Game Theory Workshop: Exploring Economic Foundations and Player Strategies

1. Residential Workshop*Template Slide-Show*The sequence of slides may vary during eitherWorkshops or Masterclass from Patrick McNutt FRSAAdditional materials can be located under eLearning & Games Academy atwww.patrickmcnutt.com

2. Economic Foundations (also go direct to Slide No 17)*from Topics 1 & 2 Market System: Technology and e-Needs *from Topics 3 & 4 Rational Behaviour The Bayesian persuasion problem

3. What is game theory about?Visit www.patrickmcnutt.com • Observed behaviour (inductive) in a game, G. • Identify the players in the game and the player’s type. Finding the patterns in rival behaviour. • Game => information on opponent type, recognised interdependence, action-reaction, belief systems. • Payoff depends on what each player believes about the other.. Updating belief systems. • What is a player’s true payoff? Independence v interdependence; one-shot v repeated play. • Consumers’ preferences as technology in a game.

4. Failure of Law of One Price Hypothesis: BIN Price < END price Are ‘onsumers’ irrational? Latent transaction costs Credible threats & belief systems

5. Prisoners’ Dilemma

10. Payoffs reflect preference order. Guaranteed a 2 but there is an elusive 3What if? Strategy I: cooperateWhat if? Strategy II: compete.Then if Strategy I is the consensus……..?

11. Topics 1 & 2 to Topics 3 & 4

12. Example A: What is type? If you believe it to be true that Leo the Liar will never tell the truth, how do you respond to his helping hand as you cling for your life over the precipice of a cliff? Do you ignore his helping? Do you rely instead on the many apps on your smartphone, so tightly grasped in your other hand, trying to make contact with your best friend to come and rescue you? Define Strategy Cooperation arises in this instance if you and Leo as players in a game can infer from past behaviour that both of you are likely to be trustworthy. Leo may forgo the short term gain of keeping to type for the long term benefit of your friendship. He rescues you from the cliff. You, however, will use the experience in order to determine whether or not to believe Leo in the future.

13. Example B: Player’s belief system Your company’s strategy is s1: delayed launch of a new innovative product for 2 years. Rumors do appear of an impending launch date. You do not deny such rumors. In the interim, an article appears a reputable trade journal reporting that a not dissimilar product is about to be launched by your competitor in the next few weeks. Define Strategy Do you stop and think about s1? Do you reshape your strategy to s2: launch the product as soon as possible?

14. Player type and signalling • Decisions are interpreted as signals • Observed patterns and Critical Time Line (CTLs).Go to Appendix in McNutt • Recognition of market interdependence (zero-sum and entropy) • Price as a signal v Baumol model of TR max • Scale and size: cost leadership • Dividends as signals in a Marris model

15. Thinking Strategically… http://www.managementinnovation.net/wp-content/uploads/2011/08/Playing-War-Games-To-Win.pdf Principles of competition and cooperation. Chess and perfect information Backward induction and forward reasoning Timing in games Normal form and Extensive form

16. Player Types I Baumol type: player in a Bertrand game who will reduce price if demand is elastic. CL type: in Cournot capacity game we have a cost-leader type, CL, with reserve capacity. Incumbent and entrant: In the geography the incumbent already exists in the geography and the entrant is intent on entering or presents a threat of entry (contestable market). Dominant incumbent is a player with at least 40% of the market share. Often linked with Stackelberg or ‘top-dog’ in Besanko.

17. Economic FoundationsClassroom Discussion on Elasticity and on Capacityhttp://www.patrickmcnutt.com/elearning/kaelo-learning-interactions-2/

19. The competitive threat! • Traditional Analysis is focused on answering this question for Company X: what market are we in and how can we do better? • Economics of strategy (T/3) asks: what market should we be in?

