Name

1. Game Trees

a. Every node is immediately preceded by at least one other node. True  False

b. No path in a tree connects a decision node to itself.  True  False

c. Every node is the successor of a unique initial, or root, node.  True   False

d. A game may have more than one initial or root node.  True   False

2. Cheap Talk Netsoft is deciding what marketing strategy to use, either slick or simple, for its new computer game. Unfortunately for Netsoft another firm, Microscape, possesses the ability to produce a legal clone of the game.  Netsoft first decides on its marketing campaign, and then Microscape decides whether or not it will enter the market.  The payoffs in the following game tree are profits.

a. If Microscape finds itself at node 2 what action should it take?

b. If Microscape finds itself at node 3 what action should it take?

c. Given your answers to a. and b., what action should Netsoft take at node 1?

d. Before either firm must make an irreversible decision Microscape makes a preemptive announcement to the press that it will enter the computer game market no matter what.  Is this a credible threat?

3. Labor Day deja vue Principal must decide to offer a labor contract to Agent.  Agent must then decide to accept or reject the contract.  Upon accepting the contract Agent must decide on her work effort: Hi or Lo.  If Agent makes a Hi effort then there is a probability of 0.9 that revenues will be high as well.  If the Agent makes a Lo effort then there is only a probability of 0.1 that revenues will be high.  Agent's payoff depends on her work effort, not on the revenues earned by Principal's firm.  The game tree is pictured below.

a. When an offer has been made and accepted and Agent makes a Hi effort what is her expected payoff?

b. When an offer has been made and accepted and Agent makes a Hi effort what is Principal's expected payoff?

c. When an offer has been made and accepted and Agent makes a Lo effort what is her expected payoff?

d. When and offer has been made and accepted and Agent makes a Lo effort what is Principal's payoff?

e. Should Agent make a Hi or a Lo effort at node 3? Hi effort  Lo effort

f. Should Agent Accept or Reject the contract offer at node 2? Accept  Reject

g. Should Principal make an offer to Agent at node 1? Yes, make and offer.   NO.