Distributed Rational Decision Making Sections By Tibor Moldovan

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

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

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.

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.

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 agent’s gains from speculation.

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.

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 producer’s production decisions affect the prices. The producer computes the highest profit that it can possibly obtain, based on what other agents might request.

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.

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 agent’s strategy is optimal for that agent no matter what strategies others choose. –Require maintenance of equilibrium at every step of the game

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

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.

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

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.

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.

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

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.

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.

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

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.