Stress, budget constraints
and expectation. Can simulation help study more precisely models that can be
deduced from experimental economics?
1
GREQAM, CNRS, 2 rue de la Charité,
13002 Marseille, France
rouchier@ehess.cnrs-mrs.fr
2
GATE, CNRS
93, chemin des Mouilles
- B.P.167
69131 ECULLY cedex, France
robin@gate.cnrs.fr
Abstract. This paper describes a multi-agent model of double-auction market in
which simulations are led with artificial agents. The study of market can be
focused on the study of information processing for the agents, and this means
that one has to make assumptions about the cognitive use that the agents do of
these information. For a few years, experiments have been used to study
auctions. The resulting data have more recently been used to make hypothesis
about learning and have occasionally been translated in algorithms. We propose
here simulations that are organised on the same model as experiments, as a
succession of auctions session where each agent is given a good at the
beginning of the session and has to exchange it before the end. Agents are
either seller or buyer and make bids and asks along the time, that can be
accepted by the others and lead to transactions. Our main result is the fact that we actually obtain convergence
although agents have no knowledge of others’ limit prices and only interact
through a completely impersonal market, which correspond to experimental data.
1 Introduction
Trading institutions, such as markets, are at the centre of economics preoccupation. However, their rules and how they are interpreted by individuals are rarely discussed in the economic literature. Indeed, a small variation in the market institution can have large effect on the behaviours and as a result, can affect price formation and market efficiency. This result is clearly demonstrated by experimental studies of market (Plott 1989).
These experiments are often interpreted in terms of information use: markets are seen as good structures that enable the aggregation of information into prices. Thus it seems necessary to understand the formation of price in diverse institutional context to create a better view of these aggregation properties. As Hayek points out in his 1945 paper, "We must look at the price system as such a mechanism for communication information if we want to understand its real function"[1]. To capture the informational aspect of market, one has to represent it as a decentralised coordination mechanism. We propose to combine the experimental method and the simulation technique to study this question. Precisely, we want to study how people behave in a market, how they communicate, get information and interpret it, by observing how they exchange. We propose an approach of price formation and market efficiency based on individual behaviour and individual learning in a market.
There exists a lot of different market institutions, each of which display different properties and performance. In the laboratory, price patterns, volume, distribution and market efficiency are the variable observed. Efficiency as introduced by Plott and Smith (1978) measures if the system attains the efficient Pareto allocation (the best global value that could be created by matching buyers and sellers, and that could occur if someone knew all the agents’ reservation price).
We are interested in the study of the Double-Auction mechanism: it is a market with buyers and sellers who all participate in this double-sided auction and come to the market with an individual limit value they are wiling to spend or get; any standing offer has to be followed by a better offer (higher for a buying proposal, lower for a selling proposal); the market clears after a certain time or when all goods have been sold. This institution is recognised as being one of the most efficient markets institutions (Holt 1995), which means that when a market is organised with this institution, prices converge quickly towards the walrasian equilibrium price and that allocation is efficient (buyers and sellers are as well off as they can be considering the repartition of goods). This result is said to be robust since it can be found in diverse organised experiments, where individuals participate in a succession of markets. It is true with a small number of participants (Smith and William 1989), when the environment is said unstable (meaning that the limit value for the participants change at each market opening, and hence that the equilibrium price vary), and even if some transaction costs are added to the participation of the market (Noussair, Robin, Ruffieux, 1998). When one sees prices converge towards the equilibrium price without agents to have any information about what it should be, one can consider that there is a collective learning taking place. The process on which this learning is based is for the moment a complete mystery and it seems then interesting to try to discriminate which data are important for the actors and which are not.
To represent the double-auction mechanism, we use a framework that is considered as typical in experimental economics, and which was proposed by Friedman (Friedman, 1993). Our main assumptions in the representation of cognition are based on the one Easley and Ledyard use in their model, putting emphasis on the evolution of a reservation price for agents that evolve because they are conscious of the end of the session and thus stressed by time (Easley and Ledyard, 1993). However we translate it in a dynamical way, whereas these authors were mainly interested in finding in which initial configuration efficiency could be attained.
