Game Theory <ul><li>Von Neuman and Morgenstern (The Theory of Games and Economic Behavior, 1944) </li></ul><ul><li>Concept...
Two Person, Zero Sum Games <ul><li>Each person knows own and opponent’s alternatives </li></ul><ul><li>All preferences are...
Strategies <ul><li>Dominant strategy </li></ul><ul><ul><li>Best regardless what others do </li></ul></ul><ul><li>Maximin s...
Unstable Games <ul><li>No equilibrium found </li></ul><ul><li>Strategy chosen leads to solution </li></ul><ul><li>Each pla...
Two Person, Non-Zero Sum Games <ul><li>The Prisoner’s Dilemma </li></ul><ul><li>Bonnie and Clyde are caught </li></ul><ul>...
Duopoly as a Prisoner’s Dilemma <ul><li>Even if both agree to a cooperative solution, one may double cross </li></ul><ul><...
Repeated Games <ul><li>Single period game predicts competition, but there are likely to be multiple periods.  </li></ul><u...
N-Person Games <ul><li>Extend to more than 2 players </li></ul><ul><li>Complications: </li></ul><ul><ul><li>Coalitions </l...
Best Pricing Practices <ul><li>Shift attention to tactics and strategy to achieve competitive advantage </li></ul><ul><li>...
Business Strategy Games <ul><li>When rivals alter products or pricing, react or adapt  </li></ul><ul><li>Anticipate action...
Business Rivalry as a Sequential Game <ul><li>The first to introduce a product, lower price, etc. often achieve recognitio...
First-Mover Games <ul><li>Game with military and civilian markets for Hum Vs.  </li></ul>
Game Tree--Illustrating Sequential Games <ul><li>Game tree  is like a decision tree </li></ul><ul><li>Schematic diagram of...
A Credible Threat <ul><li>A  credible threat-- an action perceived as a possible penalty in a noncooperative game.  </li><...
Mechanisms for Credible Threats and Commitments <ul><li>Contractual side payments, but these may violate antitrust laws. <...
Hostage Mechanisms in Oligopoly <ul><li>Best Buy’s offer:   If you find a lower advertised price, you’ll get the differenc...
Excess Capacity, Scale of Entry, and Entry Deterrence <ul><li>Building excess capacity can deter entry.  Potential entrant...
Size Barriers <ul><li>Sometimes market entry requires large scale </li></ul><ul><li>Incumbents may accommodate entrant, al...
Sorting Rules <ul><li>Brand loyalty </li></ul><ul><li>Efficient rationing </li></ul><ul><li>Random rationing </li></ul><ul...
Theory of Contestable Markets <ul><li>High prices encourage entry </li></ul><ul><li>When barriers are low, even monopolist...
Simultaneous Games <ul><li>A sealed bid auction is a simultaneous game </li></ul><ul><li>A dominant strategy is the best d...
Nash Equilibrium <ul><li>When all players make their best reply responses (so changing their choices cannot improve their ...
Repeated Games <ul><li>Escape from the prisoner’s dilemma </li></ul><ul><li>If games are repeated, there is a greater expe...
Repeated Game Strategies <ul><li>Grim trigger strategy--violations never forgotten </li></ul><ul><ul><li>Alternatively, pu...
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Game Theory Von Neuman and Morgenstern (The Theory of Games ...

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  • Game theory is used to describe situations where individuals or organizations have conflicting objectives. A theory of decision making in a conflict-of-interest situation. Consider actions of rivals in advance. Examples: Pricing and output decisions with only a few firms in the market, strategic arms race, advertising plans in an oligopolistic situation, market power in pain relief market, colas, theme parks, airlines. Game Strategy--a course of action Payoff--outcome of the strategy Payoff matrix--listing of payoffs
  • Alice’s payoffs appears in upper triangle and Bob’s appear in the bottom Bob c d e a 5 1 -1 Alice -5 -1 1 b 3 7 -8 -3 -7 8 Find Maximin Solution Is it an Equilibrium? Worst for Alice with a- strategy is -1 Worst for Alice with b -strategy is -8 Worst for Bob with c -strategy is -5 Worst for Bob with d- strategy is -7 Worst for Bob with e -strategy is 1 Solution strategy {a,e}
  • Bob c d Alice a 3, - 3 1, - 1 b 2, - 2 4, - 4 In the Alice-Bob Game, Maximin Strategies lead to solution {b, c} But Alice has an incentive to switch to strategy {a} Then Bob has an incentive to switch to strategy {d}, etc., etc . There is no, single stable equilibrium. Each player may elect a random strategy.
