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Negotiation: Markets, Rationality, and Games

Negotiation: Markets, Rationality, and Games. Intro. Once agents have discovered each other and agreed that they are interested in buying/selling, they must negotiate the terms of the deal. Might be simple (take it or leave it) or complex (iterated bargaining)

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Negotiation: Markets, Rationality, and Games

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  1. Negotiation:Markets, Rationality, and Games

  2. Intro • Once agents have discovered each other and agreed that they are interested in buying/selling, they must negotiate the terms of the deal. • Might be simple (take it or leave it) or complex (iterated bargaining) • Might involve only price, or many other dimensions (quality, service contract, warranty, delivery, payment terms, etc.)

  3. Mechanism Design • By setting up the rules that agents use to negotiate, we can ensure that particular sorts of behavior or solutions occur. • Truth-telling • Maximize profit • Maximize social welfare • Maximize participation • Reach solutions quickly • Etc. • Choosing rules that lead to a particular outcome is known as mechanism design

  4. Supply and Demand • Supply and demand are the two parameters that govern a market’s behavior • Supply: quantity of product available • Demand: amount of product wanted at a particular price.

  5. Demand • We can visualize demand as a downward-sloping curve Quantity demanded Price

  6. Supply • Similarly, supply can be visualized as an upward-sloping curve. Quantity demanded Quantity supplied Price

  7. Equilibrium • The point at which supply and demand intersect is called the competitive equilibrium Quantity demanded Quantity supplied Price In a perfect world, prices will drive supply and demand to the equilibrium

  8. Equilibrium • One of the central tenets of market economies is the invisible hand • If there is too much supply, prices will fall due to competition – this increases demand. • If there is too much demand, prices will increase – this encourages supply. • In equilibrium, the quantity supplied will equal the quantity demanded.

  9. Breaking an Equilibrium • There are many things that can keep a market from equilibrium • Lack of sellers (monopoly/oligopoly) • “Lock-in” among buyers • Incomplete or slow-moving information • Collusion among (usually) sellers or buyers • External price controls • Etc.

  10. Properties of an Equilibrium • Equilibria have some nice properties: • Everyone who wants to buy/sell at this price can. • This sort of solution is called “efficient” • Given this price, no one wants to change. • The system is stable; given that you are at an equilibrium you will stay there.

  11. Rationality • Rationality is the assumption that an agent (human or software) will act so as to maximize its happiness or advantage. • We often try to measure this advantage numerically using utility • Money can sometimes serve as a substitute for utility

  12. Markets and Games • Markets are useful for understanding interactions among a large group of agents • No need to speculate about individual actions • In many e-commerce settings, negotiation takes place in a one-on-one format • In this case, game theory is a more useful analytical tool. • Also very useful for designing agents that operate in open environments.

  13. Game Theory • Developed to explain the optimal strategy in two-person interactions. • Initially, von Neumann and Morganstern • Zero-sum games • John Nash • Nonzero-sum games • Harsanyi, Selten • Incomplete information

  14. An example:Big Monkey and Little Monkey • Monkeys usually eat ground-level fruit • Occasionally climb a tree to get a coconut (1 per tree) • A Coconut yields 10 Calories • Big Monkey expends 2 Calories climbing the tree. • Little Monkey expends 0 Calories climbing the tree.

  15. An example:Big Monkey and Little Monkey • If BM climbs the tree • BM gets 6 C, LM gets 4 C • LM eats some before BM gets down • If LM climbs the tree • BM gets 9 C, LM gets 1 C • BM eats almost all before LM gets down • If both climb the tree • BM gets 7 C, LM gets 3 C • BM hogs coconut • How should the monkeys each act so as to maximize their own calorie gain?

  16. An example:Big Monkey and Little Monkey • Assume BM decides first • Two choices: wait or climb • LM has four choices: • Always wait, always climb, same as BM, opposite of BM. • These choices are called actions • A sequence of actions is called a strategy

  17. An example:Big Monkey and Little Monkey c w Big monkey c w c Little monkey w 0,0 9,1 6-2,4 7-2,3 • What should Big Monkey do? • If BM waits, LM will climb – BM gets 9 • If BM climbs, LM will wait – BM gets 4 • BM should wait. • What about LM? • Opposite of BM (even though we’ll never get to the right side • of the tree)

  18. An example:Big Monkey and Little Monkey • These strategies (w and cw) are called best responses. • Given what the other guy is doing, this is the best thing to do. • A solution where everyone is playing a best response is called a Nash equilibrium. • No one can unilaterally change and improve things. • This representation of a game is called extensive form.

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