This classical approach has been widely complemented by experiments (Holt 1995; Plott 1989; Noussair, Robin and Ruffieux, 1998), and also the building of artificial societies where agents are put in settings that are equivalent to the experimental ones. Several learning algorithms have been proposed to reach convergence in these markets. This institution is however so “strong” for participants, that it seems that even a Zero-Intelligence agent (acting randomly but following the rules of behaviour defined by the institution) could be a quite good participant in such a simulated environment (Gode and Sunder 1989, 1991). Indeed, the double-auction puts such a constraint on the possible proposals for both buyers and sellers, that anyone who conforms to the rule helps the system get closer to the equilibrium price. This very high efficiency is not true of any market institution that can be designed (Smith, 1994 ; Noussair and Ruffieux, 2003). However, it can be put forward that there still exists an issue for convergence in the case when the environment is not stable (limit values change over time) in which case, one need a real learning algorithm for agents, not just a randomised behaviour (Brewer et al, 2002).
The joint use of experimental results and building of artificial societies is an exercise that is now spreading in economics, certainly due to the fact that in both fields, researchers are keen to identify, model and test the actual behaviour of individuals when faced with some economic choices (Duffy, 2001). At the moment, both approaches, viewing social systems as emergent structure based on dynamical interactions of learning agents, are interested in the coherence and applicability of theories more than their exactness in an abstract setting (Smith, 2002). Although the DA (Double-Auction) has been studied intensively in the laboratory, only recently have tools started to become available to provide a behavioural theory of DA market. To participate in the development of such a theory, we want to test a set of hypothesis regarding behaviours of agents in the context of this market, and hence we created a multi-agent platform that allows the test of several types of cognition.
Our approach is to test different cognitive characteristics of artificial agents, a “cognition” being here defined as how much information the agent gets from the environment (is it interested in only private knowledge or does it know about all offers), his memory (how far can it go back in time) and a way to process the information. By comparing results of simulations and results of experiments we would like to see if it’s possible to evaluate our learning models according to the relative proximity to actual humans behaviours. This can help us understand what do humans actually learn when they are faced with that type of exchange institution, and hence build artificial agents that might adapt to closely related institutions.
It can be noted that, as we said previously, Gode and Sunder (1993) made an important paper on the cognition of agents places in a double-auction setting, showing that any automated action that obeys the rule of the auction would get to convergence to the equilibrium price. What Brewer et al. (2002) showed, however, is that this convergence would only be attained if the limit prices of the agents were staying the same (see next section to see why this is a special case of the double-auction), and that it is an intra-period convergence, with no convergence from one time-step to another. From this they conclude that not any simple algorithm could help attain a good representation of global behaviour or the system, not to speak of the imperfection of the represented individual cognition. The assessment of the cognition then has to be based on experimental data, treated through a precise protocol of econometric comparison to evaluate the likeliness of the convergence.
In this paper we present briefly the DA institution and the mains results observed in experimental DA market. Then we describe a multi-agent system that organises a framework of DA auction and includes several proposals for an agent cognition (made of a decision-making process and a learning algorithm). Our first results consist of a set of observed data from artificial markets sessions, based on some usual indicators like the existence of a convergence towards equilibrium or the efficiency globally attained, that enable us to assess some aspects of our model as well as correct others. Eventually, we propose the methodology we want to use to carry on in our research.
2 DA institution and experimental market
2.1 Double auction markets rules
The
continuous double auction is a two-sided progressive auction. We use here one
of the typical situations used in experiments (Friedman, 1993). Agents are
divided in two groups: buyers and sellers. Both have limit prices for the
commodities traded, that are private information. Here, there is only one type
of good that is exchanged and each agent possesses only one unit of that good.
At any moment, buyers can submit price-quantity pairs, called bids, which are
offers to buy the specified quantity of units at the indicated per unit price.
