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Sequential bargaining on a perishable goods market: The influence of the seller’s beliefs and the buyers’ times constraints. S. Moulet and J. Rouchier mettre greqam logo. The Presentation. Introduction: Our question and the studied case Bargaining models Economics and games theory

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Sequential bargaining on a perishable goods market: The influence of the seller’s beliefs and the buyers’ times constraints

S. Moulet and J. Rouchier mettre greqam logo

the presentation
The Presentation
  • Introduction:
    • Our question and the studied case
    • Bargaining models
      • Economics and games theory
      • Multi agents-based simulations
  • Our model
    • General setting and agents
    • Bargaining process
    • Learning process
    • Individual choice
      • Buyers
      • Sellers
  • Our results
    • Observed data
    • Some simulations and results
      • false beliefs’ effects
      • Time effect for buyers
  • Concluding remarks
    • Comparison with initial data
    • Conclusion
introduction our question and the case study
Introduction: Our question and the case study

We looked at the process that leads to the transaction price and more generally to the state of the market (prices, nature of meetings…).

We have made a survey on the individuals’ behaviour on the MIN

to get a better understanding in sellers attitude facing their customers: We have constructed a learning process model

We studied results and compared them to empirical facts.

the case study the min 1
The case study : The MIN (1)
  • Marché d’Interet National, Marseilles.
  • The actors:
    • Sellers : local producers and import wholesalers
    • Professional buyers : retailers, caterers, local authorities, central buying.

* wholesalers

    • They are integrated in some supply networks.
    • They purchase products or resort to the « after sale price » principle.

* Retailers

    • They visit sellers
    • They Keep trading links
    • They look for the lowest price or the best value for money.

*Their relationships:

    • Purchase and sales.
    • Communicate
    • Credit
the case study its process 2
The case study: its process (2)

It is face to face institutional form.

  • Prices are not disclosed and the results of negotiation are customized and private.
  • Transactions are decentralised
  • Information is asymetric and imperfect on both sides.
  • Individuals’ reservation values evoltion are based on:
    • updating core beliefs
    • Individuals’ variation on the market.
why studying this market
Why studying this market?
  • Economically: Important Platform in fresh fruit and vegetables exchanges in our region. It could disappear…
  • Intellectually: None existing model in the literature can be applied on the studied market.
    • Negotiation theory
    • Reservation prices assumptions.
our goal
Our goal
  • A better understanding of the perishable goods markets running.
  • Setting up a theoretical resolving model.
the starting point 1
The starting point (1):
  • “Transaction that did not happen and their influence on prices”, In Press, Journal of Economic Behaviour and Organisation. A. Kirman, R. Schulz, W. Hardle and A. Werwatz, (2005).
  • And idea of H. Pagels: « …l’apparente complexité du système que l’on tente de modéliser est due à quelques composantes simples interagissant sur des règles simples »
2 data study
(2)Data study
  • Data for:
    • Intermediate offers
    • Transactions prices
    • Period without customers (idle periods)
  • Positive points:
    • Transaction or not, intermediate offers exist during bargains.
    • Stylised facts are revealed.
  • Negative points:
    • Only one seller is concerned.
    • We cannot distinguish buyers.
    • No details on the supply price and the retaillers’ sales price are given.
how to remedy to the negative points what problems can emerge
How to remedy to the negative points, What problems can emerge?
  • Is the sampling of sellers representative of the relevant market?
  • What is the seller’s degree of knowledge?
  • What are the effects of the seller’s core beliefs?
a few models of bargaining 1
A few models of bargaining(1)
  • In Economics and games theory: 2 approaches:
    • The first attempts to identify possible strategies and to assist a negociator in achieving optimal results.
    • The second attempt to construct formal models of negotiation environments (Nash) and to prove different theorems about best strategies. It is divided in two subparts: the Strategic approach and the Axiomatic approach.
multi agents based simulations 1
Multi agents-based simulations(1)
  • Tool capable to study heteregeneous agents defined by evolving the decentralisation beliefs evolution in their environment.
  • “To understand the dynamics of interactive market processes, and the emergent properties of the evolving markets structures and outcomes, it might pay to analyze explicitly how agents interact with each other, how information spreads through the market, and how adjustments in disequilibrium takes place” (Vriend and Kirman).
sma definition 3
SMA: Definition (3)
  • System where agents (computing entity):
    • Cooperate
    • Collaborate
    • Bargain
    • Coordinate between each other.
sma reality and simulation 4
SMA: Reality and Simulation (4)
  • Creation: Based on empirical observations we created behavioural models that matches with observed individuals.
the sma 5
The SMA (5)

