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) Might involve only price, or many other dimensions (quality, service contract, warranty, delivery, payment terms, etc.)

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

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.

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

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

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

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.

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.

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.

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

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.

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

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.

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? 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 An example: Big Monkey and Little Monkey

Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 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)

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. An example: Big Monkey and Little Monkey