Similarly, sellers can submit price-quantity pairs, called asks, which are
offers to sell units at the indicated per-unit price. Both, buyers and sellers
may propose an offer or accept the offer made by agents on the other side of
the market. If a bid or ask is accepted, a transaction occurs at the offer
price. An improvement rule is typically imposed on new offers entering the
market, requiring submitted bids (asks) to exceed (be less than) the standing
bid (ask). Each time an offer is satisfying for one of the participant, he/she
announces that he/she accepts the trade at the given price, and the transaction
is completed. Once a transaction is completed the market is cleared (there is
no standing bid or ask any more) and the agents who have traded go out of the
market. At that moment, like at the very opening of the market, the first offer
can take any value, and the price proposed imposes a constraint on any following
offer. When the market closes, agents who have not traded yet cannot do it anymore.
Studying auctions, we consider that the agents have strong incentive to exchange,
and that there is a cost associated to this failure. In experiments, participants
just get no reward instead of getting some otherwise.
Usually, an experiment on double auction market is organized as a succession of market period. Here we are interested in markets where the same situation applies at the beginning of each market, agents being given exactly the same good to sell or buy. What is observed is the evolution of prices of transaction along the time: one can consider that it indicates how well participants adapt to the opportunities offered by the market setting. In most experiments there is a global “learning” taking place at two levels: during each market period the prices converge to the theoretical equilibrium; from one period to the other the initial transaction prices get closer to that equilibrium (as can be seen on Figure 1). One evaluates the efficiency of the market, as a comparison of the surplus made by the individuals with the best surplus they could get.
Fig 1. Bids, asks and prices of transactions as a function of time for an experiment with 4 sellers and 4 buyers trading for 15 periods. Vertical lines represent opening and closing moment of market periods, the horizontal black line represents the equilibrium value. Each dot is a bid or an ask that is expressed as a proposed price for transaction. Actual transactions occur when a bid proposed by a buyer (ask proposed by a seller) is accepted by a seller (buyer). Red circles that are linked together indicate these prices of transactions. One can see a clear convergence towards the equilibrium price within each market opening and along the time high efficiency after the fourth period. (results from experiments by Robin, with students of the ENSGI school in Grenoble, 1999).
The convergence needs to be explained in the context of private information, as the result of individual learning sustained by some common knowledge. Multi-agent modelling enables us to create a simulation platform in which different cognition can be tested. The platform is built so that to inspect several aspects of the cognition, which is defined as the information perception and processing that leads to action by the agents. We consider to be a parameter of cognition:
· The type of which information the agents get: can they perceive all transactions that take place or do they witness only their own transactions (global or local point of view)
· Do they use a long term or short term memory? We consider then the number of transaction prices that are taken into account.
· The way they update their reservation price at a given moment, according to all the information they possess. Several assumptions can then be made.
2.2 Experimental economics and Multi-agent model
Experimental economics is a field of economics that studies actual behaviour of individuals when they are faced with certain economical setting (Smith, 1994). The idea is that the experimenter creates a situation that is linked to a theoretical issue, where it is possible to calculate the equilibrium behaviour when one possesses all the individual information of the agents. In that setting, the experimenter then puts individuals who are then given only partial information on the system, which can be private knowledge (unknown from the others) and public or common knowledge (Tuomela and Bonnevier-Tuomela 1995). The setting that is chosen can be a controlled market, or the production of a game-like situation (“game” understood as in “game theory”): it is always a very archetypical setting in which the role, ability to act, and communication rules for each actor are very clear, quite limited and very easy to observe. When the actual experiment takes place, humans are isolated to play the defined game, their behaviours are observed and compared to the one exhibited by a perfectly rational agent, as predicted by economic theory. Differences can be interpreted as alternate motivational aspects from the classical approach, where actions are not led only by wealth increase, or as signs of limited cognitive ability when optimal calculus is too difficult or not relevant (see for example Allais’ paradox). By varying the information that the individual gets during an experiment and analysing the different results that are globally produced, it is possible to put forward which bit of knowledge is actually used. From this work, it is possible to formulate positive assumptions about the decision process of individuals.
