Suggested exercises

8.4 Strategic games

Nearly all the exercises are interesting. Some suggestions:

1. Centipede game …

  • Note that considering social preferences this is used to consider ‘trust and trustworthiness’

  • Note that even though this is a sequential game it can be modeled as a strategic game (strategic form)

Hint:

Let the players’ sets of actions be \(A1 = \{1,3,5,...,99,\infty\}\) and $A2 = \(\{2,4,6,...,100,\infty\}\), where the action \(t\) means stop at period \(t\) and the action \(\infty\) means “never stop.”

3. War of attrition

5. Guessing two-thirds of the average

I discuss a similar game here at about 40:00, accessible to BEEM101 students only. I am slightly imprecise here, but I convey the intuition for why this is a unique strategy that survives Iterated Strict Dominance.

AKA the ‘beauty contest’

6. “Cheap talk”

Note that ‘cheap talk’ is a big topic in game theory.

8. All pay auction

There has been some literature arguing that such auctions could have certain benefits in fundraising for charity/public goods, at least relative to ‘standard charity auctions’.

9. Another version of the location game

This relates to Public Choice and Political Science; see the ‘Median Voter Theorem’

11. Contribution game

Very relevant to public goods, cooperation, and Public Economics

15. Hawk or dove

A model from biology (I think) that is applied widely, e.g., to competition between firms

8.5 Extensive games

OR-1: Trust game

This setup is used (even more often than Centipede) in the social preferences literature to measure ‘trust and trustworthiness’. But note that the payoffs in a game we model should include any social preferences (unlike you are asked to do in this problem).

OR-4: Comparative statics

OR-5: Auctions

OR-6: Solomon’s mechanism

This relates a bit to the field of ‘mechanism design’… we see this procedure didn’t require King Solomon to even know which player was the ‘true owner’… thus this ‘works’ even under asymmetric information.

OR-8: Race

OR-10: Implementation

Again, this touches on ‘mechanism design’