Multi-Battle Contests, Finite Automata, and the Tug-of-War

University of Zurich, Department of Economics, Working Paper No. 318, 2019

47 Pages Posted: 20 Mar 2019

See all articles by Christian Ewerhart

Christian Ewerhart

University of Zurich, Department of Economics

Julian Teichgräber

University of Zurich

Date Written: February 25, 2019

Abstract

This paper examines multi-battle contests whose extensive form can be represented in terms of a finite state machine. We start by showing that any contest that satisfies our assumptions decomposes into two phases, a principal phase (in which states cannot be revisited) and a concluding tie-breaking phase (in which all non-terminal states can be revisited). Degenerate cases are the finite-horizon contests on the one hand (e.g., the match race), and the tug-of-war on the other. Next, assuming a probabilistic technology in each battle, we show that any contest satisfying our assumptions, with either finite or infinite horizon, admits a unique symmetric and interior Markov perfect equilibrium. This entails, in particular, a complete characterization of the equilibrium in the tug-of-war. Finally, we explore, both analytically and numerically, the intricate problem of a contest designer that maximizes expected total effort. In the absence of a complexity constraint, the revenue-maximizing contest is always a match race, where the optimal length of the race increases as the technology of the component contest becomes more noisy. If, however, the complexity constraint is binding, then the optimal contest is typically (but not always) a tug-of-war.

Keywords: Dynamic contests, finite automata, match race, tug-of-war, Markov perfect equilibrium, contest design

JEL Classification: C62, C63, C72, D72

Suggested Citation

Ewerhart, Christian and Teichgräber, Julian, Multi-Battle Contests, Finite Automata, and the Tug-of-War (February 25, 2019). University of Zurich, Department of Economics, Working Paper No. 318, 2019, Available at SSRN: https://ssrn.com/abstract=3343709 or http://dx.doi.org/10.2139/ssrn.3343709

Christian Ewerhart (Contact Author)

University of Zurich, Department of Economics ( email )

Schoenberggasse 1
Zurich, CH-8001
Switzerland

Julian Teichgräber

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
51
Abstract Views
420
rank
509,057
PlumX Metrics