The comparison between experimental results and the building of
artificial society is an exercise that is now spreading in economics, certainly
due to the fact that in both fields, researchers are keen to identify, model
and test the actual behaviour of individuals when faced with some economic
choices (Duffy 2001). Vernon Smith (Smith 2002) explains that no experiment can
actually destroy a theory, but that it can be used to ask new questions, and
more importantly to identify situations where theory cannot help anticipate all
results, hence the limits of existence of a phenomena. This approach is very
close to what most researchers using artificial agent-based worlds do state:
simulations are not used to create an alternative theory but to try to reproduce
known situations and find out how the theory of individual actions can sustain
this creation of an artificial universe. Hence, Agent-Based Social Simulation
(ABSS) looks at coherence and applicability of theories more than their exactness
in an abstract setting. Like experimental economics, ABSS look at the dynamical
co-action of individual and the way these different actions, some of them being
interactions, get organized as emergent situations in the society. This issue
is almost absent of recent classical economics, and both approaches have to
invent tools to organize the research and the observation so that to reveal, capture
and test the explanatory cognitive elements. This leads to the apparition of
new ways to describe and consider scientific results, with issues being not
solely focused on positive results, but also on applicability in systems (Barreteau
and Bousquet, 2000; Smith, 2002).
Indeed for the moment, it is still difficult to establish results that are general enough to give theoretical knowledge on artificial systems, like experimental settings or purely artificial universe. Actually, multi-agent simulations have been widely used in a looping process (called “companion modelling”): assumptions about a given reality are modelled and lead to simulations, the results of simulations can usually be contradicted by some elements observed in reality and hence help at focusing at other elements than the one that were previously observed. After a few loops between artifice and observation, the model usually captures social reality in a good way (Bousquet et al., 1999). Following the tradition of participatory approaches in decision making research, the simulated model can even be use to discuss the representation of social organisation and individual cognition with the actors that are represented in the model. The description that is more spontaneous to understand than centralised model helps the communication between stakeholders and scientists and reveals itself quite useful to capture better diverging rationalities (Bousquet et al., 2002).
Independently from purely applicative approach, experimental
economists have started to use artificial agents to complement their
experiments. One aspect is the use of experiments to roughly calibrate some
parameters of the setting, using multi-agent simulation (which they call
“experiments with artificial agents”). This common practice is rarely described
in publications but appears as quite common via (diverse personal
communications).
A more elaborated approach consists in proposing cognitive algorithms for the
agents and then to validate the algorithm or more reasonably to calibrate them
in relation to results obtained by human participants playing in a completely
equivalent setting. This is what Gode and Sunder propose about a double-auction
market (1994). Duffy (2001) describes this process on the topic of speculation,
and he even proposes some mixed simulation where humans are exchanging with
other humans as well as with artificial agents (being conscious there are
artificial agents, but not knowing who they interact with at a time-step).
Eventually, Janssen and Ahn propose a very precise calibration work to compare
two models of rationality in a common-good provision game: the Experience-Weighted
Attraction by Camerer (EWA) and the Best Response with Signalling (BRS)
(Janssen and Ahn, 2003). Our work is thought as related to these research programs.
3 Multi-agent model of a double auction market and simulation protocol
3.1 Artificial setting and agents’ learning
The model we built represents the institution of double auction market and is populated by agents who are either buyers or sellers. A simulation is organised like the experiments that were described in the previous section, as a succession of market opening period where agents can exchange only when the market is open. During one market period, the auction is defined in an non-continuous way, as a succession of steps: for one step buyers announce their ask or accept a transaction, for a second step sellers announce their bid. This succession, easier to implement than a continuous auction, has been shown to be a good approximation of a continuous situation (Gode and Sunder, 1993).
