Discussion Questions on Section 14.1

Note:  at this initial point in our discussion, take "strategies" to be "pure strategies" only.

1.  To define a game, one needs to specify the players, the strategies, the payoffs, and the capacities of the players, especially their knowledge. Though it is easy to define a player, the definitions of strategies and payoffs are more difficult. Define "strategies" and "payoffs" in your own words.  What is the difference between the moves available to a player and the strategies available to a player?  In what units are payoffs measured?

2.  Consider the following game.  Jill proposes either to divide $10 evenly between herself and Jack or proposes to give $1 to Jack and keep $9 for herself.  Then Jack gets to accept what Jill proposed or to reject it.  If Jack accepts, they get the amounts Jill proposed.  If Jack rejects Jill's proposal, both get nothing.

a. How many strategies does Jill have?  What are they?

b. How many strategies does Jack have?  What are they?

c.  List all the strategy pairs and the monetary payoffs to Jill and Jack resulting from each pair.

d.  What more do you need to know (or assume) in order to specify the payoffs.

e.  Make any needed assumptions in order to specify the payoffs resulting from each strategy pair and write out the extensive form (game tree) of the game.

f.  Using the same assumptions write out the normal or strategic form of the game.

g.  Circle the Nash equilibrium (or Nash equilibria if there is more than one) in the normal form of the game.

3.  Consider the following normal form:

Jack

Left

Right

Jill

Up

3, 3

1, 4

Down

4, 1

2, 2

a. Circle the Nash equilibrium (or Nash equilibria if there is more than one) in this normal form.

b. What is odd or interesting about this game?