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Chapter 13 Strategic Games COPYRIGHT © 2008 Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license.

Chapter 12 – Take Aways When a seller cannot identify low- and high-value consumers or cannot prevent arbitrage between two groups, it can still discriminate, but only indirectly, by designing products or services that appeal to groups with different price elasticities of demand, who identify themselves based on their purchase patterns. If you offer a low-value product that is attractive to high-value consumers, you may cannibalize sales of your high-price product. When bargaining with a customer, do not bargain over unit price; instead, bargain over the price of a bundle. Bundled pricing can allow a seller to extract more consumer surplus if willingness to pay for the bundle is more homogeneous than willingness to pay for the separate items in the bundle.

Review of Chapter 12 Conditions associated with indirect price discrimination  You cannot identify low- and high-value consumers or  You cannot prevent arbitrage between two groups You can still discriminate, but only indirectly, by designing products or services that appeal to different groups If you offer a low-value product that is attractive to high-value consumers, you may “cannibalize” sales of your high-price product. Bundling products “flattens out” the demand curve, and makes it possible to capture more of the consumer surplus. When bargaining with a customer, do not bargain over unit price; instead bargain over the price of a bundle.

Introductory Anecdote China 1995  Rural Credit Union raised rates from 9.2% to 10.8% on one-year savings  Hunan Development bank matched  Capital costs increased at both banks, without a corresponding increase in deposits, and profit at both banks declined.  1996, Central Bank ended “ruinous competition”

Game Theory Games  Players, strategies, payoffs  For analyzing interdependence  One firm’s profits depend on rival actions If each player acts optimally, rationally, and selfishly, we can compute the likely outcome or “equilibrium” of the game Why use game theory?  Helps implement the third “generic strategy” of controlling competition  Study outcome or equilibrium of game and perhaps figure out how to change the game to your advantage

Sequential Move Games Players take turns moving, and each player observes what its rival did before it has to move. To compute the equilibrium of a sequential game, it is important to look ahead and reason back. Example: simple two-move game  First player anticipates how the second will react to various moves and the payoffs associated with outcomes  Each player chooses her best move knowing how the other will react. Analyze using tree form

Nash Equilibria Named for John Nash  The "father" of non-cooperative game theory  Proved the existence of the Nash equilibrium in his doctoral dissertation at Princeton University Definition  A set of strategies, one for each player, such that no player has incentive to unilaterally change her action  Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy Practice 

Entry Game (Sequential Move) Entry Accommodation But, remember, one of the points of studying game theory is to figure out how to gain an advantage

Entry Game (Sequential Move) Entry Deterrence A credible threat to price low if entry occurs will deter entry  Difficult to make this threat credible

Simultaneous Move Games Players move simultaneously  Does not require players moving “at same time”  Requires that each player makes move without knowing other player’s move in advance Analyze using matrix or reduced form

Prisoners’ Dilemma Prisoners’ dilemma  Two suspected criminals being interrogated  If only one confesses, the one who confesses goes free, while the other one receives ten years in jail.  If they both confess, each receives five years in jail.  If neither confesses, they both serve two years.

Why the PD is interesting Equilibrium is for both to confess But, they BOTH would be better off if neither confessed By following self interest, the players make the group worse off Tension between conflict (self interest) and cooperation (group interest) inherent in the game Need to devise ways to escape the dilemma

Prisoners’ Dilemma in Business Pricing dilemma  Both would be better off if they could Price High  But, that outcome is not an equilibrium  Need to find a way to “coordinate” actions  BUT, beware violating the law

More Dilemmas Price discrimination dilemma

Even More Dilemmas Advertising dilemma

Even More Dilemmas Free riding dilemma

Lessons of Prisoners’ Dilemma Don’t get caught in one  Change payoff structure of game so your profits are not dependent on others’ actions Differentiate product Lower costs How to get out of one (Axelrod’s Tournament)  Be nice: no first strikes  Be forgiving  Be easily provoked  Don’t be envious  Be clear Control competition LEGALLY!!

Game of Chicken Two equilibria Try to manipulate game to get the one you want Coordination or communication is important

Game of Chicken (Market Entry) Exploit first-mover advantage

Dating Game Cooperation between divisions

Shirking/Monitoring Game No equilibrium in pure strategies So “mix” to avoid being taken advantage of

Alternate Intro Anecdote In 1992, America Airlines (AA) announced a new pricing strategy - Value Pricing.  American narrowed the number of fares possible from 500,000 to 70,000 by classifying each into one of four classes (first class, coach, discounted 7 and 21 day purchase) and began pricing based on flight length.  Changes resulted in lower list prices for both business and leisure travelers. According to AA, Value Pricing was to create “simplicity, equity, and value” in their prices Company expectations  Demand would be stimulated  Volume on AA planes would increase  Overall growth in market share and profitability would follow What really happened??  Competitors responded aggressively by cutting prices  Industry profits plummeted  Value Pricing initiative abandoned within months of its launch