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This thesis explores and explains a stochastic model in Evolutionary Game Theory introduced by Dr. Nicolas Lanchier. The model is a continuous-time Markov chain that maps the two-dimensional lattice into

This thesis explores and explains a stochastic model in Evolutionary Game Theory introduced by Dr. Nicolas Lanchier. The model is a continuous-time Markov chain that maps the two-dimensional lattice into the strategy space {1,2}. At every vertex in the grid there is exactly one player whose payoff is determined by its strategy and the strategies of its neighbors. Update times are exponential random variables with parameters equal to the absolute value of the respective cells' payoffs. The model is connected to an ordinary differential equation known as the replicator equation.

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