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1 Agents – Background Vicki H. Allan

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2 An Agent in its Environment AGENT ENVIRONMENT Sensor Input action output

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3 “Agent enjoys the following properties: autonomy - agents operate without the direct intervention of humans or others, and have some kind of control over their actions and internal state; social ability - agents interact with other agents (and possibly humans) via some kind of agent-communication language; reactivity: agents perceive their environment and respond in a timely fashion to changes that occur in it; pro-activeness: agents do not simply act in response to their environment, they are able to exhibit goal-directed behaviour by taking initiative.” (Wooldridge and Jennings, 1995)

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4 Agents Need for computer systems to act in our best interests “The issues addressed in Multiagent systems have profound implications for our understanding of ourselves.” Wooldridge Example – how do you make a decision about buying a car

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5 Agent Environments not have complete control (influence only) (Ex: elevators in Old Main) deterministic vs. non-deterministic effect accessible (get complete state info) vs inaccessible environment (Ex. stock market) episodic (single episode, independent of others) vs. non-episodic (history sensitive) (Ex. grades in class)

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6 Exercise There are three blue hats and two brown hats. The men are lined up such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can’t see anybody. One of the five hats is placed on each man's head. The remaining two hats are hidden away. The men are asked what color of hat they are wearing. Time passes. Front man correctly guesses the color of his hat. What color was it, and how did he guess correctly?

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7 Concept Everyone else is as smart as you

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8 Game of Chicken Consider another type of encounter — the game of chicken: (Think of James Dean in Rebel without a Cause: swerving = coop, driving straight = defect.) Difference to prisoner’s dilemma: Mutual defection is most feared outcome.

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9 Question: How do we communicate our desires to an agent? May be muddy: You want to graduate with a 4.0, have a job making $100K a year, have opportunities for growth, and have quality of life. If you can’t have it all, what is most valued?

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10 Answer: Utilities Assume we have just two agents: Ag = {i, j} Agents are assumed to be self-interested: they have preferences over how the environment is Assume { 1 2 …}is the set of “outcomes” that agents have preferences over We capture preferences by utility functions which map an outcome to a rational number. Utility functions lead to preference orderings over outcomes.

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11 What is Utility? Utility is not money (but it is a useful analogy) Typical relationship between utility & money:

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12 Dominant Strategies Recall that –Agents’ utilities depend on what strategies other agents are playing –Agents’ are expected utility maximizers A dominant strategy is a best-response for player i –They do not always exist –Inferior strategies are called dominated

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13 Dominant Strategy Equilibrium A dominant strategy equilibrium is a strategy profile where the strategy for each player is dominant (so neither wants to change) Known as “DUH” strategy. Nice: Agents do not need to counter speculate (reciprocally reason about what others will do)!

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14 Prisoners’ dilemma -10, -100, -30 -30, 0-1, -1 Confess Don’t Confess Ned Kelly Two people are arrested for a crime. If neither suspect confesses, both get light sentence. If both confess, then they get sent to jail. If one confesses and the other does not, then the confessor gets no jail time and the other gets a heavy sentence.

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15 Prisoners’ dilemma -10, -100, -30 Confess Don’t Confess Ned Kelly Kelly will confess. Same holds for Ned.

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16 Prisoners’ dilemma -10, -10 Confess Don’t Confess Ned Kelly So the only outcome that involves each player choosing their dominant strategies is where they both confess. Solve by iterative elimination of dominant strategies

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17 Example: Prisoner’s Dilemma Two people are arrested for a crime. If neither suspect confesses, both get light sentence. If both confess, then they get sent to jail. If one confesses and the other does not, then the confessor gets no jail time and the other gets a heavy sentence. (Actual numbers vary in different versions of the problem, but relative values are the same) -10,-10 0,-30 -30,0-1,-1 Confess Don’t Confess Dom. Str. Eq not pareto optimal Optimal Outcome Don’t Confess Pareto optimal

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18 Example: Bach or Stravinsky A couple likes going to concerts together. One loves Bach but not Stravinsky. The other loves Stravinsky but not Bach. However, they prefer being together than being apart. 2,10,0 1,2 B BS S No dominant strategy equilibrium

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19 Example: Paying for Bus fare Getting back to the Gatwick airport. Steve had planned to pay for all of us, but left to find son. Came for funds. Do I pay, or say my husband will? 0,0-25, -25 -100,-1000,0 Pay for 2 Pay for 4 Not Pay No dominant strategy equilibrium

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20 Research Questions Can we apply game theory to solve seemingly unrelated problems? Ex: traffic control Ex: sharing Operating System resources

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21 Exercise You participate in a game show in which prizes of varying values occur at equal frequency. Two of you win a prize. There are 10 types of prizes of varying values. Assume, a prize of type 10 is the best and a prize of type 1 is the worst. Without knowing the other’s prize, both asked if they want to exchange the prizes they were given. If both want to exchange, the two exchange prizes. What is your strategy?

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22 Employee Monitoring Employees can work hard or shirk Salary: $100K unless caught shirking Cost of effort: $50K Managers can monitor or not Value of employee output: $200K Profit if employee doesn’t work: $0 Cost of monitoring: $10K

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23 What is your strategy? Work hard? Shirk?

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24 No equilibrium in pure strategies What do the players do? Employee Monitoring Manager MonitorNo Monitor Employee Work 50, 9050, 100 Shirk 0, -10100, -100

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25 Mixed Strategies Randomize – surprise the rival Mixed Strategy: Specifies that an actual move be chosen randomly from the set of pure strategies with some specific probabilities.

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26 Research question What features does a good solution have?

