Download Constructing Computational Traders with Learning Capabilities

Leigh Tesfatsion/Econ 308
Constructing Computational Traders
with Learning Capabilities
GENERAL DISCUSSION QUESTION:
Suppose you are tasked with designing a tradebot (computational
trader) with learning capabilities.
This tradebot must be able to survive and if possible prosper within
a particular specified computational economic world.
The computational economic world is populated by a collection of
other tradebots also striving to survive and prosper.
How would you go about this task?
ILLUSTRATIVE EXAMPLE:
A COMPUTATIONAL MARKET ECONOMY
MARKET STRUCTURE:
• Consider a dynamic economy with trading periods T = 1, 2, . . . , ∞.
• Suppose this economy is populated with:
– 6 bean-producing firms;
– 6 hash-producing firms (hash=fried potatoes!);
– 100 consumers.
• Beans and hash are perishable (non-storable) goods.
• All of the above market structure information is common knowledge to all market participants.
THE BEAN FIRMS:
• Each bean firm Bn desires to survive and prosper over time,
where prosperity is measured by earned profits.
• Each bean firm Bn has a production capacity (size) CapBn
measured in pounds of beans.
• Each bean firm Bn has an initial net worth level, NetWorthBn ,
measured in dollars.
• At the beginning of each trading period, each bean firm Bn can
choose to produce anywhere from 0 to CapBn pounds of beans.
• For each bean firm Bn, the cost of producing b pounds of beans
is cBn · b, where the marginal cost cBn is positive (so production
costs strictly increase with increases in production of b).
• If a bean firm Bn sells bn pounds of beans at unit (per pound)
price pBn, its profits (revenues minus costs) are
[PROFITBn] = [pBn · bn − cBn · bn]
• The specific values for CapBn, NetWorthBn , and cBn are private
attributes of bean firm Bn .
THE HASH FIRMS:
• Each hash firm Hj desires to survive and prosper over time,
where prosperity is measured by earned profits.
• Each hash firm Hj has a production capacity (size) CapHj measured in pounds of hash.
• Each hash firm Hj has an initial net worth level, NetWorthHj ,
measured in dollars.
• At the beginning of each trading period, each hash firm Hj can
choose to produce anywhere from 0 to CapHj pounds of hash.
• For each hash firm Hj , the cost of producing h pounds of hash
is cHj · b, where the marginal cost cHj is positive (so production
costs strictly increase with increases in production of h).
• If a hash firm Hj sells hj pounds of beans at unit (per pound)
price pHj , its profits (revenues minus costs) are
[PROFITHj ] = [pHj · hj − cHj · hj ]
• The specific values for CapHj , NetWorthHj , and cHj are private
attributes of hash firm Hj .
THE CONSUMERS:
• Each consumer k has an income Inck (measured in dollars) in
each trading period t.
• Each consumer k has nonnegative minimum subsistence consumption levels (b̄k , h̄k ) for beans and hash that must be met
in each trading period t in order to survive to the next trading
period t + 1.
• Each consumer k obtains utility (happiness) from the consumption of beans b and hash h, measured by a utility function
Uk (b − b̄k , h − h̄k ) which is an increasing function of b and h
(more consumption of either good is strictly preferred to less).
• Given any particular posted prices for beans and hash, the objective of each consumer k is to demand (buy) “feasible” amounts bk
and hk of beans and hash to maximize his utility of consumption
Uk (bk − b̄k , hk − h̄k ).
• Feasibility means that consumer k’s bean and hash demands
(bk , hk ) are nonnegative and that the expenditures needed to
satisfy these demands do not exceed consumer k’s income. That
is, if pB and pH are the prices that must be paid by consumer k,
pB bk + pH hk ≤ Inck .
• Inck , b̄k , h̄k , and Uk are private attributes of consumer k.
MARKET PROTOCOLS:
• At the beginning of each trading period t, each bean firm Bn
produces a supply of beans and publicly posts a unit price for
beans.
• At the beginning of each trading period t, each hash firm Hj
produces a supply of hash and publicly posts a unit price for
hash.
• In each trading period t, each consumer k attempts to maximize
his utility by buying feasible amounts of beans and hash at the
lowest possible posted prices.
• At the end of each trading period t, positive profits accrued by
a firm during t add to the current net worth of that firm and
negative profits accrued by a firm during t must be paid out of
that firm’s current net worth.
• Any firm that becomes insolvent (negative net worth) must
immediately exit the economy.
A TRADEBOT TOURNAMENT PROBLEM:
• Suppose we are participating in a TRADEBOT TOURNAMENT
in which various people have been tasked with designing tradebots to carry out decision making for the bean firms, hash firms,
and consumers in the Computational Market Economy.
• Suppose that we have been specifically tasked with the design of
a bean tradebot for bean firm 1, (our CLIENT bean firm) with
attributes CapB1 = 100 pounds, NetWorthB1 = $10, 000, and
cB1 = $1.00 per pound of beans
• The objective of our client bean firm is to stay in business over
the long haul, making as much profit as possible.
• How should we design our bean tradebot to make price and
quantity decisions for our client bean firm in each trading period
t, starting with period t = 1?
• Specifically, what kind of STRATEGY should we build into our
bean tradebot for making price and quantity decisions in the first
few trading periods?
• And what kind of LEARNING capabilities should we build into
our bean tradebot to enable it to update its strategy over time
in an attempt to survive and prosper?