  • Clyde Don’t confess Confess Bonnie 1 0 Don’t confess 1 15 15 5 Confess 0 5 Non-cooperative solutions prohibit collusive communication, side payments, third-party enforceable binding agreements. Maximin strategy--concept of a security level or minimum payoff.
  • Firm 1 S L Firm 2 S 100, 100 10, 150 L 150, 10 20, 20
  • Predict rival behavior Non-cooperative sequential game Non-cooperative, repeated, simultaneous game No side payments No binding contracts between rivals
  • Managerial purpose of game theory --proactive behavior requires accurate and reliable predictions of rival’s initiatives and responses. Pepsi List price Discount Coke 12,000 17,000 List price 12,000 6,000 6,000 8,000 Discount 17,000 8,000 What if $6,000 outcome were changed to $9,000?
  • Firm 1 Civilian Military Firm 2 C -10, -10 30, 15 M 15, 30 -10, -10 In a simultaneous game, both would want the civilian market. But in a sequential game, the first to get the civilian market preempts it. The other firm takes the military market.
  • End game reasoning --looking ahead to the final play in an ordered sequence of plays, identifying the player who controls the final outcome, and predicting that player’s preferred choice. Nash equilibrium strategy --a decision maker’s optimal action such that the payoff, when all other players make best-reply responses, exceed payoff from any other action.
  • 6 Must know What makes rivals tick What true goals they seek What are the consequences of actions on goals
  • 7 Self-enforcing agreements Credible threat --a conditional strategy the threat maker is worse off ignoring than implementing. Credible commitment --obligation the commitment maker is worse off ignoring than fulfilling. Mechanisms for establishing credibility--bond or contractual side payment, investing in nonredeployable reputation assets, entering into profit sharing alliances, arranging an irreversible or irrevocable hostage mechanism. Close-end leases with preset residual values are a mechanism for a durable good’s manufacturer to establish a commitment to early buyers.
  • 8 26 Incumbents may try to deter potential entrants by using excess capacity precommitments or credible threats of advertising campaigns and price discounts. Deterring or accommodating potential entrants depends on first-mover advantages, how customers sort across the low-priced capacity, etc.
  • 10
  • Looking at impact on new entrant, low-priced capacity. Brand loyalty--customers reject new entrants, even when incumbents’ prices are higher. Efficient rationing--Those with highest willingness-to-pay will exert effort to seek out low-priced capacity. Favorable to low-price entrants Random rationing--random behavior by customers. Everyone has equal opportunity to secure low-priced capacity. Inverse intensity rationing--lowest willingness-to-pay customers absorb the capacity of the low-priced entrant.
  • Low barriers =&gt; hit-and-run tactics in search of short-run profits. Proactive incumbents invest in excess capacity and nonredeployable assets in order to deter entry.
  • Simultaneous games occasionally arise in pricing and promotion rivalry. Essence of business strategy is sequential reasoning (order of play matters; must be able to predict best-reply responses).
  • Reexamine the Coke-Pepsi rivalry. Nash equilibrium requires the action be optimal given a best-reply response of the rival.
  • Game Theory Von Neuman and Morgenstern (The Theory of Games ...