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27 Pareto Efficient Solutions: f represents possible solutions for two players U1U1 U2U2 f 1 f 2 f 4 f 3

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28 Pareto Efficient Solutions U1U1 U2U2 f 1 f 2 f 4 f 3 f 2 Pareto dominates f 3

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29 Auctions Dutch English First Price Sealed Bid Second Price Sealed Bid

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30 Auction Parameters Goods can have –private value (Aunt Bessie’s Broach) –public/common value (oil field to oil companies) –correlated value (partially private, partially values of others): consider the resale value Winner pays –first price (highest bidder wins, pays highest price) –second price (to person who bids highest, but pay value of second price) Bids may be –open cry –sealed bid Bidding may be –one shot –ascending –descending

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31 Dutch (Aalsmeer) flower auction

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33 Research Questions How can we design an agent to function in the electronic marketplace? Give the new possibilities, made possible via an electronic auction, what “mechanisms” can be designed to elicit desirable properties?

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34 How do you counter speculate? Consider a Dutch auction While you don’t know what the other’s valuation is, you know a range and guess at a distribution (uniform, normal, etc.) For example, suppose there is a single other bidder whose valuation lies in the range [a,b] with a uniform distribution. If your valuation of the item is v, what price should you bid? Thinking about this logically, if you bid above your valuation, you lose. If you bid lower than your valuation, you increase profit. If you bid very low, you lower the probability that you will ever get it.

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35 What is expected profit (Dutch auction)? Try to maximize your expected profit. Expected profit (as a function of a specific bid) is the probability that you will win the bid times the amount of your profit at that price. Let p be the price you bid for an item. v be your valuation. [a,b] be the uniform range of others bid. The probability that you win the bid at this price is the fraction of the time that the other person bids lower than p. (p-a)/(b-a) The profit you make at p is v-p Expected profit as a function of p is the function = (v-p)*(p-a)/(b-a) + 0*(1- (p-a)/(b-a))

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36 Finding maximum profit is a simple calculus problem Expected profit as a function of p is the function (v-p)*(p-a)/(b-a) Take the derivative with respect to p and set that value to zero. Where the slope is zero, is the maximum value. (as second derivative is negative) f(p) = 1/(b-a) * (vp -va -p 2 +pa) f’(p) = 1/(b-a) (v-2p+a) = 0 p=(a+v)/2 (half the distance between your bid and the min range value)

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37 Ultimatum Bargaining with Incomplete Information

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38 Ultimatum Bargaining with Incomplete Information Player 1 begins the game by drawing a chip from the bag. Inside the bag are 30 chips ranging in value from $1.00 to $30.00. Both must agree to split the amount. Player 2 does not see the chip. Player 1 then makes an offer to Player 2. The offer can be any amount in the range from $0.00 up to the value of the chip. Player 2 can either accept or reject the offer. If accepted,Player 1 pays Player 2 the amount of the offer and keeps the rest. If rejected, both players get nothing.

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39 Experimental Results Questions: 1)How much should Player 1 offer Player 2? 2)Does the amount of the offer depend on the size of the chip? 2) What should Player 2 do? Should Player 2 accept all offers or only offers above a specified amount? Explain.

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40 Coalition Formation Tasks need the skills of several workers Tasks have various worth Agents have various costs How do you decide who works together? What do you pay each one?

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41 Research Questions Computing the optimal coalition is NP- hard. How do you form good coalitions in an efficient manner? How do you form coalitions when the information is incomplete? How do you form coalitions in a dynamic environment – with agents entering/leaving?

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42 Voting Mechanisms How do we make decisions that respond to various individuals preference funtions? Ex: selecting new faculty based on various different evaluations Want to decide what to serve for refreshments the last day of class. How do we decide?

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43 Borda Paradox – remove loser, winner changes (notice, c is always ahead of removed item) a > b > c >d b > c > d >a c > d > a > b a > b > c > d b > c > d> a c >d > a >b a ** b > c n b > c >a n c > a > b n a > b > c n b > c > a n c > a >b n a
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44 Research Question Do individuals always act the way the theory says they should? If not, why not? Is the theory wrong?

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45 Allais Paradox In 1953, Maurice Allais published a paper regarding a survey he had conducted in 1952, with a hypothetical game. Subjects "with good training in and knowledge of the theory of probability, so that they could be considered to behave rationally", routinely violated the expected utility axioms. The game itself and its results have now become famous as the "Allais Paradox".

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46 The most famous structure is the following: Subjects are asked to choose between the following 2 gambles, i.e. which one they would like to participate in if they could: Gamble A: A 100% chance of receiving $1 million. Gamble B: A 10% chance of receiving $5 million, an 89% chance of receiving $1 million, and a 1% chance of receiving nothing. After they have made their choice, they are presented with another 2 gambles and asked to choose between them: Gamble C: An 11% chance of receiving $1 million, and an 89% chance of receiving nothing. Gamble D: A 10% chance of receiving $5 million, and a 90% chance of receiving nothing.

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47 This experiment has been conducted many, many times, and most people invariably prefer A to B, and D to C. So why is this a paradox?.

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48 The expected value of A is $1 million, while the expected value of B is $1.39 million. By preferring A to B, people are presumably maximizing expected utility, not expected value. By preferring A to B, we have the following expected utility relationship: u(1) > 0.1 * u(5) + 0.89 * u(1) + 0.01 * u(0), i.e. 0.11 * u(1) > 0.1 * u(5) + 0.1 * u(0) Adding 0.89 * u(0) to each side, we get: 0.11 * u(1) + 0.89 * u(0) > 0.1 * u(5) + 0.90 * u(0), implying that an expected utility maximizer consistent with the first choice must prefer C to D. The expected value of C is $110,000, while the expected value of D is $500,000, so if people were maximizing expected value, they should in fact prefer D to C. However, their choice in the first stage is inconsistent with their choice in the second stage, and herein lies the paradox.

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