Equilibrium in secure strategies in the Tullock contest

The Tullock contest is widely used in economic theory, with applications in blockchain and decentralized finance systems. This study examines the contest under the concept of equilibrium in secure strategies (EinSS), which extends the Nash equilibrium in pure strategies to settings with cautious players who prioritize secure positions and avoid potential threats. Using a formal theoretical analysis, the study characterizes equilibrium outcomes under varying elasticity parameters. The analysis demonstrates that the Tullock contest may admit an asymmetric EinSS outcome when a firm finds it more profitable to increase its effort — thereby rendering the contest unprofitable for its rivals — than to compete symmetrically. Specifically, when the elasticity parameter is sufficiently high, an EinSS solution emerges in which one player sustains a high level of effort to create an entry barrier, while the others exert zero effort. When a symmetric Nash equilibrium does not exist (i.e., for elasticity parameters greater than two), the resulting monopolistic configuration constitutes the unique EinSS solution (up to player permutation) and yields lower rent dissipation than a mixed-strategy Nash equilibrium. These findings confirm the tendency toward winner-takes-all outcomes in Tullock contests with high elasticity and show that such outcomes may be stable and efficiency-enhancing under secure strategies. The results provide theoretical support for the emergence of dominant players and entry barriers in decentralized finance systems and transport edge computing, highlighting how contest sensitivity to effort shapes market concentration and rent dissipation.