A blockchain is a fully distributed system in which the user behavior, actions and decisions are crucial for its operation. This paper discusses how to handle conflict situations affecting a blockchain system. Specifically, we model two real-world conflict scenarios - the Lazy Miner dilemma and the Impatient Seller dilemma - by proposing a novel multi-layer framework coupled with a heuristics-based game-theoretic modeling. The multi-layer approach provides a way to include cross-modality integration (human quality factors, such as reliability) and human actions on the blockchain. We design a multi-agent game-theoretic methodology combined with some statistical estimators derived from the heuristics. Our model also includes the concept of homophily, a human-related factor connected to the similarity and frequency of interactions on the multi-layer network. Based on the heuristics, a dynamically evolving measure of weights is further defined such that an agent increases or decreases the link weights to its neighbours according to the experienced payoffs. We show how data mining in blockchain data could be incorporated into a heuristic model which provides parameters for the game-theoretic payoff matrix. Thus, this work represents a platform for simulating the evolutionary dynamics of the agents' behaviors, including also heuristics and homophily on a multi-layer blockchain network.