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Lect02_Slides

# Lect02_Slides - Sequential Move Games Using Backward...

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S ti l M G Sequential Move Games Using Backward Induction (Rollback) to Find Equilibrium

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Sequential Move Class Game: Century Mark Played by fixed pairs of players taking turns. At each turn, each player chooses a number between 1 and 10 inclusive. This choice is added to sum of all previous choices (initial sum is 0). The first player to take the cumulative sum above 100 loses the game. No talking! Who are my first two volunteers?
Analysis of the Game • What is the winning strategy? What is the winning strategy? Broadly speaking, bring the total to 89. Then your opponent cannot possibly win Then, your opponent cannot possibly win and you can win for certain. Th fi t t i ! The first mover can guarantee a win! How to do this: to get to 89, need to get to 78, which can be done by getting to 67, 56, 45, 34, 23, 12, etc.

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Sequential Move Games with Sequential Move Games with Perfect Information Models of strategic situations where there is a strict order of play. Perfect information implies that players know everything that has happened prior to making a decision decision. Sequential move games are most easily represented in extensive form, that is, using a game tree . The investment game we played in class was an l example.
Constructing a sequential move game Who are the players? What are the action choices/strategies available to each player. When does each player get to move? How much do they stand to gain/lose? Example 1: The merger game. Suppose an industry has six large firms (think airlines). Denote the largest firm as firm 1 and the smallest firm as firm 6. Suppose firm 1 proposes a merger with firm 6. Firm 2 h d id h h i h fi 5 2 must then decide whether to merge with firm 5.

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The Merger Game Tree Firm 1 Since Firm 1 moves first, they are placed at the root node of the game tree. Buy Firm 6 Don’t Buy Firm 6 Firm 2 Firm 2 Buy Fi 5 Don’t Buy Fi 5 Buy Fi 5 Don’t Buy Fi 5 Firm 5 Firm 5 Firm 5 Firm 5 1A, 2A 1B, 2B 1C, 2C 1D, 2D What payoff values do you assign to firm 1’s payoffs 1A, 1B, 1C, 1D? To firm 2’s payoffs 2A, 2B, 2C, 2D? Think about the relative profitability of the two firms in the four possible outcomes, or t i l d f th t U i i t iti t k th terminal nodes of the tree. Use your economic intuition to rank the outcomes for each firm.
Assigning Payoffs Firm 1 D ’t B Buy Firm 6 Don’t Buy Firm 6 Firm 2 Firm 2 Buy Firm 5 Don’t Buy Firm 5 Buy Firm 5 Don’t Buy Firm 5 1A, 2A 1B, 2B 1C, 2C 1D, 2D Firm 1’s Ranking: 1B > 1A > 1D > 1C. Use 4, 3, 2, 1 Firm 2’s Ranking: 2C > 2A > 2D > 2B. Use 4, 3, 2, 1

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The Completed Game Tree Fi 1 Firm 1 Buy Firm 6 Don’t Buy Firm 6 Firm 2 Firm 2 Buy Don’t Buy Buy Don’t Buy Buy Firm 5 Don t Buy Firm 5 Firm 5 Don t Buy Firm 5 3 3 4 1 1 4 2 2 What is the equilibrium? Why?
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