Game Redesign in No-regret Game Playing
This addresses the problem of influencing multi-agent systems for designers or attackers, but it is incremental as it builds on no-regret learning frameworks.
The paper tackles the game redesign problem where an external designer modifies payoff functions to incentivize players toward a target action profile while minimizing design costs, achieving that the target is played in T-o(T) rounds with o(T) cumulative cost.
We study the game redesign problem in which an external designer has the ability to change the payoff function in each round, but incurs a design cost for deviating from the original game. The players apply no-regret learning algorithms to repeatedly play the changed games with limited feedback. The goals of the designer are to (i) incentivize all players to take a specific target action profile frequently; and (ii) incur small cumulative design cost. We present game redesign algorithms with the guarantee that the target action profile is played in T-o(T) rounds while incurring only o(T) cumulative design cost. Game redesign describes both positive and negative applications: a benevolent designer who incentivizes players to take a target action profile with better social welfare compared to the solution of the original game, or a malicious attacker whose target action profile benefits themselves but not the players. Simulations on four classic games confirm the effectiveness of our proposed redesign algorithms.