1. Market/Agent-Oriented Programming
What Lies Beneath?
S Kameshwaran
Oct 09, 2002

2. Optimization: Shortest Path Problem
Given:
Graph G=(V, E)
Nodes x and y
Cost c(e) on each edge e
Find the shortest path between x and y
Applications: Routing of a call/packet, Transportation Networks
Polynomial Time
Oct 09, 2002
S Kameshwaran

3. Optimization: Marriage Problem
Given:
Set of men M, and women W
Profit (Happiness measure) of matching m with w: cmw
Find one-to-one matching pairs such that  cmw
Applications: Assignment of jobs to machines, personnel to projects.
Polynomial Time
Oct 09, 2002
S Kameshwaran

4. Common Features
A single Mind possesses all information: c(e) in Shortest Path Problem and cmw in the Marriage Problem
The Mind instructs which node should carry the packet and which man should marry which woman.
System wide goal and centralized decision making
Oct 09, 2002
S Kameshwaran

5. Centralized  Decentralized
Shortest Path Problem  Routing Problem
Every node is owned by different companies and the traffic in the outgoing edges are known only to that node
Oct 09, 2002
S Kameshwaran

6. Centralized  Decentralized
Marriage Problem  Trading Problem
Let the set of men M are buyers and women W are sellers
bm=Buying Price of m and sw=Selling Price of w
cmw= sw - bm (Profit of selling a good from seller w to buyer m)
cmw and c(e) are not known to the single mind
Oct 09, 2002
S Kameshwaran

7. Centralized  Decentralized
Will the traders and the nodes tell the true value (cmw and c(e)) to the Mind?
Oct 09, 2002
S Kameshwaran

8. Centralized  Decentralized
Will the traders and the nodes tell the true value (cmw and c(e)) to the Mind?
Yes: If it is profitable for them to do so..
Oct 09, 2002
S Kameshwaran

9. Centralized  Decentralized
Will the traders and the nodes tell the true value (cmw and c(e)) to the Mind?
Yes: If it is profitable for them to do so..
No: If they can gain by cheating..
Oct 09, 2002
S Kameshwaran

10. Centralized  Decentralized
Will the traders and the nodes tell the true value (cmw and c(e)) to the Mind?
Yes: If it is profitable for them to do so..
No: If they can gain by cheating..
Self interested, rational and intelligent
Self interest need not be consistent with the objective of the Mind
Oct 09, 2002
S Kameshwaran

11. Distributed AI Routing Problem: Multi-Agent System
Trading Problem: ECommerce Market Design
Features:
Multiple self-interested, rational, intelligent agents
Agents have to coordinate with each other to achieve their goals
No single Mind to implement/force solutions on them
Oct 09, 2002
S Kameshwaran

12. Focus
To achieve system-wide goals, where the system is made up of machines (Agents) that have been programmed by different entities to pursue differing goals
A CPU marketplace (processors bidding for free CPU time with one another)
We are not addressing the issues of distributed computer systems that have been centrally designed to pursue a single global goal
Distributed Operating System
Oct 09, 2002
S Kameshwaran

13. Market-oriented Programming
Market-oriented programming (MOP) is a mathematical programming approach to distributed computation using selfish agents, based on market price mechanisms
MOP exploits the institution of markets to solve particular problems of distributed resource allocation
Comprises of two problems: Allocation and Pricing
Inspired in part by economists (market mechanisms) and also by AI (heterogeneous, self interested agents)
Oct 09, 2002
S Kameshwaran

14. Algorithms  Mechanisms
Centralized  Decentralized :: Algorithms  Mechanisms
Mechanism
Protocol governing the high-level behavior of agents: offers, counter-offers, threats, promises, concessions…
Rules of the game: constrain the public behavior of the agents
Publicly known and agreed upon ahead of time
Agents cannot violate the rules of the game
Eg: Chess
Oct 09, 2002
S Kameshwaran

15. Strategy of an Agent
Strategy determines which among the possible alternative public actions the agent will choose at each step
Eg: Chess: Decision of Black to make a particular move among the allowable moves
Strategy adopted by an agent may be hidden from the other agents
Outcome of the mechanism depends on the individual strategies adopted by the agents
Oct 09, 2002
S Kameshwaran

16. Design Mechanism Strategy Public behavior of agents
Private behavior of agents
Social Engineering
Designed in view of achieving private goals
Oct 09, 2002
S Kameshwaran

17. Design
By adjusting the Mechanism (rules of the game), we can influence the private strategies that designers put into their agents
Mechanism
Strategy
Public behavior of agents
Private behavior of agents
Social Engineering
Designed in view of achieving private goals
Oct 09, 2002
S Kameshwaran

