README-1 Markov-Chain_Akerlof.txt

Markov Chain Simulation of a Market
This simulation models the interactions between buyers and sellers in a market using a discrete Markov chain. The market consists of regular sellers and a fraction of opportunistic sellers who may deceive the buyers. The simulation tracks the evolution of buyer perception over time, influenced by encounters with these opportunistic sellers.

Parameters:
beta: Initial perception rate of buyers, set to 1, indicating perfect initial information.
alpha: Critical perception rate, set at 0.4, below which buyers no longer trust high-quality products.
opportunisticSellerRate: Proportion of sellers in the market who are opportunistic, set at 0.02 (2%).

Process:
The simulation runs for n = 1000 steps, representing time in the market.
At each step, beta decreases by 0.1 if a buyer randomly encounters an opportunistic seller, but never falls below alpha.
The market state transitions between High-quality (H) and Low-quality (L) products based on the current beta.

Model:
transitionMatrix[beta_, alpha_]: Defines the transition probabilities between states H and L, dependent on the current beta.
markovProcess[beta_]: Represents the Markov chain process initialized with state H and the transition matrix.

Simulation Execution:
The simulation uses a loop to iterate through each time step, updating beta and recording the state transition of the market.
simulationResults stores the outcome of each step.

Analysis:
initialProperties and finalProperties: Capture the properties of the Markov process at the start and end of the simulation.
Two graphs are generated to visualize the state transition probabilities at the beginning (beta = 1) and end (beta = 0.4 or the final beta), showing how the likelihood of staying in or transitioning between states changes over time.

Visualization:
Graphs illustrate the transition dynamics within the market's Markov chain, highlighting how the system's behavior shifts as beta decreases due to the influence of opportunistic sellers.
This description provides a comprehensive overview of your simulation, explaining the parameters, process, and analytical insights derived from the model.