Current assignments:

• The homework will be due Tuesday, Feb. 11.

• North Korea escalation activity: Discussion
• The dollar auction as an escalation model
• Decision trees

Nuclear escalation: North Korea

• Review of scenario
• Most scenarios lead to nuclear war.
• The U.S. prefers sanctions to aid.
• If it chooses sanctions, it gets nuclear war.
• If it chooses aid, it gets disarmament.
• Disarmament is preferable to nuclear war.
• Must use long-term strategy.
• North Korea's preferences depend on what has come before.
• If U.S. imposes sanctions, N.K. prefers war to disarmament.
• If U.S. gives aid, N.K. prefers disarmament to war.
• Optimal strategy for both:
• N.K. builds nuclear weapons
• U.S. offers aid
• N.K. dismantles nuclear weapons
• Another strategy avoiding nuclear war:
• N.K. builds nuclear weapons
• U.S. ignores threat ("mutual assured destruction")
• U.S. will not do this because it prefers giving aid to ignoring the threat
• Another strategy:
• N.K. does not build nuclear weapons
• N.K. will not do this because it definitely leads to conventional war, which it will lose
• Another strategy:
• N.K. builds nuclear weapons
• U.S. imposes sanctions
• N.K. dismantles weapons
• N.K. will not do this because it prefers war to disarmament under sanctions
• North Korea has an advantage:
• Under optimal strategy, North Korea gets aid
• U.S. cannot "win"
• Question: Is this scenario realistic?
• Determining the optimal strategy (decision tree):
• Step 1: the full tree
• Step 2: prune N.K.'s choice
• Step 3: prune U.S.'s choice
• Step 4: prune N.K.'s choice

Escalation in general

• Preferences can change depending on circumstances
• e.g. North Korea prefers war to peace after sanctions
• but prefers peace to war after aid
• Short-term victory may lead to long-term loss
• e.g. U.S. prefers imposing sanctions at step 2
• but this leads to nuclear war, which U.S. does not want
• To determine optimal strategy:
• both parties need to know the other's preferences
• each one makes choices based on expected response of the other
• both parties need to look several steps ahead
• if the tree stops somewhere, you can do "pruning"
• Examples of conflict escalation
• U.S.-Vietnam war (1959-1975)
• U.S.-Colombia war (1998-present)
• U.S.-China spy plane conflict (2001)
• U.S.-U.S.S.R. nuclear arms race (1945-1990)

The dollar auction

• Rules:
• Bid in increments of $0.05
• High bidder gets $1.00 and pays bid
• Second-highest bidder pays bid
• Why is this an escalation model?
• If two people get into the bidding, they have already invested, win or lose
• At each step it makes sense to continue bidding; in the long run it does not
• Bidders may bid over $1.00; eventually it becomes about minimizing losses, not trying to win
• Analogous to Vietnam war: U.S. did not want to pull out even though it knew it would not win in mid 1960s
• If both players can keep going indefinitely, it does not make sense to bid
• To determine an optimal strategy, we will impose a bankroll b on both players
• If the bid reaches b, the game stops
• This way the decision tree stops
• One last rule: the conservative convention
• Suppose that a player could make two bids that lead to the same result
• Both players need to know what would be chosen in order to determine the optimal strategy
• Textbook uses the "conservative (cautious) convention":
• If two bids would both lead to the same expected outcome, the bidder will choose the cheaper one
• The full dollar auction is too big to work out explicitly. Simpler version:
• Two players bid for a stakes s of $3
• Bid increments are $1
• If the bid reaches bankroll b, also $3, game stops
• Both players assumed to use conservative convention
• Set up the full decision tree: p corresponds to passing, i.e. not bidding
• Decision tree slide show
• The optimal strategy is for player one to bid $1
• Player two will then pass
• Player one earns $2, player two gets $0
• Notice how important the conservative convention is here
• Suppose player two is not cautious, but instead belligerent
• After player one bids $1 or $2, player two will always bid $3
• It makes no difference to player two, but player one always loses
• In this case the optimal strategy is for player one to bid $3 to start
• Conclusion: it's very important to know what strategy each bidder is using
• Question:
• In the real dollar auction with nickel bids and a $1.00 prize, what is the optimal strategy?
• Need to know a bankroll; let's suppose the auctioneer cuts it off when it reaches $5.00
• A bid of $0.95 is a good idea, since nobody will bid $1.00 and you're guaranteed $0.05
• But the optimal bid is actually $0.25 (B. O'Neill)
• We will prove this later