18. Mechanism Design (Implementation Theory)
Given:
System comprising of self-interested, rational agents
Set of system wide goals
Mechanism Design
Does there exist a mechanism that can implement the goals?
Implementation of the goals depends on the individual behavior of the agents
Oct 09, 2002
S Kameshwaran

19. Example: System xXx xXx: A new breed of software agents?? System:
One Seller with a single indivisible good
N buyers (agents) each with value vi for the good (money value)
vi is known only to agent i
Value vi: Maximum value agent i is willing to pay for the good (Agent is indifferent between the good and the money value vi)
Goals:
G1: Sell the good to agent (buyer) with highest vi
G2: The buying agent pays vi to the seller for the good
Oct 09, 2002
S Kameshwaran

20. xXx: First Price Sealed Bid Auction
Mechanism
Each agent submits a sealed bid to the seller
Good is sold to the agent with the highest bid
The winning agent pays the quoted bid value to the seller
Does this mechanism implements G1 and G2?
Oct 09, 2002
S Kameshwaran

21. First Price Sealed Bid Auction: Agent Strategy
Overbid
Bid True Value vi
Underbid
Oct 09, 2002
S Kameshwaran

22. First Price Sealed Bid Auction: Agent Strategy
Overbid
If the agent wins, it has to pay more than it is worth X
Bid True Value vi
Underbid
Oct 09, 2002
S Kameshwaran

23. First Price Sealed Bid Auction: Agent Strategy
Overbid
If the agent wins, it has to pay more than it is worth X
Bid True Value vi
If the agent wins, it has to pay its original value and the agent gains nothing X
Underbid
Oct 09, 2002
S Kameshwaran

24. First Price Sealed Bid Auction: Agent Strategy
Overbid
If the agent wins, it has to pay more than it is worth X
Bid True Value vi
If the agent wins, it has to pay its original value and the agent gains nothing X
Underbid
Reduces the chance of winning
Less the agent pays than vi more it gains
Strategy: Bid slightly more than the expected second highest price 
Oct 09, 2002
S Kameshwaran

25. xXx: First Price Sealed Bid Auction
G1: Probabilistically Achieved (depends on the beliefs of the agents about the other agents’ bid values)
G2: No
Oct 09, 2002
S Kameshwaran

26. xXx: Vickrey Auction Mechanism
Each agent submits a sealed bid to the seller
Good is sold to the agent with the highest bid
The winning agent pays the second highest bid value to the seller
Does this mechanism implements G1 and G2?
Oct 09, 2002
S Kameshwaran

27. Vickrey Auction: Agent Strategy
Overbid
Underbid
Bid True Value vi
Oct 09, 2002
S Kameshwaran

28. Vickrey Auction: Agent Strategy
Overbid X
If the agent is the real winner and wins, it gains nothing
If the agent is not the real winner and wins by overbidding, it may pay more than its value
Underbid
Bid True Value vi
Oct 09, 2002
S Kameshwaran

29. Vickrey Auction: Agent Strategy
Overbid X
If the agent is the real winner and wins, it gains nothing
If the agent is not the real winner and wins by overbidding, it may pay more than its value
Underbid X
The agent may lose by underbidding
Bid True Value vi
Oct 09, 2002
S Kameshwaran

30. Vickrey Auction: Agent Strategy
Overbid X
If the agent is the real winner and wins, it gains nothing
If the agent is not the real winner and wins by overbidding, it may pay more than its value
Underbid X
The agent may lose by underbidding
Bid True Value vi 
Best Strategy
Tell the truth independent of what agents do (Dominant Strategy)
Oct 09, 2002
S Kameshwaran

31. xXx: Vickrey Auction G1: Yes
G2: Never (Winning agent pays the second highest value)
Inferences
Change of a single rule changes the agents’ behavior
Incentive Compatible: Mechanism provides incentive for the agents to tell the truth
Dominant Strategy: Agent need not deliberate about other agents
Oct 09, 2002
S Kameshwaran

32. xXx: English Auction Mechanism
Open out-cry ascending price auction
Starts with a minimum bid value quoted by the seller
Agent can revise the bid amount upward by a minimum increment 
Auction ends when bidding stops
Highest bidder gets the object and pays the amount quoted
Does this mechanism implements G1 and G2?
Oct 09, 2002
S Kameshwaran

33. English Auction: Agent Strategy
Keep bidding upwards till value vi
Dominant Strategy: Independent of other agents’ behavior
Oct 09, 2002
S Kameshwaran

34. xXx: English Auction G1: Yes
G2: Never (Price paid  [2nd Highest Valuation, 2nd Highest Valuation + ])
Inferences
The ending time of auction is not known apriori, but it ends in finite time
Design of mechanism should also account for the convergence/termination
How many more mechanisms should we check?
Oct 09, 2002
S Kameshwaran

