Distributed Rational Decision Making

1
Distributed Rational Decision Making

• Sections 5.6-5.9
• By
• Tibor Moldovan

2
5.6 General Equilibrium Market Mechanisms

• .1 Properties of General Equilibrium
• .2 Distributed Search for a General Equilibrium
• .3 Speculative Strategies in Equilibrium Markets
• Case A Speculating Consumer
• Case B Speculating Producer
• Reaching equilibrium under speculation Driving
  the Market
• Strategic Behavior by multiple agents

3
What is General Equilibrium?

• General Equilibrium theory provides a distributed
  method for efficiently allocating goods and
  resources among agents based on market prices.
• General Equilibrium Demands that
• I Markets Clear
• II Each consumer maximizes its preferences
• III Each Producer maximizes its profits

4
Properties of General Equilibrium

• Thm. 5.10 Pareto efficiency
• Each general equilibrium is Pareto Efficient,
  i.e. no agent can be made better off without
  making some other agent worse off.
• Thm. 5.11 Coalitional stability
• Each general equilibrium with no producers is
  stable in the sense of the core solution concept
  of coalition formation games no subgroup of
  consumers can increase their utilities by pulling
  out of the equilibrium and forming their own
  market.
• Thm. 5.12 Existence
• If a society-wide bundle is producible where the
  amount of each commodity is positve, a general
  equilibrium exists.
• Thm. 5.13 Uniqueness under gross substitutes
• A general equilibrium is unique if the
  society-wide demand for each good is
  nondecreasing in the prices of the other goods.

5
Distributed Search for a General Equilibrium

• The most popular algorithm that searches for a
  general equilibrium is Price Tâtonnement
  Algorithm. (steepest descent method)
• However, this algorithm may sometimes fail to
  find an equilibrium even if one exists.
  
• There is a guarantee Thm 5.14 Convergence
• The PTA converges to a general equilibrium if the
  consumers save more money satisfying their
  preferences than the producers make in profit.

6
Speculative Strategies in Equilibrium Markets

• If an agent wishes to maximize its utility
  function it can over/under represent the price.
• It can then speculate how this lying affects
  other agents, and drive the market to a solution
  that maximizes the agents gains from speculation.

7
Case A Speculating Consumer

• The goal of a self-interested consumer is to find
  the consumption bundle that maximizes its
  utility. To do this the agent must speculate how
  other agents respond to prices.
• Using the model of other agents, the consumer
  computes its optimal demand decision.

8
Case B Speculating Producer

• The goal of a self-interested producer is to find
  the production vector that maximizes its profits.
• Again, this requires a model of how others react
  to prices because the producers production
  decisions affect the prices.
• The producer computes the highest profit that it
  can possibly obtain, based on what other agents
  might request.

9
Reaching equilibrium under speculation Driving
the Market

• By speculating, the agent tries to reach a price
  it would like to drive the market to.
• However, there is a risk for the speculator that
  even though such an equilibrium exists, the
  market algorithm would not find it.
• The best strategy is to declare demand plans such
  that the market clears at the desired prices and
  that the market process will find it.

10
Strategic behavior by multiple agents

• In the analysis so far, one agent designed its
  speculative strategy while the others strategies
  were fixed.
• One can use strategic solution concepts from game
  theory to design market protocols.
• Each agents strategy is optimal for that agent
  no matter what strategies others choose.
• Require maintenance of equilibrium at every step
  of the game

11
5.7 Contract Nets

• .1 Task Allocation Negotiation
• Convergence to the globally optimal task
  allocation
• Insincere agents in task allocation
• .2 Contingency Contracts and Leveled Commitment
  Contracts

12
Task Allocation Negotiation

• Instead of task allocation being set in stone,
  agents are allowed to trade tasks amongst
  themselves.
• Gives more control to the agents, which may be
  better suited to make decisions in their local
  environments.
• The agent can take on the role of both a
  contractor and contractee.

13
Convergence to the globally optimal task
allocation

• Task allocation can lead to local optima, but may
  fail to find global optimum.
• Workarounds
• Cluster contracts
• A set of tasks is atomically contracted
• Swap contracts
• A pair of agents swaps a pair of tasks
• Multiagent contracts
• More than two agents are involved in atomic
  exchange

14
Insincere agents in task allocation

• In order to maximize its utility an agent can lie
  about its state, or preferences for tasks.
• For example, an agent can lie by hiding tasks,
  declaring phantom tasks which do not exist, or
  it may announce decoy tasks, which do not exist
  but can be generated on demand.

15
Contingency Contracts and Leveled Commitment
Contracts

• Contingency contracts can be made in situations
  where the original goal has changed due to the
  dynamic environment.
• Instead of canceling the contract completely an
  in-between solution can be reached
• Leveled contracts provide unilateral decommitting
  at any point in time. This is achieved by
  specifying decommitment penalties, one for each
  agent.

16
5.8 Coalition Formation

• .1 Coalition Formation Activity 1 Coalition
  Structure Generation
• .2 Coalition Formation Activity 2 Optimization
  Within a Coalition
• .3 Coalition Formation Activity 3 Payoff Division

17
Coalition Formation Activity 1 Coalition
Structure Generation

• Formation of coalitions by the agents such that
  agents within each coalition coordinate their
  activities, but agents do not coordinate between
  coalitions.
• This means partitioning the set of agents into
  exhaustive and disjoint coalitions.

18
Coalition Formation Activity 2 Optimization
Within a Coalition

• Pooling the tasks and resources of the agents in
  the coalition, and solving this joint problem.
• Objective is to maximize monetary value money
  received from outside the system for
  accomplishing tasks minus the cost of using
  resources.

19
Coalition Formation Activity 3 Payoff Division

• Dividing the value of the generated solution
  among agents.
• This value may be negative because agents incur
  costs for using their resources

20
Conclusions

• Multiagent systems consisting of self-interested
  agents are becoming ever-present. As such, they
  can not be coordinated externally, but instead
  the interaction protocols have to be designed so
  that each agent is motivated to follow the
  strategies it was designed to follow.
• In the future, systems will be designed built and
  operated in a distributed manner. The problem of
  coordinating such systems and avoiding
  manipulation will only be achieved by deep
  understanding and hybridization of technological
  and economic methods.