Transcript econ lecture

Negotiation:
Markets, Rationality, and Games
Intro
• Once agents have discovered each other and
agreed that they are interested in buying/selling,
they must negotiate the terms of the deal.
• Might be simple (take it or leave it) or complex
(iterated bargaining)
• Might involve only price, or many other
dimensions (quality, service contract, warranty,
delivery, payment terms, etc.)
Mechanism Design
• By setting up the rules that agents use to negotiate,
we can ensure that particular sorts of behavior or
solutions occur.
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Truth-telling
Maximize profit
Maximize social welfare
Maximize participation
Reach solutions quickly
Etc.
• Choosing rules that lead to a particular outcome is
known as mechanism design
Supply and Demand
• Supply and demand are the two parameters
that govern a market’s behavior
• Supply: quantity of product available
• Demand: amount of product wanted at a
particular price.
Demand
• We can visualize demand as a downwardsloping curve
Quantity
demanded
Price
Supply
• Similarly, supply can be visualized as an
upward-sloping curve.
Quantity
demanded
Quantity
supplied
Price
Equilibrium
• The point at which supply and demand
intersect is called the competitive equilibrium
Quantity
demanded
Quantity
supplied
Price
In a perfect world, prices will drive supply and demand
to the equilibrium
Equilibrium
• One of the central tenets of market
economies is the invisible hand
• If there is too much supply, prices will fall
due to competition – this increases demand.
• If there is too much demand, prices will
increase – this encourages supply.
• In equilibrium, the quantity supplied will
equal the quantity demanded.
Breaking an Equilibrium
• There are many things that can keep a
market from equilibrium
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Lack of sellers (monopoly/oligopoly)
“Lock-in” among buyers
Incomplete or slow-moving information
Collusion among (usually) sellers or buyers
External price controls
Etc.
Properties of an Equilibrium
• Equilibria have some nice properties:
– Everyone who wants to buy/sell at this price
can.
– This sort of solution is called “efficient”
– Given this price, no one wants to change.
– The system is stable; given that you are at an
equilibrium you will stay there.
Rationality
• Rationality is the assumption that an agent
(human or software) will act so as to
maximize its happiness or advantage.
• We often try to measure this advantage
numerically using utility
• Money can sometimes serve as a substitute
for utility
Markets and Games
• Markets are useful for understanding interactions
among a large group of agents
– No need to speculate about individual actions
• In many e-commerce settings, negotiation takes
place in a one-on-one format
• In this case, game theory is a more useful
analytical tool.
– Also very useful for designing agents that operate in
open environments.
Game Theory
• Developed to explain the optimal strategy in
two-person interactions.
• Initially, von Neumann and Morganstern
– Zero-sum games
• John Nash
– Nonzero-sum games
• Harsanyi, Selten
– Incomplete information
An example:
Big Monkey and Little Monkey
• Monkeys usually eat ground-level fruit
• Occasionally climb a tree to get a coconut
(1 per tree)
• A Coconut yields 10 Calories
• Big Monkey expends 2 Calories climbing
the tree.
• Little Monkey expends 0 Calories climbing
the tree.
An example:
Big Monkey and Little Monkey
• If BM climbs the tree
– BM gets 6 C, LM gets 4 C
– LM eats some before BM gets down
• If LM climbs the tree
– BM gets 9 C, LM gets 1 C
– BM eats almost all before LM gets down
• If both climb the tree
– BM gets 7 C, LM gets 3 C
– BM hogs coconut
• How should the monkeys each act so as to
maximize their own calorie gain?
An example:
Big Monkey and Little Monkey
• Assume BM decides first
– Two choices: wait or climb
• LM has four choices:
– Always wait, always climb, same as BM,
opposite of BM.
• These choices are called actions
– A sequence of actions is called a strategy
An example:
Big Monkey and Little Monkey
Little monkey
c
w
Big monkey
w
c
w
c
0,0
9,1 6-2,4 7-2,3
What should Big Monkey do?
• If BM waits, LM will climb – BM gets 9
• If BM climbs, LM will wait – BM gets 4
• BM should wait.
• What about LM?
• Opposite of BM (even though we’ll never get to the right side
of the tree)
An example:
Big Monkey and Little Monkey
• These strategies (w and cw) are called best
responses.
– Given what the other guy is doing, this is the best thing
to do.
• A solution where everyone is playing a best
response is called a Nash equilibrium.
– No one can unilaterally change and improve things.
• This representation of a game is called extensive
form.