In our market, there are thus buyers and sellers, which are given limit prices at the beginning of the simulation. By choosing these values in an appropriate way, one can decide how many agents can participate in the market when exchanges take place at the equilibrium price. The simulation is made of a number of successive markets, which length is given by a certain number of steps. It is important to make this number relatively high compared to the number of participating agents so that they can all make proposals if they wish. At each moment (or “step”) the market is defined by either a couple of outstanding bid and offer, which constraint the agents’ proposals, or by an clear situation, with any proposal being acceptable. Stress times (as explained below) are randomly attributed to agents at the beginning of the simulation.
To structure the learning of our agents, we took as a reference
the paper by Easley and Ledyard (1993). They propose to structure the
individual decision-making process around two elements defining an agent:
reservation price and stress. The reservation price evolves in time; for a
seller, it is the minimal price for a transaction at a given moment: it thus
has to be higher than or equal to the limit price and can decrease along the
time; for a buyer it is the maximum price for a transaction and thus is always
less than or equal to the limit price and can increase in time. When an agent
proposes a price, it is always its reservation price. Stress is the time-pressure
that is perceived by the agent: it expresses the fact that the agents know they
have to exchange before the end of the market period.
An agent is defined by its attributes: Type (seller or buyer), Limit price, Stress time, Memory (either “global” and the agents remembers all transactions that take place or “local” and the agents only remembers its own transactions), Memory length: (the number of past transactions remembered), Reservation price.
Here we keep the same conditions for each successive market: agents always keep the same role, either buyer or seller; have the same private limit price. The memory is a list that evolves each time a transaction occurs.
Stress. The time pressure is defined by the individual stress-time of the agent, also used by Easley and Ledyard (1993). At any time-step after that time limit, the agent has a chance to revise its reservation price. This opportunity changes at each period T and results from a random test. An agent with stress time ST participating in a session of length L revises if:
|
U [0 ;1] > (L – T) / (L – ST). |
(1) |
This means that the probability to revise gets greater as time passes[2].
We led two types of simulations, some where the stress time would evolve in time and some with a constant stress time given at the beginning of the simulation. The evolution of stress time takes place at the end of a session and depends on the success of the agent:
If the agent made a transaction then the stress time is chosen randomly as later period in the session (ST = U [ST + 1; L-1]),
If the agent fails to transact, its stress time is lowered (ST = U [1 ; ST – 1]).
Reservation price. The reservation price is the maximum price a buyer is ready to pay or the minimum price a seller wants to get for its good. It evolves at each period, and within a period at each time-step after the agent’s stress time, when it decides to revise[3]. The definition of the reservation price depends on initial values and on past transactions, which are stored in the memory of the agents. In this paper we are interested in testing the influence of different ways of learning on the convergence of prices, hence we consider several parameterisations of memory. Agents use the average value of the past prices so that to decide of their revised price[4]. A “local” memory will only take into account transaction in which the agent was involved. A “global” memory is based on all transactions in the society. The memory length represents the number of transactions that are considered to produce the referential average for the agent[5]. Reservation price and limit price are very different even if they are linked: the limit price is exogenous and stable over the whole market; the reservation evolves as an endogenous variable that can vary at each time step once the stress time has been attained. At the beginning of the simulation, this reservation price is defined as a function of the limit value of the agent and the space of possible values, which size is called Diff:
|
Diff = minimum value for sellers – maximum value for buyers. |
(2) |
Then the initial reservation price of a seller is randomly chosen such that:
|
RP = U [Limit value ; Limit value + (Diff / 2)]. |
(3) |
The initial reservation price of a buyer will then be:
|
RP = Max (U [Limit value - (Diff / 2) ; Limit value] ; 0)[6]. |
(3) |
At the beginning of each session, the reservation price will vary depending on the success of the agent in the previous session:
· If it succeeded to make a transaction then the price of exchange is its new reservation price,
· If it did not exchange, then its reservation price is unchanged.
