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Review Questions

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- Two Dogs
- Two dogs, Rusty and Bowser go to the park. Once there they can engage in one of their two favorite activities, harassing squirrels or harassing joggers.
- Harassing joggers is more fun than harassing squirrels, but runs the risk that if one of them engages in this activity alone they will be caught and sent to the pound.
- Harassing squirrels together is more fun that doing so alone.
- Construct a suitable payoff matrix for this game.
- Suggest how the two dogs might coordinate on the good (harassing joggers) equilibrium.
- How might the outcome of the game depend of how often it is played?
- Why is important to you answer to part 3 that both dogs harassing squirrels is a Nash equilibrium.

Games People Play.

Two Dogs – Assurance Game

- The equilibria are at {S,S} and {J,J}.
- To select an equilibrium requires some kind of selection device “we always chase Joggers on Wednesday”
- If the game is repeated an infinite or unknown number of times Rusty and Bowser may adopt a trigger strategy to enforce {J,J}
- I

Games People Play.

- The “I love her she’s my cousin” game

- Many generations of the Strategorie and Umm families have lived in the hills of Oregon. They have had little or no genetic contact with the outside world. As a consequence of their isolation the two families have lost the capacity to think through problems using backwards induction.
- Each clan only engages in two activities “court’n” or “shoot’n”.
- The Strategories spend 90% of their time “court’n” the Umm’s spend 80% of their time “shoot’n”.
- There are initially as many Stretegories as Umms, N of each.
- The clan members encounter each other at random.
- If two “court’n” Umms or two “court’n” Strategories meet we get another member of the respective clan.
- If different clan members meet and both are “court’n” the lack of firearms means that neither clan’s population changes
- If two individuals of different clans meet but one is court’n and the other “shoot’n” one dies and one survives.
- If two individuals of the same clan meet but one is court’n and the other “shoot’n” neither dies but there are no children.
- If two individuals of either clan meet and both are “shoot’n” both die.
- How many members of each clan will there be in the next period?

Games People Play.

- The “I love her she’s my cousin “ game.

N/2 U’s meet N/2 S’s

Probabilities of events

We get the effects on the populations

S: 0.08(0) + 0.02(N/2) + 0.72(0) + 0.18(N/2) = 0.2(N/2)

U: 0.08(0) + 0.02(0) + 0.72(N/2) + 0.18(N/2) = 0.9(N/2)

Games People Play.

- The “I love her she’s my cousin“ game.

N/4 U’s meet N/4 U’s

Probabilities of events

We get the effects on the population

U: 0.64(0) + 0.16(N/2) + 0.16(N/2)+ 0.04(N/2)(1.5) = 0.38(N/2)

Games People Play.

- The “I love her she’s my cousin“ game.

N/4 S’s meet N/4 S’s

Probabilities of events

We get the effects on the population

S: 0.01(0) + 0.09(N/2) + 0.09(N/2)+ 0.81(N/2)(1.5) = 1.395(N/2)

Games People Play.

- The “I love her she’s my cousin“ game.

We get the total effects on the populations

U: 0.9(N/2) + 0.38(N/2) = 0.64N

S: 0.2(N/2) + 1.395(N/2) = 0.7975N

Games People Play.

- Who gets the cod?
- Two fishermen Salty Pete and Salty Joe decide to go fishing together as it takes two to man an offshore cod fishing boat.
- Before departing the two must decide how they will divide their catch.
- Salty Joe is a much better inshore fisherman than Salty Pete and can catch 20 cod on his own. Pete on his own cannot catch any cod.
- Together the Salts can catch 50 cod.
- How many cod do you expect each Salt to agree to get from the trip?
- Draw a diagram to illustrate your answer.
- Suppose Salty Pete could poison the fishing ground near shore so that Salty Joe on his own could catch 0 cod, but the two salts together could catch 40. Should Salty Pete do this? Why or why not?
- Suppose Salty Joe discovers dynamite fishing and can catch 40 cod on his own. How does this change their agreement and why.

Games People Play.

- Who gets the cod?
- Two fishermen Salty Pete and Salty Joe decide to go fishing together as it takes two to man an offshore cod fishing boat.
- Before departing the two must decide how they will divide their catch.
- Salty Joe is a much better inshore fisherman than Salty Pete and can catch 20 cod on his own. Pete on his own cannot catch any cod.
- Together the Salts can catch 50 cod.
- Surplus = 50 – 20, Share of the surplus Joe = 15, Pete = 15, so Joe gets 20 + 15 = 35 and Pete gets 0 + 15 = 15.
- See bargaining notes.
- Surplus = 40, share of Joe =20, share of Pete = 20. Pete should poison the fishing ground it lowers Joes threat point by enough to more than compensate for the reduction in the catch.
- Surplus = 50 – 40, Share of surplus Joe = 5, Pete = 5. Joe gets 40 + 5 = 45, Pete gets 5. Joe’s improved threat point increases his share of the surplus.

Games People Play.