My house is in a recently identified coastal flood risk zone. In 31 days, the government will use its power of eminent domain to seize it and I will receive $100k (i.e. $10 thousand) compensation. Until then I may negotiate with the government and they will make offers on the property so I may leave earlier. Each day I must decide whether to accept the offer or wait another day. If on one day I receive an offer P, next day I know that the best offer will be P with probability 0.6, P- 20k with 0.15 chance and P 20k with probability 0.25. You know that you will only receive offers between 140k and 200k and offers are made in multiples of 20k. If the daily best offer ever reaches 140k, you know it will not go up again. If the daily best offer ever reaches 200k, then it will go down by 20k with probability 0.6 and not change with probability 0.4.
Formulate this problem as an MDP, clearly stating the decision epochs, states, actions, transition probabilities and rewards.