Here we give the algorithm of revision for a seller, knowing that the calculus is symmetrical for a buyer, provided the value stays positive. In any case, once the reservation price equals the Limit Value, the agent does not revise anymore.
· If the seller can calculate the average value of transactions and if its reservation price is higher than that value, then the new RP is the maximum of this Average and the Limit Value of the agent,
|
RP = Max (Average, Limit value). |
(4) |
· If the seller cannot calculate the average value of transaction or if its reservation price is lower than the average value, then it reduces its reservation price to get to a value that is still higher than its limit value by:
- (random) Choosing randomly a value between the actual Reservation
Price and the Limit Value: if the r follows a uniform law, and S the step
to be subtracted to RP:
|
r
= U [0 ; 1] S
= (RP – VL) * r2 RP
= RP – S. |
(5) |
- (individual step) Defining an individual
step that represents the value to take off so that to get to Limit Value
at the end of the session if the agent was revising at each time-step:
|
IS
= (RP –LV) / (T – L) RP
= Max (LV ; RP – IS ). |
(6) |
- (general step) Taking a general step,
common to all agents, off the actual value. This step is defined as the
portion of the space of possible transaction (Diff, defined earlier)
divided by the time that is left until the end of the session:
|
GS
= Diff / (T – L) RP
= Max (LV ; RP –GS ). |
(7) |
The reservation price is used by the agents to make offers and bids on the market as described in the following section.
3.2 Simulations and initialisation
Time-steps. A simulation is a succession of market sessions, organised as a succession of period. At each odd period, buyers make a proposal and at each even period, sellers make a proposal. Each time a transaction is concluded, the market is cleared, which means that there is no outstanding bid or offer, and hence that there is no constraint on the proposal of the agents[7].
At each period, agents first revise their reservation price. Then, one agent is randomly selected among those which reservation price allow to accept the offer. For example, a seller can make a transaction if its reservation price is lower than the last bid made by a buyer. In that case, the transaction price is the one that had been proposed by the buyer. If no one can exchange, one seller is chosen among those that can make an offer (ie. which reservation price is lower than the outstanding offer). Then, one goes to the next period.
Initialisation. To define a simulation, one needs to state some parameters.
A simulation is defined by the simulator as:
v A
number of sellers and buyers;
v The
number of period of a session and the number of number of sessions in a simulation;
v A
minimum and a maximum price are chosen for each type of agents so that to define
the set of possible limit prices;
v The
type of memory: local or global; the number of transactions that are taken into
account
When the universe is created:
v Agents
are created as sellers or buyers;
v Each
agent gets its limit price that is randomly chosen following a uniform law
between the values chosen by the simulator;
v
Each agent gets its stress time, randomly chosen
between the first time-step of the period and the one before last.
Simulations. In this paper we study simulations with 30 buyers and 30 sellers, with 15 market period each of which lasting for 200 time-steps. The structure of offer and demand is stable over the 15 periods, and is represented in figure 2. Several type of simulation could then be organised in the system, as shown in table 1. In the paper, agents have a memory of 10 time-steps and use global time-step. only simulations when agents have global memory In the simulations, agents have a memory length of 10 transactions, which represents the maximum number that could occur over a period, according to the given limit prices.
Table 1. diverse simulations in our system
|
Calculus of the revision
step |
Local knowledge |
Global knowledge |
|
Random Step |
Value of memory length from 0 to 20 |
Value of memory length from 0 to 20 |
|
Individual Step |
Value of memory length from 0 to 20 |
Value of memory length from 0 to 20 |
|
Global Step |
Value of memory length from 0 to 20 |
Value of memory length from 0 to 20 |
Sim1 is a simulation where
agents have global memory and Sim2 is a simulation where they have local
memory.
Figure 2: the
equilibrium price is an equilibrium “corridor” 1525 and 1550 (any price in this
corridor is an equilibrium price): it is calculated on the basis of the limit
values of the agents.
