  In social sciences, simulating opinion dynamics to study the interplay
between homophily and influence, and the subsequent formation of echo chambers,
is of great importance. As such, in this paper we investigate echo chambers by
implementing a unique social game in which we spawn in a large number of
agents, each assigned one of the two opinions on an issue and a finite amount
of influence in the form of a game currency. Agents attempt to have an opinion
that is a majority at the end of the game, to obtain a reward also paid in the
game currency. At the beginning of each round, a randomly selected agent is
selected, referred to as a speaker. The second agent is selected in the radius
of speaker influence (which is a set subset of the speaker's neighbors) to
interact with the speaker as a listener. In this interaction, the speaker
proposes a payoff in the game currency from their personal influence budget to
persuade the listener to hold the speaker's opinion in future rounds until
chosen listener again. The listener can either choose to accept or reject this
payoff to hold the speaker's opinion for future rounds. The listener's choice
is informed only by their estimate of global majority opinion through a limited
view of the opinions of their neighboring agents. We show that the influence
game leads to the formation of "echo chambers," or homogeneous clusters of
opinions. We also investigate various scenarios to disrupt the creation of such
echo chambers, including the introduction of resource disparity between agents
with different opinions, initially preferentially assigning opinions to agents,
and the introduction of committed agents, who never change their initial
opinion.
