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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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