20. Perfect market: perfect competition • Defining a perfect market as follows: If ΔPi increases, then the firm’s output = 0 or rivals follow the price increase. • In a perfect market price differences cannot persist across time • Perfect competition = perfect market + near rivals So perfect market ≠> perfect competition but perfect competition => perfect market

21. Reasons to Play

22. Costs of not being a Player • No playbook • Bounded rationality and opportunity costs with trade-offs • Make or Buy dilemma • First Mover Advantage (FMA) v Second Mover Advantage (SMA) or Play to win v Play not to lose! • Fail to anticipate competitor reactions • Follower status ‘behind the curve’ • Technology lag and failure to differentiate ‘fast enough’ to sustain a competitive advantage • Near rival will try to minimise your gains by playing a minimax strategy

23. Non Co-operative Strategic Games

24. Oligopoly,Games & T/3 Framework Study of strategic interactions: how firms adopt alternative strategies by taking into account rival behaviour Structured and logical method of considering strategic situations. It makes possible breaking down a competitive situation into its key elements and analysing the dynamics between the players. Key elements: Players. Company or manager. Strategies. Payoffs Equilibrium. Every player plays her best strategy given the strategies of the other players. Objective. To explore oligopolistic industries from a game embedded strategy (GEMS) perspective. The use of T/3 framework, which considers 3 key dimensions (Type, Technology & Time), will allow players to better predict the likely strategic response of competitors when analysing rival competition.

25. Decoding Strategy & Pattern Sequencing Complete knowledge on the type and complete information of the identity of a near rival: Actionyou -> Reactionnear-rival ->… ..-> Reactions……NashReplyyou….. Strategy defined in terms of an equilibrium: how well either player does in a game depends on what each player believes the other player will do.

26. Surprise and Noise • Binaryreaction: • Will Player B react? Yes or No? • If YES, decision may be parked as ‘do-nothing strategy’ • If NO, decision proceeds on error • Surprise, bias and noise • Non-binaryreaction: Player B will react. Probability = x% • Probability (1-x)% ANOther player will react? • Decision taking on conjecture of likely reaction • No Surprise with Contingent risk profile

27. Player Types II Extant incumbent: An incumbent that has survived a negative event such as a price war of a failed innovation or technology-lag. De novo entrant: An entrant intent on entering – the incumbents can observe plant building or product launch. Potential entrant: An entrant that presents a threat of entry into a game through signalling with noise or ‘moonshot’ or planned capacity building in another game [with economies of scope). Stackelberg type: A price leader in a Bertrand game moving first in the belief that others will follow or in the knowledge that other are disciplined (often linked to collusive behaviour).

28. Two basic forms of model are used to analyse games: The Normal (Strategic) Form of a game •Summarises players, strategies and payoffs in a ‘payoff matrix’ •Particularly suitable for analysing static games (e.g. games with simultaneous moves). Making choices simultaneously The Extensive Form of a game •Summarises players, strategies and payoffs in a ‘game tree’ •Useful where the timing of players actions, and the information they will have when they must take these actions, is important (e.g. games with sequential moves)

29. Strategy & Games

30. Player’s Irrational Behaviour from Topic 3 to Topic 4

31. Failure of Law of One Price BIN Price < END price Game Dimension Sufficiently Intelligent Algorithm v Rational ‘onsumer’

32. Game Strategy • Nash premise: Action, Reaction and CV matrix • Non-cooperative sequential (dynamic) games • TR Test McNutt pp48..one-shot move • Limit price [to avoid entry] and predatory pricing to force exit. • Near rival plays Minimax, so I play Maximin [focus on my worst minimum payoff and try to maximise]. • Segmentation strategy to obtain FMA • Relevance of ‘chain-store’ tumbling price paradox • Dark Strategy and 3 Mistakes in McNutt pp117-118

33. Nash Equilibrium •Many common games (and therefore many common strategic situations) are not solvable. Is behaviour irrational? • Search for a solution in Nash equilibrium • Nash Equilibrium, is now one of the most fundamental concepts in the economics of strategy

34. In order for the NE of a game to be a compelling solution assumes: Players are rational The rules of the game are common knowledge Common knowledge of players’ rationality A source of ‘Common Beliefs’ •Focal Points •Pre-game communication •Learning •Convention

35. Describe (prices as signals) game dimension • Players and type of players • Prices interpreted as signals • Understand (price) elasticity of demand and cross-price elasticity • Patterns of observed behaviour • Leader-follower as knowledge • Accommodation v entry deterrence • Reaction, signalling and Nash equilibrium: ‘best you can do, given reaction of competitor’

36. Player A’s Conjectural Variation [CV] Matrix In a what-if scenario, a player creates a CV matrix to allow (i) filtering of the competitors (ii) that are likely to react to each action.

