2475-1502 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TG.2018.2806302, IEEE Transactions on Games > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract— Diffusion of information is a key factor in many social and political situations. This work presents a strategic game called “Spread-It,” which models the spread of information through social network structures. In the game, two competing parties must decide on the allocation and timing of their limited resources with the goal of increasing their influence in the network. Since present decisions affect the future level of network penetration, their effort allocation must be carefully planned. The work starts by defining the mathematical characteristics of the game, followed by analytical results derived by implementing several strategies for winning the game. Analyzing the experiments provides few observations regarding the role of influencers (‘hubs’) under different game conditions, the superiority of Monte Carlo tree search strategy over traditional game-tree search methods, and the budget required to guarantee the game’s finalization. Index Terms— B2B Marketing, Game Theory, Information Diffusion, Political Games, Social Network I. INTRODUCTION PREAD-IT is a proposed two-player zero-sum game aimed at analyzing strategic thinking in the art of acquiring influence through social networks. The game can be played on a virtual or physical board that represents an organization’s social graph, where the set of vertices (nodes) is associated with members in the network, and the set of edges defines the connectivity between these members. Two opposing parties (players) compete on the board to increase their dominance, as a single choice of the organization. “Spread-It” can be played over any undirected graph representing the game’s board, unlike other board games, e.g., Chess, Checkers and Othello, which are played on specific boards. The reality that the game simulates can be seen as a case of two opposing attitudes trying to win a group of decision- makers. Such scenarios are seen, for example, in politics between two parties or in a bidding process where two suppliers are submitting competing proposals. Thus, the game can mimic two suppliers trying to win a bid within an organization by influencing different decision-makers to adopt their product / service. In large organizations, bids are applied regularly to choose between suppliers, and only one supplier is eventually chosen. Each of the two players represents an attitude (supplier), and the players are lobbyists of the supplier within the organization, trying to advance their attitude within the social graph of decision-makers. In each move, each player must decide on what node (key decision maker) to invest its convincing efforts, where each unit of ‘convincing effort’ is represented by a token, with different colors representing different attitudes for each of the lobbyists. Influencing someone to adopt an alternative is seldom completed in a single interaction and is instead often accomplished through repeated efforts. This logic is embedded in the proposed game, where each player adds a single unit of influence (a colored token) to a chosen node during his/her turn. The token represents a limited (e.g., marketing) resource, such as budget or energy, required to influence the selected member. Then, when the total number of tokens in a node reaches the node’s threshold, the node ‘fires’ or ‘explodes’ (we use both terms interchangeably), indicating that the associated member adopts the alternative of the player that gains the majority of tokens on the node. This adoption of an opinion by a node is named “an explosion” in the game’s terminology. When an explosion occurs, first, all the tokens on a node are changed to the color of the winning party. This represents the loss of the effort of the losing party, and the effort invested by the winning party that increases its strength by winning its opponent. Furthermore, when an explosion occurs, after having the color of the losing party changed to that of the winning party, the tokens are distributed to the neighboring nodes. This process, represented by the “explosion,” may repeat itself in a cascade manner, where one converted member influences another, thus representing the influence that the exploding node has on its neighbors toward adopting the alternative that it has. As in many games, this game is a simplified set of rules that mimics a certain aspect of a highly complex reality. This simplification clearly implies limitations for the scenarios that the game represents. For example, the game does not represent the scenario in which an effort to influence opinions is performed through mass media such as the use of TV, radio or billboards, but only an effort to influence opinions through a personal one-to-one contact. Moreover, “Spread-It” falls under the category of sequential games (sometimes called dynamic games), where players move at different points of time and can observe some, if not all, the choices of other players before deciding upon their optimal response. This contrasts with static games (or simultaneous game) where players making their moves simultaneously. A broader discussion of the limitations of the game’s model as well as the reality represented by its set of rules is discussed in subsection III.C. The game includes two variations that represent opposite real- life scenarios: a Zero Loyalty variant and a Full Loyalty variant. In the Zero Loyalty variant, each node can flip and change its color (alternative) repeatedly without being “loyal” to any player, even the one that initiated the interaction with the node. This variant can represent a social dynamics case where people “Spread-It”: A Strategic Game of Competitive Diffusion through Social Networks Shimon Ben-Ishay, Alon Sela, and Irad Ben-Gal Dept. of Industrial Engineering, Tel Aviv University S