# Warm-Up 4, Due Monday, September 8, 23:59.

Warm-up questions usually either address material we handled during last class, or material you were to read in preparation for class, or you are supposed to answer questions based on your common sense alone. Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try to tell me why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

## Question 1

Play the so-called Location Game on this page. Play the first graph, the first white box. Here we want to play the simultaneous version, where both players place their restaurant simultaneously. Since you want to play against the computer, click the yellow "sim You|Comp" button before you select a village by clicking on it. Do this several times, then describe how to play this game well, and how high a payoff you would expect. Use the labeling as in the picture to the right.

## Question 2

This question refers to the sequential Location Game, where both players place their one restaurant one after the other. Play the first graph, the first white box. Click the yellow "seq1 You|Comp" button or the yellow "seq1 Comp|You" button, depending on whether you want to move first or not. Play this several times, then describe how to play this game well, and how much payoff you would expect, in both cases of you or the other player moving first.

Also answer the following question: If there a simultaneous game is made into a sequental game with both players doing their move one after the other, whose advantage is this, the advantage of the player who has to move first, or the advantage of the player who moves second?

## Question 3

Look at the following game:
NIM(6,2): 6 stones lie on the desk. Beginning with White, Black and White alternate to remove either one or two stones from the desk. Whoever first faces an empty desk when having to move loses. The winner gets \$1, the loser loses \$1. What are the best strategies for the two players?

Play this game at against the computer. Play ten rounds where you start with 7 stones. Then play ten rounds where you start with 9 stones. Then play ten rounds where you start with 8 stones. Note that you alsways start. Discuss your observations. How should the two players, the one who starts, and the one who moves next, play the game?