Observations. The way to judge the learning process that has been designed is to evaluate the properties of that market in terms of coordination of agents, by comparing it to the knowledge that the experimentalist has of humans’ actual behaviours in that context.
The criteria that are used are:
- The average price of transaction on a
market and the MSD,
- The number of deals that actually take
place, considering that in the system 20 agents of each kind should be
able to exchange.
- The global surplus that is made over a
period by the agents (the transaction price compared to their limit price.
- The
efficiency that compares this surplus to the ideal surplus.
4 Results
4.1
Simulation 1
: Perception globale et mémoire longue
We give here the results for one typical simulation of each type and give a short interpretation of these data.
Figure 3: Values
of prices along the time during 15 market openings with agents with global
memory. The convergence to equilibrium is visible in the evolution of average
price and the MSD of prices.
Table 2: In simulations with global perception,
convergence to the equilibrium converges quickly from one tome-step to another.
There is a reduction of dispersion along the time and a high efficiency for the
system.
|
Period |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
|
Price |
Average |
1498 |
1555 |
1577 |
1602 |
1620 |
1620 |
1617 |
1607 |
1607 |
1604 |
1603 |
1602 |
1602 |
1601 |
1602 |
|
Stand.
Dev. |
238 |
212 |
164 |
106 |
45 |
41 |
34 |
20 |
15 |
10 |
9 |
9 |
7 |
6 |
5 |
|
|
Quantity
|
|
24 |
25 |
24 |
21 |
20 |
20 |
19 |
17 |
18 |
19 |
19 |
19 |
19 |
19 |
18 |
|
Surplus |
|
18500 |
17825 |
17900 |
18825 |
18150 |
18950 |
17625 |
16825 |
17800 |
17575 |
18425 |
19225 |
19225 |
18175 |
18100 |
|
Efficiency |
|
95% |
91% |
92% |
97% |
93% |
97% |
90% |
86% |
91% |
90% |
94% |
99% |
99% |
93% |
93% |
When agents have information about all transactions that take place, and use 10 last transactions, exchanges prices get quickly close to the equilibrium price. However, there is still a marginal, but significant, inefficiency. One can understand it by analysing individual data. The representation of average price is common and converges quickly, being the basis of all agents’ revision process. Hence prices do converge to equilibrium price and the acceptable price for transaction is close to it. Agents whose limit price does not allow to go under that value (or above) are excluded of the transaction process. This is the results one could expect for that type of simulation. The transactions mostly take place at the beginning of the period. This shows that the agents still have in memory the reasonable price that had been attained previously and that their reservation price has adapted to that value.
However, in our simulations, some agents do not exchange although they theoretically could. At the end of each period, there is an accumulation of transactions in a very short time, but he remaining time does not allow all of the remaining agents to exchange. Apparently the fact that the time is discrete has an impact at that point, that was unsuspected (because some authors has announced that it didn’t have any influence) and that will have to be taken into account in the next observation we lead. What is interesting in our biased dynamic, here, is that agents who had the ability to trade at the previous time-step have a stress time that comes later than before and hence tend to want to trade later. They have the opportunity to make money, and some of them could have the best surplus in the trade, but the reduction of stress they acquired by their success becomes a burden to action.
Figure 4: quick convergence of prices of transactions for the
simulation with local perception for agents.
Table 3: Average price converges quickly towards
equilibrium when agents perceive only their own transactions. All along the
simulations, prices are more dispersed than when agents choose with a general
perception of the transaction.