Difficult to modelize in a analytical way:

Allows toreproduce« in vitro » phenomenons


  • a powerful tool of simulation
  • a method to discover new rules of social interactions and organisation.
differences with some existing models and our model
differences with Some existing models and our model
  • On Perishable goods:
    • Kirman and Vriend:  « Evolving Market Structure: An ACE Model of Price Dispersion and Loyalty»
    • Rouchier: « Interaction routines and selfish behaviours in an artificial market »
  • On bargaining process under time constraints:
    • Kraus, Wilkenfed, Zlotkin « Multiagent Negotation Under Time Constraints »
    • Brenner « A Behavioural Learning Approach to the Dynamics of Prices »
characteristics 2
  • 2 types of agents: Ns sellers and Nb buyers with a bilateral relationship focused on the price of unique and perishable good.
  • Our agents meet up and operate each day:
    • Before market openings, sellers buy their supply for a price which becomes their limit value.
    • When the market opens, all buyers enter with one unit of goods needed. Each of them chooses a seller and starts bargaining.
    • Their bargain follows a process described hereafter. At the end of one sequence of bargaining, buyers who have not acquired good, choose another seller within their time limits. If a transaction is made, they can leave the market.
agent s characteristics
Agent’s characteristics:
  • Type: a seller or a buyer
    • Buyer’s concerns
      • time constraint for staying on the market.
    • Seller’s concerns :
      • Initial stock evolving in time.
  • Memory of past interactions
  • Level of loyalty
  • Limit value
  • Core beliefs concerning the other’ s agent limit value.
agents core beliefs
Agents core beliefs

By the time gathered information transformed core beliefs’ agents.

  • For sellers’ agents:
    • Core beliefs are represented by a value corresponding to its valuable reservation price.
  • For a buyers’ agents:
    • Core beliefs are defined by a uniform distribution on an interval
  • Agents are also characterized by a learning process .
  • Thanks to it, agents respond to the signals transmitted by interlocutors during different meeting.
  • It is defined via iterative algorithm:
    • Each iteration includes beliefs data :
    • Agents act on their environment and get a feedback which updates beliefs.
  • The completed updating help them to take the best decisions according to types and the other ones behaviour.
bargaining process
The buyer chooses a seller.

The seller makes an offer p

The buyer accepts p.


It decides if it wants to make a counter-offer


The buyer makes a counter-offer c

The seller accepts c


The seller makes a second offer s


The buyer accepts the second offer. s



Bargaining process
at the initialisation
At the initialisation
  • Agents from each type have a same:
    • Learning process
    • Limit value
    • Memory capacities.
  • Buyers considerations can be different according to the precision given by simulations parameters such as:
    • Degree of loyalty
    • Time to spend on the market,
    • Initial reservation value.
  • Sellers considerations can be different according to:
    • Initial stock
    • Initial reservation value.
in the simulations
In the simulations

* We consider:

  • Values of the limit values for each type
  • Sellers’ initial stock
  • Degree of loyalty
  • Number of agents per type

are set as equal for all simulations.

* Parameters :

  • Market’s value in time limit
  • Core beliefs
learning process
Learning process

The learning takes place through reinforcement :

  • Buyers’ concerns:

At the beginning:

No precise idea of the sellers’ price.

Same limit value for all sellers

Behavioural adaptation according to the new information: the seller’s price and it adapts its.

At each moment,

Decision to take:

Either they benefit from the actual situation

Or continue to acquire information.


Maximize the probability to acquire the good without losing money.


