Game Theory

1. Game Theory • Von Neuman and Morgenstern (The Theory of Games and Economic Behavior, 1944) • Conceptual Framework • Game strategy • Components of a game

2. Two Person, Zero Sum Games • Each person knows own and opponent’s alternatives • All preferences are known • Single period game • Sum of payoffs zero • Equilibrium reached when neither of the participants can improve payoff

3. Strategies • Dominant strategy • Best regardless what others do • Maximin strategy • Choice that maximizes across the set of minimum possible payoffs • Best of the worst

4. Unstable Games • No equilibrium found • Strategy chosen leads to solution • Each player then has incentive to switch

5. Two Person, Non-Zero Sum Games • The Prisoner’s Dilemma • Bonnie and Clyde are caught • Dilemma: Confess or not • 1 period game • Non-cooperative solution: Both confess • Cooperative solution: Both do not confess • Off diagonal represents double cross

6. Duopoly as a Prisoner’s Dilemma • Even if both agree to a cooperative solution, one may double cross • Two firms: decision on amount of output {Small or Large} • {L,L} represents normal profits

7. Repeated Games • Single period game predicts competition, but there are likely to be multiple periods. • Multiple periods allow for retribution, not found in single period games • Duopoly as a Multiperiod Game • More likely to collude

8. N-Person Games • Extend to more than 2 players • Complications: • Coalitions • Cooperation and duplicity • Solutions can be difficult • Still gives insight into nature of conflict, posturing, and resolution

9. Best Pricing Practices • Shift attention to tactics and strategy to achieve competitive advantage • Examine rival firm behavior as if it were a game • First-mover advantages • Credible threats to alter rival behavior • Stresses interdependency in oligopoly

10. Business Strategy Games • When rivals alter products or pricing, react or adapt • Anticipate actions; be proactive • Sequential game--specific order of play • E.g.; One firm announces a price cut; decision is to respond or not respond • Simultaneous game--all players choose actions at same time

11. Business Rivalry as a Sequential Game • The first to introduce a product, lower price, etc. often achieve recognition and advantage--first-mover advantage • When games last several periods, actions can be rewarded or punished in subsequent periods • Entry of a new firm often discouraged by threat of existing firms dropping prices to unprofitable levels.

12. First-Mover Games • Game with military and civilian markets for Hum Vs.

13. Game Tree--Illustrating Sequential Games • Game tree is like a decision tree • Schematic diagram of decision nodes (or focal outcomes) • Solutions parallel board games like chess • One approach to solution--end-game reasoning--start with the final decision and use backward induction to find the best starting point.

14. A Credible Threat • A credible threat--an action perceived as a possible penalty in a noncooperative game. • Its existence sometimes induces cooperative behavior. • A credible commitment--a mechanism for establishing trust • Such as a reward for good behavior in a noncooperative game. 1999 South-Western College Publishing

15. Mechanisms for Credible Threats and Commitments • Contractual side payments, but these may violate antitrust laws. • Use of nonredeployable assets such as reputation. • Entering alliance relationships which may fall apart if any party violated their commitments. • Using a "hostage mechanism”--irreversible and irrevocable can deter breaking commitments. • Examples: "double your money back guarantees," and "most favored nation" clauses. 1999 South-Western College Publishing

16. Hostage Mechanisms in Oligopoly • Best Buy’s offer:If you find a lower advertised price, you’ll get the difference back • This makes Best Buy cut prices whenever local stores cuts prices • Local stores realize they can’t undercut Best Buy • Customers realize it is unlikely to find lower prices • If potential entrants think they can get a foothold in area, they know that Best Buy’s pricing is a credible commitment. 1999 South-Western College Publishing 1999 South-Western College Publishing

17. Excess Capacity, Scale of Entry, and Entry Deterrence • Building excess capacity can deter entry. Potential entrants know that the price can be driven down to unprofitable levels upon entry of new firms. • The building of extra capacity is an action in a sequential game, often with the intent of forestalling entry. This is called a precommitment game. 1999 South-Western College Publishing

18. Size Barriers • Sometimes market entry requires large scale • Incumbents may accommodate entrant, allowing a niche • Incumbents may take entry deterring actions, such as cutting prices at the threat of entry

19. Sorting Rules • Brand loyalty • Efficient rationing • Random rationing • Inverse intensity rationing

20. Theory of Contestable Markets • High prices encourage entry • When barriers are low, even monopolist must be careful about raising prices too high. • Contestable markets tend to have competitive prices and low or zero economic profits • Potential entry matters more than actual number of firms

21. Simultaneous Games • A sealed bid auction is a simultaneous game • A dominant strategy is the best decision, no matter what anyone else does. • When no Nash equilibrium exists, it is useful to hide one’s strategy by randomly changing strategies. Called a “mixed Nash equilibrium” strategy

22. Nash Equilibrium • When all players make their best reply responses (so changing their choices cannot improve their situation) then the game is in Nash Equilibrium • Since game trees have several branches, we can examine the concept in each part of the tree, called a subgame.

23. Repeated Games • Escape from the prisoner’s dilemma • If games are repeated, there is a greater expectation that firms will achieve a cooperative solution • Firms signal by their behavior whether they want to cooperate or not • Firms that expand output show that they do not want to cooperate

24. Repeated Game Strategies • Grim trigger strategy--violations never forgotten • Alternatively, punishment can be short-lived • For multiperiod games, usually some period of punishment that can induce cooperation • Trembling hand trigger--when slight defections go unpunished • One non-cooperative act may be forgiven, but not two