Equalizer zero-determinant strategy in discounted repeated Stackelberg asymmetric game

TL;DR

This paper investigates the use of equalizer zero-determinant strategies in discounted repeated asymmetric Stackelberg games, offering a computationally simpler alternative to strong Stackelberg equilibrium strategies with effective utility control.

Contribution

It introduces the application of equalizer ZD strategies in asymmetric Stackelberg games, analyzing their existence, performance bounds, and effectiveness through simulations.

Findings

Equalizer ZD strategies can restrict opponent utilities effectively.

Performance bounds of ZD strategies are comparable to SSE strategies.

Simulations demonstrate the approach's effectiveness in UAV and MTD scenarios.

Abstract

This paper focuses on the performance of equalizer zero-determinant (ZD) strategies in discounted repeated Stackerberg asymmetric games. In the leader-follower adversarial scenario, the strong Stackelberg equilibrium (SSE) deriving from the opponents' best response (BR), is technically the optimal strategy for the leader. However, computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states. To this end, we propose to adopt an equalizer ZD strategy, which can unilaterally restrict the opponent's expected utility. We first study the existence of an equalizer ZD strategy with one-to-one situations, and analyze an upper bound of its performance with the baseline SSE strategy. Then we turn to multi-player models, where there exists one player adopting an equalizer ZD strategy. We give bounds of the sum of opponents' utilities, and compare it with the SSE strategy. Finally, we give simulations on unmanned aerial vehicles (UAVs) and the moving target defense (MTD) to verify the effectiveness of our approach.