With our learning process we consider that potential buyers visit more (in probability) the sellers who have already conclude in the past a transaction at a low price during the first step.

The buyer has got in its mind an idea of the seller’s reservation value. At each step, it will offer the best price that maximise its probability to acquire the good according to its beliefs.)

Sellers’ concerns:

At each step:

    • Beliefs are based on unique value
    • Updating beliefs is made according to new information.
  • we consider that:
    • sellers have a different aspiration level from buyers
    • Sellers react only if they enter in a repeated behaviour.
  • Simulations

we assume that:

according to the nature of buyers’ answer (acceptance/refusal), sellers update their beliefs involving an increase or decrease function

The variation depends only on the stage of the bargain in which the answer is made.

b uyers customised choice
Buyers:Customised choice:
  • (1) The buyer chooses a seller:
    • After each meeting:
      • calculates its cumulated and composed payoff realized.
      • takes into account its profit
      • defines the probability to choose the seller.
  • (2) decisions and reactions facing the seller’s offer:
    • Accepts if the offer is lower than its reservation value
    • Decide if it wants to bargain with the same seller or visits another one according to expected profits.
  • (3)Information on price to propose:
    • At each step a current reservation value is proposed.
      • truncates the distribution at the first price when receiving the seller’s offer.
      • chooses the best price according to its distribution view .
      • proposes the optimal price according to its beliefs and its limit value.
  • Notes: When a seller proposes a price, its limit value is bigger than its offer.
sellers customised choice
Sellers: Customised choice
  • (1)Before the market openings:

Decision on quantity to supply

    • On a day to day basis, the supply process is:

the same sold quantity than added to a fixed quantity (m).

    • Notes: (Abel)

Two reasons to optimize the profits keeping one margin:

keeping good contacts with their suppliers

not losing opportunities in the future.

  • (2)Decision on prices to propose when facing the buyer
    • Proposes its actual reservation price.
    • Decides according to the past experiences and core beliefs on the state of the market
    • cannot make distinction between buyers.
    • Notes: The offer is completely independent from bargainers’ relationships.
(3) Reaction according to the acceptance or refusal on step 1
    • At each meeting:
      • checks up if its customers have the same behaviour (acceptation/refuse/ bargaining interruption)
      • updates its beliefs
      • Increases or decreases its reservation price

Notes: The discount depends only on the time.

  • (4)Know how for proposals
    • In case of a 1st price refusal and a buyer’s counter offer too high
    • Price with a decreasing function of the remaining stock
    • Price with a decreasing function with matter of time.

Notes: To simplify, we can consider that the price is negatively correlated to the ratio: remaining stock/ remaining time.

our results
Our results
  • Observed data
  • Some simulations and results
    • Agent’s false core beliefseffects
    • Buyers’ time impact constraints.
observed data
Observed data
  • Results of the simulations are used for calculation
    • frequencies of different of meeting natures
    • transactions price evolution
    • number of visit before transaction
    • Evolution of sellers power negotiation
    • Heterogeneity for both types of agents.
  • Influent parameters:
    • Sellers initial stock (A and B)
    • Bargaining costs:
      • cost for meeting a seller (β)
      • cost for negotiating after a previous offer made by the seller (α)
    • Number of agents per type.
    • Agents’ core beliefs .
relevant parameters
Relevant parameters
  • We choose to fix some parameters among in respect of some characteristics of the real market:
    • Number of agents per type: We respect the ratio observed in the reality (1/30) and the convergence between the agents (Nb =1500 and Ns=50).
    • Observation signalling that buyers are limited by:
      • the number of sellers to visit
      • the duration of the bargain
effects of the agent s false beliefs
Effects of the agent’s false beliefs
  • We demonstrate:
  • That if agents per type have the same core beliefs then for all situation the market converges toward a situation where agents have same beliefs and are willing to sell or buy goods at sellers’ limit value.
  • We prove the robustness of the model in beliefs and in initial heterogeneity regarding sellers’ core beliefs.
Sellers population of is homogeneous and it seems to be reasonable to take only one seller.
buyers time constraints effects
Buyers’ time constraints effects
  • agents’ satisfaction: Does an increase of the exploitation possibilities drag more satisfaction?
  • dynamic of prices: Does more exploitation gives lower price?
  • Nature of meetings: Do the agents bargain to make transaction? By the time, Is there any behaviours’ variation?
  • Sellers’ negotiation power : Does the power decrease when buyers have more opportunities?
Agents’ satisfaction:
    • Buyers (figure 1):Number of satisfied buyers increases together with the longest time that can be spent on the market.

