The prisoner's dilemma, conceptualized by Merrill Flood and Melvin Dresher at the Rand Corporation in 1950, is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome.

70 years later, we want to use this game and apply it to our current situation when the world is dealing with Covid19 and the problem of Vaccination and how to deal with the "Anti Vax" Movement. Our goal is to find out: "Is the Pandemic a Prisoner's Dilemma Game'?"

To do so, imagine each individual of us in our society is a player of a game. And each player has two choices: To get the vaccine (V) or not to get the vaccine (NV). [Note: We assume Vaccination (V) is a good practice and it is a term we loosely use for all safety measures like wearing masks, social distancing or getting an actual vaccine. And Not Vaccination (NV) is the opposite.]

Clinical studies show that vaccines have an efficacy rate, which means it doesn't guarantee those who get the vaccine will not get infected by COVID. Statistics demonstrate:

-If two individuals are both vaccinated, with 90 percent chance they will stay safe and healthy for more than 6 months, and only with 10 percent probabilities, the vaccinated people will go to the hospital due to COVID infection.

-If one individual is vaccinated and the other one is not, the vaccinated one will remain healthy with 80 percent chance and with 20 percent he or she will end up going to the hospital due to COVID infection.

-And if both individuals are not vaccinated with 75 percent probabilities they will get infected, while they only have 25 percent chance of remaining safe while they are not jabbed.

			Player2
		Vaccination (V)			Not Vaccination (NV)
		Prob o infection V,	0.9		Prob o infection V,	0.8
	Vaccination
		Prob (InfectionIV, V)	0.1		Prob (InfectionlV, NV)	0.2
Player I
		Prob (No infectionlNV,V)	0.8		Prob (No infectionINV, NV)	0.25
	Not Vaccination
		Prob (InfectionlNV, V)	0.2		Prob (InfectionINV, NV)	0.75

We know the cost of getting a vaccine (opportunity cost of going to the clinic to get the vaccine, after vaccination symptoms, opportunity cost of resting home a day after and so on) is 60 units. Needless to say, this cost is zero if the player decides not to take the vaccine option.

Let's assume the benefit or the value of not infection is 100 units and the value of infection is zero.

given the table above:

1. If player I decide to get the job, how much would be the net benefits of vaccination for her?
2. If she decides not to get the vaccine, how much would be the net benefits for her?

Now think about both players and their decisions and try to find their payoff given the other player's action by computing the Expected Value. [Note: Expected value = Probability of event I x Net Benefit of event 1+ Probability of event 2 x Net Benefit of event 2.]

1. Calculate the Expected value of their decisions if both players get vaccinated E(V,V)?
2. Calculate the Expected value of their decisions if both players get not vaccinated E(NV NV)?
3. Calculate the Expected value of their decisions if one player gets vaccinated and the other one not, E(V,NV) and
4. Now, construct a pay-off matrix for both players?
5. What will be the equilibrium? Why?
6. Is this a prisoner dilemma game? Why?
7. What kind of policy recommendations do you have to improve the game's equilibrium?

Benefit Cost Net Benefit No Infection 100 Vaccination (V) Infection 0 Player 1 Benefit Cost Net Benefit No Infection 100 Not Vaccination (NV) Infection 0 Benefit Cost Net Benefit No Infection 100 Vaccination (V) Infection 0 Player 1 Benefit Cost Net Benefit No Infection 100 Not Vaccination (NV) Infection 0