    1. 1. Game Theory <ul><li>Von Neuman and Morgenstern (The Theory of Games and Economic Behavior, 1944) </li></ul><ul><li>Conceptual Framework </li></ul><ul><ul><li>Game strategy </li></ul></ul><ul><ul><li>Components of a game </li></ul></ul>
    2. 2. Two Person, Zero Sum Games <ul><li>Each person knows own and opponent’s alternatives </li></ul><ul><li>All preferences are known </li></ul><ul><li>Single period game </li></ul><ul><li>Sum of payoffs zero </li></ul><ul><li>Equilibrium reached when neither of the participants can improve payoff </li></ul>
    3. 3. Strategies <ul><li>Dominant strategy </li></ul><ul><ul><li>Best regardless what others do </li></ul></ul><ul><li>Maximin strategy </li></ul><ul><ul><li>Choice that maximizes across the set of minimum possible payoffs </li></ul></ul><ul><ul><li>Best of the worst </li></ul></ul>
    4. 4. Unstable Games <ul><li>No equilibrium found </li></ul><ul><li>Strategy chosen leads to solution </li></ul><ul><li>Each player then has incentive to switch </li></ul>
    5. 5. Two Person, Non-Zero Sum Games <ul><li>The Prisoner’s Dilemma </li></ul><ul><li>Bonnie and Clyde are caught </li></ul><ul><li>Dilemma: Confess or not </li></ul><ul><li>1 period game </li></ul><ul><li>Non-cooperative solution: Both confess </li></ul><ul><li>Cooperative solution: Both do not confess </li></ul><ul><li>Off diagonal represents double cross </li></ul>
    6. 6. Duopoly as a Prisoner’s Dilemma <ul><li>Even if both agree to a cooperative solution, one may double cross </li></ul><ul><li>Two firms: decision on amount of output {Small or Large} </li></ul><ul><li>{L,L} represents normal profits </li></ul>
    7. 7. Repeated Games <ul><li>Single period game predicts competition, but there are likely to be multiple periods. </li></ul><ul><li>Multiple periods allow for retribution, not found in single period games </li></ul><ul><ul><li>Duopoly as a Multiperiod Game </li></ul></ul><ul><ul><li>More likely to collude </li></ul></ul>
    8. 8. N-Person Games <ul><li>Extend to more than 2 players </li></ul><ul><li>Complications: </li></ul><ul><ul><li>Coalitions </li></ul></ul><ul><ul><li>Cooperation and duplicity </li></ul></ul><ul><li>Solutions can be difficult </li></ul><ul><ul><li>Still gives insight into nature of conflict, posturing, and resolution </li></ul></ul>
    9. 9. Best Pricing Practices <ul><li>Shift attention to tactics and strategy to achieve competitive advantage </li></ul><ul><li>Examine rival firm behavior as if it were a game </li></ul><ul><ul><li>First-mover advantages </li></ul></ul><ul><ul><li>Credible threats to alter rival behavior </li></ul></ul><ul><ul><li>Stresses interdependency in oligopoly </li></ul></ul>
    10. 10. Business Strategy Games <ul><li>When rivals alter products or pricing, react or adapt </li></ul><ul><li>Anticipate actions; be proactive </li></ul><ul><li>Sequential game --specific order of play </li></ul><ul><ul><li>E.g.; One firm announces a price cut; decision is to respond or not respond </li></ul></ul><ul><li>Simultaneous game --all players choose actions at same time </li></ul>
    11. 11. Business Rivalry as a Sequential Game <ul><li>The first to introduce a product, lower price, etc. often achieve recognition and advantage--first-mover advantage </li></ul><ul><li>When games last several periods, actions can be rewarded or punished in subsequent periods </li></ul><ul><ul><li>Entry of a new firm often discouraged by threat of existing firms dropping prices to unprofitable levels. </li></ul></ul>
    12. 12. First-Mover Games <ul><li>Game with military and civilian markets for Hum Vs. </li></ul>
    13. 13. Game Tree--Illustrating Sequential Games <ul><li>Game tree is like a decision tree </li></ul><ul><li>Schematic diagram of decision nodes (or focal outcomes) </li></ul><ul><li>Solutions parallel board games like chess </li></ul><ul><li>One approach to solution-- end-game reasoning --start with the final decision and use backward induction to find the best starting point. </li></ul>
