Deviate or Not: Learning Coalition Structures with Multi-bit Observations in Games
Abstract
We consider the Coalition Structure Learning (CSL) problem in multi-agent systems, motivated by the existence of coalitions in many real-world systems, e.g., trading platforms and auction systems. In this problem, there is a hidden coalition structure within a set of $n$ agents, which affects the behavior of the agents in games. Our goal is to actively design a sequence of games
for the agents to play, such that observations in these games can be used to learn the hidden coalition structure. In particular, we consider the setting where in each round, we design and present a game together with a strategy profile to the agents, and receive a multiple-bit observation -- for each agent, we observe whether or not they would like to deviate from the specified strategy in this given game. Our contributions are three-fold: First, we show that we can learn the coalition structure in $O(\log n)$ rounds if we are allowed to choose any normal-form game in each round, matching the information-theoretical lower bound, and the result can be extended to congestion games. Second, in a more restricted setting where we can only choose a graphical game with degree limit $d$, we develop an algorithm to learn the coalition structure in $O(n/d+\log d)$ rounds. Third, when we can only learn the coalition structure through running second-price auctions with personalized reserve prices, we show that the coalition structure can be learned in $O(c\log n)$ rounds, where $c$ is the size of the largest coalition.
for the agents to play, such that observations in these games can be used to learn the hidden coalition structure. In particular, we consider the setting where in each round, we design and present a game together with a strategy profile to the agents, and receive a multiple-bit observation -- for each agent, we observe whether or not they would like to deviate from the specified strategy in this given game. Our contributions are three-fold: First, we show that we can learn the coalition structure in $O(\log n)$ rounds if we are allowed to choose any normal-form game in each round, matching the information-theoretical lower bound, and the result can be extended to congestion games. Second, in a more restricted setting where we can only choose a graphical game with degree limit $d$, we develop an algorithm to learn the coalition structure in $O(n/d+\log d)$ rounds. Third, when we can only learn the coalition structure through running second-price auctions with personalized reserve prices, we show that the coalition structure can be learned in $O(c\log n)$ rounds, where $c$ is the size of the largest coalition.