|
Period |
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
|
Price |
Average |
1727 |
1672 |
1639 |
1584 |
1579 |
1565 |
1571 |
1563 |
1560 |
1552 |
1548 |
1550 |
1550 |
1550 |
1550 |
|
Stand. Dev. |
156 |
144 |
105 |
83 |
67 |
50 |
38 |
29 |
27 |
29 |
19 |
16 |
11 |
11 |
10 |
|
|
Quantity |
|
22 |
23 |
22 |
22 |
21 |
20 |
20 |
20 |
20 |
19 |
18 |
19 |
20 |
19 |
20 |
|
Surplus |
|
18400 |
17275 |
17150 |
18950 |
18675 |
17300 |
17550 |
18550 |
18750 |
18475 |
16750 |
18875 |
19500 |
18725 |
19500 |
|
Efficiency |
|
94% |
89% |
88% |
97% |
96% |
89% |
90% |
95% |
96% |
95% |
86% |
97% |
100% |
96% |
100% |
In Sim2 agents use their own transaction only to evaluate past prices. Average transaction prices are quickly close to the equilibrium, but dispersion of prices is higher than in Sim1. Individual history can make us understand that. Even if the market gets close to equilibrium, agents who have transacted far from that value will store this data and use it as new reservation price and as its reference of market price. Less agents are excluded from exchange because more have a false representation of the market prices, is enables a higher number of unefficient exchanges to take place. More goods are thus exchanged, but less efficiently, than with global knowledge of price.
5 Conclusion
The reason why we started doing this work first place was to establish a new link between experimental economics and simulations and to try to see which kind of data could be used from one field to adapt to the other. Hence we developed a model and a simulation platform to represent a double-auction institutional setting in which agents could interact to exchange. We wanted to relate simulated data to existing experimental data, that had been gathered by one of the authors.
The model has been built on several type of knowledge: first we use some hypothesis enunciated by other researchers (Easley and Ledyard 1993) on the cognitive abilities of agents when they are faced with a market situation that is impersonal and limited in time; then we adapted the mechanisms of price revision by referring to the expertise of the experiment specialist. More than producing hypothesis, he could also assess simulation results.
The cognition model we build enables us to represent convergence of the prices towards the equilibrium, and a reduction of deviation of prices in time. Moreover, we attain a inter-period convergence, showing that the agents actually learn some elements of their environment. However, we have not led enough simulations nor econometric tests to decide which of our algorithm gives results would be reasonably close to humans’ behaviours. We thus have to progress in the methodological aspect of our work to relate simulations and experiments.
Even more worrying for our platform is the issue of time representation, which might have to be revised. For the moment, our artificial agents behave globally in a non assessable manner. Indeed, although convergence is attained, the repartition of exchanges is clearly different from the one witnessed in experiments. Our agents wait for several time-step before performing an exchange, and eventually transact when their stress time is attained. The changing stress time pushes the successful agents to stress later than they used to be. Adding to this the fact that the time was made discrete, and hence there are transaction jams at the end of the market opening, we get a strange fact for agents: the more successful, the less chances to exchange at the next time-step. This puts a strong bias that certainly reduces the number of agents who can exchange.
This result made us look at simulations where stress time would be reduced and let identical during the whole simulation, and the first quick observations showed that the results seemed more reasonable than the one we had. This hypothesis that seemed reasonable (agents are less stressed when they succeed) and that we added to the Easley and Ledyard framework, seems to create trouble in the global functioning of the system. Further work will be done to refine the description of the cognition, removing the hypothesis of stress evolution, and getting closer to the analysis of data.
The next step in our work is to try to assess this cognition in a new way, using plainly the association between simulations and experiments. First we want to check behaviours on a step by step individual basis: giving our artificial agents the information of a human past actions at each time-step and see if it behaves in the same way as the human did. This evaluation brings us to an IA approach where individual cognition is studied. To go back to a more contemporary DIA approach, we want to integrate the represented humans in the assessment of the actions a bit more. We would like to make experiments mixing agents and humans in the same setting. Either humans would play with artificial agents being other potential transaction partners, like Duffy did in his experiments on speculation (2001), and in this case one could try to see if some strange phenomena occur with our agents, if the human players could spot anomalies or if the behaviours are plausible. We also would like to use our artificial agents as advisers for humans, and then evaluate how much this transforms the behaviour of humans. All this approaches rely a lot on our ability to build an econometric precise evaluation of the data, now that our platform has been tested.
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