A Game Theoretic Approach to Ad-Hoc Coalitions in Human-Robot Societies

As robots evolve into fully autonomous agents, settings involving human-robot teams will evolve into humanrobot societies, where multiple independent agents and teams, both humans and robots, coexist and work in harmony. Given such a scenario, the question we ask is How can two or more such agents dynamically form coalitions or teams for mutual benefit with minimal prior coordination? In this work, we provide a game theoretic solution to address this problem. We will first look at a situation with full information, provide approximations to compute the extensive form game more efficiently, and then extend the formulation to account for scenarios when the human is not totally confident of its potential partner’s intentions. Finally we will look at possible extensions of the game, that can capture different aspects of decision making with respect to ad-hoc coalition formation in human-robot societies. Robots are increasingly becoming capable of performing daily tasks with accuracy and reliability, and are thus getting integrated into different fields of work that were until now traditionally limited to humans only. This has made the dream of human-robot cohabitation a not so distant reality. In this work we envisage such an environment where humans and robots participate autonomously (possibly with required interactions) with their own set of tasks to achieve. It has been argued (Chakraborti et al. 2016) that interactions in such situations are inherently different from those studied in traditional human-robot teams. One typical aspect of such interactions is the lack of prior coordination or shared information, due to the absence of an explicit team. This brings us to the problem we intend to address in this paper given a set of tasks to achieve, how can an agent proceed to select which one to achieve? In a shared environment such as the one we described, this problem cannot be simply solved by picking the goal with the highest individual utility, because the utility, and sometimes even the success of the plan (and hence the corresponding goal) of an agent are contingent on the intentions of the other agents around it. However, such interactions are not adversarial it is just that the environment is shared among self-interested agents. Thus, an agent may choose to form an ad-hoc team with another agent in order to increase its utility, and such coalition formation should preferably be feasible with minimum prior coordination. For example, a human with a goal to deliver two items to two different locations may team up with a delivery robot that can accomplish half of his task. Further, if the robot was itself going to be headed in one of those directions, then it is in the interest of both these agents to form this coalition. However, if the robot’s plan becomes too expensive as a result, it might decide that there is not enough incentive to form this coalition. Moreover, as we highlighted before, possible interactions between agents are not just restricted to cooperative scenarios only the plans of one agent can make the other agent’s plans fail, and it may happen that it is not feasible at all for all agents to achieve their respective goals. Thus there are many possible modes of interaction between such agents, some cooperative and some destructive, that needs to be accounted for before the agents can decide on their best course of action both in terms of which goal to choose and how to achieve it. In this paper we model this problem of optimal goal selection as a two player game with perfect information, and propose to cut down on the prior coordination of forming such ad-hoc coalitions by looking for Nash equilibriums or socially optimal solutions (because neither agent participating in such a coalition would have incentive to deviate). We subsequently extend it to a Bayesian game to account for situations when agents are not sure of each other’s intent. We will also look at properties, approximations, and interesting caveats of these games, and motivate several extensions that can capture a wide variety of ad-hoc interactions.