actively participates, and in this equilibrium a bigger team is more likely to win if the aggregation function is concave, less likely if convex, or equally likely if linear. In the third essay, I study a situation in which a group of people working on a common objective want to share information. Oftentimes information sharing via precise communication is impossible and instead information is aggregated by institutions within which communication is coarse. The paper proposes a unified framework for modeling a general class of such information-aggregating institutions. Within this class, it is shown that institution A outperforms institution B for any common objective if and only if the underlying communication infrastructure of A can be obtained from that of B by a sequence of elementary operations. Each operation either removes redundant communication instruments from B or introduces effective ones to it.PhDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133250/1/wqg_1.pd