Emergent Spatial Characteristics from Strategic Games Simulated on Random and Real Networks

P dilemma is a paradox where two parties competing to maximize self interest do not result in the optimal output for both. While a stable Nash equilibrium where both parties defect is reached in a single round situation, iterated versions are easily perturbed by initial conditions as well as probabilistic or conditional decisions made during each iteration. One such simulation to model various routes of evolution is the Evolution of Trust (1) — an online game where simulations of single shot and iterated prisoner’s dilemma are shown. This game features an array of players, which includes, but is not limited to, the copycat, which copies whatever move the opponent made the previous iteration, the always cooperate, the always defect, and grudges, who cooperates until the opponent defects for the first time, after which the grudges always defects, and the detective, that begins with a set number of cooperates and defects and determines from there if a copycat strategy or an always cheat strategy should be employed. In their simulations, in a world with equal number of copycats, always defects, and always cooperates, copycat dominates. If filled with equal parts copycat, grudger, and detective, copycat still wins. However, if the payoff matrix was altered in favor of defecting, or if the proportion of players changed, the outcome could be a different dominant player type, or an infinite oscillation between two player types. However, that model only presented game simulations in which the entire network was completely connected, such that during every iteration, every player would interact with every other player. In real world models, however, that is not the case. Barabási-Albert (BA) Model (2) and Watts-Strogatz (WS) models (3) that we used were more representative of the actual clustering of nodes in real life network. Also, the simulation presented above used nodes that had different strategies which was effective in presenting the dominant player type. We, on the other hand, also want to investigate into the long run convergence of players with similar strategies, varying only the network structure, and observe how initial network structures impacted emergent dominance of a binary node type (i.e. always cooperating or always defecting), rather than players whose strategies would never change and would eventually die out similar to natural evolution. Previous literature have looked into similar processes of analyzing the effects of the iterated prisoner’s dilemma game on network structure. When edge reformation and semiomnipotent strategies are incorporated into simulations on Erdõs-Renyi (4) networks, overall cooperation density increases (5). Initial network structure also plays a role in the progression of an iterated prisoner’s dilemma game. Cooperation strategies converge faster to a Nash Equilibrium when the initial network has a higher clustering coefficient and lower geodesic distance (6). There has however not been a substantial amount of previous work done on comparing the iterated prisoner’s dilemma game on randomly generated models to real life social networks which is the focus of this paper. When constructing strategies for our models, we examined many popular strategies, including the tit-for-tat strategy that has commonly won in many different simulation that used the prisoner’s dilemmas as a basis. We also took note of the relatively novel zero-determinant strategies proposed by Press and Dyson (2012) in which players can unilaterally force a linear payoff relationship between themselves and an opponent (7). We also considered players with m-level thinking, where nodes are able deduce using the logic of "I know that you know that I know", for N rounds of recursion (8). We also looked at strategies that were effective in evading a certain Markov equilibrium, by playing within a certain timescale (9). In the end, we chose to use a few simpler strategies, partly because the some of the math presented were difficult to translate into code under the constraints of our simulation, and partly