    14. 14. A Credible Threat <ul><li>A credible threat-- an action perceived as a possible penalty in a noncooperative game. </li></ul><ul><ul><li>Its existence sometimes induces cooperative behavior. </li></ul></ul><ul><li>A credible commitment-- a mechanism for establishing trust </li></ul><ul><ul><li>Such as a reward for good behavior in a noncooperative game. </li></ul></ul> 1999 South-Western College Publishing
    15. 15. Mechanisms for Credible Threats and Commitments <ul><li>Contractual side payments, but these may violate antitrust laws. </li></ul><ul><li>Use of nonredeployable assets such as reputation. </li></ul><ul><li>Entering alliance relationships which may fall apart if any party violated their commitments. </li></ul><ul><li>Using a &quot;hostage mechanism”--irreversible and irrevocable can deter breaking commitments. </li></ul><ul><ul><li>Examples: &quot;double your money back guarantees,&quot; and &quot;most favored nation&quot; clauses. </li></ul></ul> 1999 South-Western College Publishing
    16. 16. Hostage Mechanisms in Oligopoly <ul><li>Best Buy’s offer: If you find a lower advertised price, you’ll get the difference back </li></ul><ul><li>This makes Best Buy cut prices whenever local stores cuts prices </li></ul><ul><ul><li>Local stores realize they can’t undercut Best Buy </li></ul></ul><ul><ul><li>Customers realize it is unlikely to find lower prices </li></ul></ul><ul><ul><li>If potential entrants think they can get a foothold in area, they know that Best Buy’s pricing is a credible commitment . </li></ul></ul> 1999 South-Western College Publishing  1999 South-Western College Publishing
    17. 17. Excess Capacity, Scale of Entry, and Entry Deterrence <ul><li>Building excess capacity can deter entry. Potential entrants know that the price can </li></ul><ul><li>be driven down to unprofitable levels upon entry of new firms. </li></ul><ul><li>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 . </li></ul> 1999 South-Western College Publishing
    18. 18. Size Barriers <ul><li>Sometimes market entry requires large scale </li></ul><ul><li>Incumbents may accommodate entrant, allowing a niche </li></ul><ul><li>Incumbents may take entry deterring actions, such as cutting prices at the threat of entry </li></ul>
    19. 19. Sorting Rules <ul><li>Brand loyalty </li></ul><ul><li>Efficient rationing </li></ul><ul><li>Random rationing </li></ul><ul><li>Inverse intensity rationing </li></ul>
    20. 20. Theory of Contestable Markets <ul><li>High prices encourage entry </li></ul><ul><li>When barriers are low, even monopolist must be careful about raising prices too high. </li></ul><ul><li>Contestable markets tend to have competitive prices and low or zero economic profits </li></ul><ul><li>Potential entry matters more than actual number of firms </li></ul>
    21. 21. Simultaneous Games <ul><li>A sealed bid auction is a simultaneous game </li></ul><ul><li>A dominant strategy is the best decision, no matter what anyone else does. </li></ul><ul><li>When no Nash equilibrium exists, it is useful to hide one’s strategy by randomly changing strategies. Called a “mixed Nash equilibrium” strategy </li></ul>
    22. 22. Nash Equilibrium <ul><li>When all players make their best reply responses (so changing their choices cannot improve their situation) then the game is in Nash Equilibrium </li></ul><ul><li>Since game trees have several branches, we can examine the concept in each part of the tree, called a subgame. </li></ul>
    23. 23. Repeated Games <ul><li>Escape from the prisoner’s dilemma </li></ul><ul><li>If games are repeated, there is a greater expectation that firms will achieve a cooperative solution </li></ul><ul><li>Firms signal by their behavior whether they want to cooperate or not </li></ul><ul><li>Firms that expand output show that they do not want to cooperate </li></ul>
    24. 24. Repeated Game Strategies <ul><li>Grim trigger strategy--violations never forgotten </li></ul><ul><ul><li>Alternatively, punishment can be short-lived </li></ul></ul><ul><ul><li>For multiperiod games, usually some period of punishment that can induce cooperation </li></ul></ul><ul><li>Trembling hand trigger--when slight defections go unpunished </li></ul><ul><ul><li>One non-cooperative act may be forgiven, but not two </li></ul></ul>

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