Mary and Raj are the only two growers who provide...

Mary and Raj are the only two growers who provide organically grown corn to a local grocery store. They know that if they cooperated and produced less corn, they could raise the price of the corn. If they work independently, they will each earn $\$ 100$ . If they decide to work together and both lower their output, and the other does not, the person who lowers output will earn $\$ 0$ and the other person will capture the entire market and will earn $\$ 200$ . Table 10.6 represents the choices available to Mary and Raj. What is the bestchoice for Raj if he is sure that Mary will cooperate? If Mary thinks Raj will cheat, what should Mary do and why? What is the prisoner's dilemma result? What is the preferred choice if they could ensure cooperation? A $=$ Work independently; $\mathrm{B}=$ Cooperate and Lower Output. (Each results entry lists Raj's earnings first, and Mary's earnings second.)

Mary and Raj are the only two growers who provide organically grown corn to a local grocery store.
They know that if they cooperated and produced less corn, they could raise the price of the corn. If they work independently, they will each earn $\$ 100$ . If they decide to work together and both lower their output, and the other does not, the person who lowers output will earn $\$ 0$ and the other person will capture the entire market and will earn $\$ 200$ . Table 10.6 represents the choices available to Mary and Raj. What is the bestchoice for Raj if he is sure that Mary will cooperate? If Mary thinks Raj will cheat, what should Mary do and why? What is the prisoner's dilemma result? What is the preferred choice if they could ensure cooperation? A $=$ Work independently; $\mathrm{B}=$ Cooperate and Lower Output. (Each results entry lists Raj's earnings first, and Mary's
earnings second.)

Key Concepts

Prisoner’s Dilemma

The prisoner’s dilemma is a fundamental framework in game theory that illustrates why two rational individuals might not cooperate, even if it appears that cooperating would lead to a better collective outcome. The dilemma shows that individual rationality leads to a less desirable result, highlighting the conflict between collective and individual interests.

Cooperation and Coordination

Cooperation in game theory involves players coordinating their actions to achieve a mutually beneficial outcome, which, in contrast to the Nash equilibrium, can lead to higher payoffs for all. However, sustaining cooperation often requires trust or binding agreements, as the temptation to deviate for an individually higher gain can undermine these cooperative efforts.

Dominant Strategy

A dominant strategy is one that results in a better payoff for a player regardless of what the other player does. In many game-theoretic scenarios, such as the prisoner's dilemma, choosing this strategy is individually rational even though it may not lead to the socially optimal outcome.

Nash Equilibrium

A Nash equilibrium occurs when each player’s strategy is optimal given the strategies of all other players, meaning no player can gain by unilaterally changing their own strategy. In the context of the prisoner's dilemma, both players end up choosing the dominant strategy, creating an equilibrium that is stable even if it is not jointly optimal.

Transcript

00:01 Let's use this table of outcomes to determine what each of these players, both mary and raj should do, depending on what they think their partner will do.

00:11 So we're given this information that mary and raj are the only two growers who provide corn to a local store.

00:21 And these are their outcomes.

00:23 So if they collaborated and both lowered their supply, then they could drive the price up, right? so they would both earn 150.

00:30 Raj's earnings are in red and mary's are in blue.

00:34 Now, if they both didn't cooperate, right, they would have their normal market share of half each rate, so they could both earn 100, which is a bit less than if they collaborated.

00:45 But here's where the tricky part comes in.

00:48 If one of them does choose to lower their output, right, and the other one doesn't, then the other one will gain the entire share of the market, and they will earn 200 while the person who chose to try and cooperate will earn zero.

01:00 So let's look at how each of these players will behave knowing each of the conditions.

01:04 So if raj is sure that mary will cooperate, right? so mary is cooperating.

01:10 What is the best choice for raj in the situation? right.

01:13 So he could either earn 150 if he cooperates to or he could earn more 200 if he doesn't.

01:19 So in this case, the best choice for him is to not cooperate, right? because he can earn 50 more than if he did...

Please give Ace some feedback