35. Revelation Principle
Revelation Principle: Every mechanism has an equivalent direct mechanism
Direct Mechanism:
Sealed bid
Incentive compatible
Search only the direct mechanism
xXx: Cannot be implemented (Agent gains nothing by paying the value of the good)
Oct 09, 2002
S Kameshwaran

36. So far so good Centralized  Decentralized Resource Allocation
Market-oriented Programming
Distributed resource allocation using market price mechanisms
Algorithms  Mechanisms
Mechanism Design
Does there exist a mechanism that can implement the given set of system wide-goals among self interested agents?
Incentive compatibility and dominant strategy
Revelation Principle: Look for direct mechanisms
Oct 09, 2002
S Kameshwaran

37. Game Theory Mechanism Design Game Theory
Does there exist a mechanism (game) that can implement the given set of goals?
Game Theory
Given a game (mechanism), predicts the outcome by analyzing the individual behavior of the players (agents)
Oct 09, 2002
S Kameshwaran

38. What is a Game?
Problem 1
Problem 2
Oct 09, 2002
S Kameshwaran

39. Should I carry my umbrella? Should I propose to my girlfriend?
What is a Game?
Problem 1
Problem 2
Should I carry my umbrella?
Should I propose to my girlfriend?
Oct 09, 2002
S Kameshwaran

40. What is a Game? Problem 1 Problem 2 Should I carry my umbrella?
Should I propose to my girlfriend?
Penalty: Carry extra weight/get drenched
Penalty: Could be fatal??
Oct 09, 2002
S Kameshwaran

41. What is a Game? Problem 1 Problem 2 Should I carry my umbrella?
Should I propose to my girlfriend?
Penalty: Carry extra weight/get drenched
Penalty: Could be fatal??
Uncertain information
Oct 09, 2002
S Kameshwaran

42. What is a Game? Problem 1 Problem 2 Should I carry my umbrella?
Should I propose to my girlfriend?
Penalty: Carry extra weight/get drenched
Penalty: Could be fatal??
Uncertain information
Rains or shrines independent of me carrying the umbrella
My decision of proposing/not may change her decision
Oct 09, 2002
S Kameshwaran

43. What is a Game? Problem 1 Problem 2 Should I carry my umbrella?
Should I propose to my girlfriend?
Penalty: Carry extra weight/get drenched
Penalty: Could be fatal??
Uncertain information
Rains or shrines independent of me carrying the umbrella
My decision of proposing/not may change her decision
I am facing Nature
I am playing against a rational and intelligent (?) agent like me (??)
Oct 09, 2002
S Kameshwaran

44. What is a Game? Problem 1 Problem 2 Should I carry my umbrella?
Should I propose to my girlfriend?
Penalty: Carry extra weight/get drenched
Penalty: Could be fatal??
Uncertain information
Rains or shrines independent of me carrying the umbrella
My decision of proposing/not may change her decision
I am facing Nature
I am playing against a rational and intelligent (?) agent like me (??)
Decision making under uncertainty, Online algorithms..
Game Theory
Oct 09, 2002
S Kameshwaran

45. What is Game Theory? Interactive Decision Theory Game: N players
Rules of encounter: Who should act when and what are the possible actions
Every possible outcome of the game
Oct 09, 2002
S Kameshwaran

46. What is Game Theory? Solution Concept
With the information at hand, choosing the best action among the possible actions is the strategy of individual agent
Combination of best strategies of each agent gives an equilibrium outcome
Best defines different equilibriums: Dominant Strategy Equilibrium, Nash Equilibrium, etc
Oct 09, 2002
S Kameshwaran

47. Summing Up… Centralized  Decentralized Resource Allocation
Market-oriented Programming
Distributed resource allocation using market price mechanisms
Algorithms  Mechanisms
Mechanism Design
Does there exist a mechanism that can implement the given set of system wide-goals among self interested agents?
Incentive compatibility and dominant strategy
Revelation Principle: Look for direct mechanisms
Game Theory
Given a game, predicts the outcome by analyzing the individual behavior of the players
Oct 09, 2002
S Kameshwaran

48. Coming Up… 16/10/02 (Wednesday): Algorithmic Mechanism Design
18/10/02 (Friday): Algorithms, Games, and the Internet
22/10/02 (Tuesday): Constraint Satisfaction Problems and Games
25/10/02 (Friday): Nash Equilibrium: P or NP?
29/10/02 (Tuesday) Combinatorial Markets (Part 1)
31/10/02 (Thursday): Combinatorial Markets (Part 2)
Oct 09, 2002
S Kameshwaran