37. Normal Game Dimension • Simultaneous games • Normal form game dimension with payoff matrices, wherein payoffs reflect preference order. • Player type and camouflage • Dominant strategy, Prisoners’ dilemma, Nash equilibrium.

38. Extensive Game Dimension • Constructing an action-reaction sequence of moves in search for a pattern. • Non-cooperative sequential (dynamic) games • Extensive form game dimension with decision tree and backward induction • Credible Threats • Commitment strategies • Signaling and Belief Systems

39. Entry Deterrent Strategy & Barriers to entry • Reputation of the incumbents • Capacity building • Entry function of the entrant • De novo and entry at time period t • Potential entrant - forces reaction at time period t from incumbent • Coogan’s bluff strategy (classic poker strategy) and enter the game.

40. Limit Pricing ModelBesanko pp207-211 and McNutt pp85-88 • Outline the game dimension: dominant incumbents v camouflaged entrant type • Define strategy set for incumbents: commitment and punishment • Allow entry and define the equilibrium • Extensive form preference - entry deterrent strategy v accommodation [next slides]

41. Extensive Form Games •The Extensive Form is particularly useful for analysing games in which players make choices sequentially •The structure of the game is represented by a game tree. Play begins at the initial node and proceeds according to the structure of the tree and the choices that players make

42. Extensive Form Games we will only consider games involving two players we will only consider games in which players can observe the moves made by players earlier on in the game (these are called games of complete information) we will allow for ‘fooling behaviour’ and camouflage by an entrant

44. Online Lecture Exercise Strategy Profile - Fid the Nash Trap Observations and Intelligence In the decision tree narrative there is no other firm to compete with in this game – it is the incumbent v entrant. But if the entrant does not enter, fight and accommodate yield the same payoffs to both players Hypothesis 1 If the entrant does not enter, it does not matter what the incumbent chooses to do. Hypothesis 2 The incumbent will not lower prices if the entrant does not enter.

45. CLASS EXERCISE QUESTIONS • Convert the decision tree into a normal form payoff matrix. • B. Find the Nash equilibria • C. Repeat A and B on the credible threat of entry from a spherical competitor • [check pp173-175 in McNutt Decoding Strategy] • D. Results in A+B+C written up as an Aide Memoire for management. • E. Strategy Profile = Aide Memoire

46. Nash Equilibrium & Define a price war • Construct the Bertrand reaction functions • Compute a Critical Time Line (CTL)from observed signals.. • Find a price point of intersection • Case Analysis of Sony v Microsoft in McNutt pp 141-144 and also in Kaelo v2.0

47. PATTERN – 2000-2006 Announcement PS3 production schedule to ship 6 million units by 31 Mar 07 at $499 PS2 launched at $299 PS2 at $199.99 PS2 at $179.99 PS2 at $149.99 100 million PS2 shipped PS2 at $129.99 11 May 04 20 April 06 8 May 06 26 Oct 00 15 Nov 01 14 May 02 15 May 02 13 May 03 14 May 03 29 Mar 04 1 Nov 05 30 Oct 05 22 Nov 05 6 Feb 06 27 April 06 Xbox at $179 22 million Xbox shipped Microsoft Xbox launched at $299 Revised production schedule for Xbox 360 to 5- 5.5 million units by 30th June 2006 Xbox 360 launched at $399 Xbox at $199 Xbox at $179 Xbox at $149

48. Classroom Exercise on Nash Reply Practical III on Price Data Trends: Compute the NE and represent the equilibrium in a Nash-Bertrand Reply Function

49. Dominant Strategy Equilibrium Iterative Deletion of Dominated Strategies Nash Equilibrium Dominant Strategies •A player has a (strictly) dominant strategy if, for each possible action that his opponent can take, that strategy leads to a payoff that is strictly greater than the payoff associated with any of his other strategies •A player can have no more than one dominant strategy and in many games, will have none

50. The ‘signalling’ payoffs & assurance • A & B have common interest in coordinating strategies. Player A never choose ‘Bottom’ if rational, only ‘Top’, and Player B should play weakly dominant ‘Left’. • Problem of coordination where players have different preferences but common interest in coordinating strategies. • Classroom discussion on Folk Theorem • Next slide for Assurance Game on coordination and trust: Payoff-dominant v risk-dominant play.