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Paper of the Month

Evolving Game Theory From Selfish to Socially Aware Agents

by Mara Munro

Mathematics, Somnath Kundu

Einstein said, “Life is just like a game, first you have to learn rules of the game, and then play it better than anyone else.” Similarly, in game theory, mathematicians seek winning, or appropriate formulas for the “game of life” as they study human behaviour in strategic settings, attempting to predict and formulate what people will do when competing with each other.

This science of decision-making is at the heart of Somnath Kundu’s graduate research work in Ryerson’s Mathematics Department under the supervision of Dr. Konstantinos Georgiou, “I was always fascinated by the process that makes social dynamics work.” recalls Kundu, “We are constantly interacting with each other and every individual is trying to maximize his/her own interest. The outcome of these interactions for an individual mainly depends on how strategically they are placed within the social network.”

Given that not everyone is placed equally within social networks, Kundu’s research paper, entitled Bargaining in Networks with Socially-Aware Agents asks: if individuals are always bargaining for their own gain, will the community come to a dynamic equilibrium where everyone is content with what they get or will it be chaos? In other words, if individuals are only looking out for their own interests, then how will this affect the society as whole?

Example of a Cost Sharing Bargaining game using a Hypergraph representation
Example of a Cost Sharing Bargaining game using a Hypergraph representation

While traditionally, game theorist have focused on studying and analyzing bargaining behavior in search of equilibrium or stability outcomes as a result of profit distribution problems, Kundu and Georgiou are the first to study the stability concept of bargaining games from a cost sharing perspective using hypergraphs and non-uniform bargaining objects, while introducing the concepts of socially aware agents. “We were interested in how agents might negotiate the cost distribution among them so as to agree on a global solution satisfying the demands of every player,” explains Kundu, “Are there specific outcomes where the payment contributions can be considered fair?”

Kundu’s work aims to understand complicated social problems by logically dissecting them through step-by-step deductive reasoning and mathematical techniques, “if something is mathematically deduced, then that will work with any data regardless of its origin because it is universal in nature,” says Kundu. So are there, in fact,  mathematical rules of the game that can be used so that everyone wins, individually and collectively? Interestingly, while his work is rooted in logic, many of Kundu’s solutions to this question came to him during his sleep, “maybe the neurons got cleared and the steps were clearer with my mind at rest, but the saying, ‘when you have an idea, sleep on it’ has been very appropriate for me during this research!”

Cost sharing for socially aware agents in a bargaining game with critical constraints
Cost sharing for socially aware agents in a bargaining game with critical constraints

The results of Kundu’s hard work and productive rest has put a new spin on the assumption of the ‘selfish agent’ traditional to game theory. “In our strict definition of stability we guessed that agents of a bargaining game would never pay for services they aren't using,” Kundu reveals, “but we found that if agents are too rigidly selfish, a deadlock situation (might) arise where there won't be any stability.” Instability is bad for the community, but it is also bad for every individual.

In fact, agents in Kundu’s research actually have the incentive to be socially aware and pay for the community, which shows a novel relationship between the ‘social perspective’ and the ‘selfish perspective’ of  individuals in his field of research. “In certain situations, if agents are willing to pay something for the community then it could guarantee a stable outcome, which would otherwise be unstable” he says, “and we also quantified how much each individual would have to pay in certain situations to avoid instability.”

“Our work has the potential to be used for real life cases in the social sciences and economics” notes Kundu, “we are showing, mathematically, that everyone should share some load for the community, which will in turn serve their own interests, and we also give a quantification of  how much load each individual must share so that the society as a whole is stable and everyone is content.” Kundu’s work, supported in part by NSERC and presented at the 9th EAI International Conference on Game Theory for Networks (GameNets’19), could have applications in solving current Canadian economic and political cost-sharing quandaries like health care and carbon taxing - as game theory models today are being applied to solving social and ethical dilemmas.