Indeed, more time to explore the market, involve receiving more information, and behavioural adaptation improves.

    • Sellers (figure 2) Number of sellers making a positive profit depends on the study parameter: If buyers cannot visit at least two sellers, there is a few sellers who realize a positive profit. Concerning, the sim 2 to 4, the relation is not clear.
  • We cannot compare these facts with reality because we do not have data on sellers’ stock and their supply prices.
prices dynamics
Prices dynamics
  • In the model we have supposed:
    • All buyers are on the market since its openings.
    • they bargain and react according to the facts observed and to the futures opportunities.
    • All agents are ruled by a times constraints.
  • First, sellers have goods for sell for the day running out, so bigger the lack of futures opportunities is, cheaper the prices are.
  • Second, buyers facing : no goods no work, bigger the lack of futures opportunities is, higher their willingness to pay are.
  • Lastly, a third fact: Buyers with a high value reservation leave quickly the market. In the end it remains only agents with no goods and a rather low reservation value.
  • => We expected decrease prices on a day long but it is not the case: prices are almost stable during the day with a positive trend (in average). We can conclude that the effect 2 is more important than the other one.
sellers negotiation power
Sellers’ negotiation power.
  • Analysis situation 1. We remark that:
    • for all simulations sellers’ negotiation power is instable
    • its value is around 0 and 4/5. It is still stronger than the buyers’ negotiation power.
concluding remarks
Concluding remarks
  • This work highlights influent parameters on the market’s dynamics: The implemented learning process gives the agents the capacities to adapt their behaviour to evolving environment.
  • It is interesting to observe such a context (where agents are heterogeneous and autonomous and where meetings are completely decentralized) a stable state appears very early.
  • Buyers make better transactions than sellers as far as all transactions are made close to sellers’ limit value. Even if both types of agents have time and budget constraints learning at the same time.

This result is not comparable from the empirical observation as far as agents’ limit value is not revealed. But it could explain a possible market disappearance in the future…

However, we have shown, that according to the empirical observations, the sellers’ negotiation power is always upper than the buyers’ one.
  • The buyers’ loyalty does not influence the transactions’ prices. This remark enhances our survey results: the major part of sellers confirm the buyers’ loyalty , it does not influence the transaction prices but only the probability to acquire goods.
  • Even if at the beginning, the agents’ core beliefs are different, they eventually converge to same beliefs. This remark is a matter of extreme importance since we may be able to compare our data to the stylised facts highlighted by Kirman and al. (which possesses a one seller database).
Our model is based on a dataset concerning fruit and vegetables wholesale in Marseille. However, rules are very general and could be used for other perishable goods markets.
  • Our process has been compiled in respect of technical constraints: Our negotiation process is simple and efficient and consumes a reasonable amount of computation resources.
  • =>That is why we have made several assumptions ignoring some present aspects on the market such as reduction of prices according to quantity or diversity of goods. Indeed, we have supposed that all buyers and sellers are on the market since openings and buyers need to purchase only one unit of an homogeneous good. So, we do not take into account the decreasing relationship between price and quantities nor the influence of goods substitutability.
However, we must specify that we study above all the negotiation and learning process. So, we have chosen relevant :
  • parameters such as the number of stages in a bargain process, time constraint and the one day life span of goods.
  • Rules according to the survey made on the market and stylised facts already put in light by Kirman and al.
  • Our model could be more developed. Future step could consist in adding in the price formation a parameter representing the two agents history. Consequently, we would take into account this absent parameter : the relationship between agents and not only the aggregate environment’ state.