Residential Workshop* Strategy & Competition Game Theory Perspective Patrick McNutt FRSA Visiting Fellow, Manchester Business School, UK Visiting Professor,

Residential Workshop* Strategy & Competition Game Theory Perspective Patrick McNutt FRSA Visiting Fellow, Manchester Business School, UK Visiting Professor, Smurfit Business School, Dublin, Ireland *some of these slides may be used at Masterclass from Patrick McNutt

Economics Foundations from Topics 1 & 2 Trade-offs Demand and e-Needs
Algorithmic pricing BIN < END Technology & Capacity

Game Theory Foundations from Topics 3 & 4 Game Design
Rational Behaviour The Bayesian persuasion problem

Is there an unbeatable strategy?
Strategy as game theory: so, what is game theory about? Winning strategy… Visit Is there an unbeatable strategy? Game Design Payoffs & Preferences Rational Behaviour Prisoners’ Dilemma

Decoding Strategy and T/3 Design
TYPE Observed behaviour (inductive) in a game, G. Players are ascribed a type and a belief system Identify the players in the game and the player’s type. Finding the patterns in rival behaviour. What is a player’s true payoff? Private information v observed behaviour Independence v interdependence; one-shot v repeated play. TECHNOLOGY Consumers’ preferences as technology in a game. Individuals ‘enveloped’ by a game evolve as players Technology per se as the competitor TIME Time, no time and timeless: dT/dt = -1

Pre-Play Game Design T/3: ‘furniture of the player mind’
To become a player in the game: (i) observe patterns (ii) recognise mutual interdependence (iii) strategy as signalling. Players have a type and a belief system. Examples: Leo the Liar and gPhone Case Study: Philip Morris & BAT Evaluation of a player’s type in terms of executing strategy Updating belief systems. Credible threats. Baumol type (don’t chase the low price?) To decode type observe timing of moves, frequency of moves, magnitude of moves, matching moves (T4T) and repetition.

INSIDE THE GAME ENVELOPE Altruism v Selfish Gene
PRE-PLAY INSIDE THE GAME ENVELOPE Altruism v Selfish Gene Co-operate (Trust) v Compete (Cheat)

How to play in the ‘envelope’ of a game?
Decode information on opponent type: observed behaviour, historic behaviour, corporate intelligence. Players recognise interdependence: action-reaction sequence. Participation in G has reward/payoff that depends on what each player believes about the other. Solution concept: Updating belief systems at an equilibrium point when neither player can do better independently of the opponent.

Reason & Rationality: Equivalence & ‘enveloped by the game’
Co-operate Tournament G1………GN Maximin Strategy as number of moves G2…G4: Learning Curve Punishment REASONABLE G1: Compete Cheat

Binary Preference Co-operate Reward Compete No Punishment No Reward Punished

Binary Preference Co-operate 1st preference Compete ? 4th

Convert Preferences into a Tucker Payoff Table
1. Payoffs are cardinal numbers 1,2 or -1 or ½ And 2 > 1 and -3 < -1 2. Payoffs reflect individual preferences 3. Cardinal ranking 1st preference = a 2nd preference = b 3rd preference…….4th preference…… Least preferred = L Cardinality a > b Transitivity a > b > L L << │a, b│

Template Payoff Table Payoffs reflect preference order
Template Payoff Table Payoffs reflect preference order. Use cardinal numbers (2 > 1 and (-2 < -1) Guaranteed a 2 but is there is an elusive b = 3? Strategy I co-operate Strategy II compete If a = (2,2) RED cheats first to get (0, 3) Blue cheats first to get (3,0) If a then L = (1,1) Nash Equilibrium

• Search for a solution in Nash equilibrium
•Many common games (and therefore many common strategic situations) are not solvable. Is behaviour irrational? RED in trying to do better than a 2 (with a 3) ends up with a 1 • Search for a solution in Nash equilibrium Nash Equilibrium, is now one of the most fundamental concepts in the economics of strategy Later we examine Thief of Nature to arrive at a solution in terms of the number of moves in a game (SMA), self-enforcing mechanism and ESS.

Prisoners’ Dilemma Co-operation v competition
Bayesian persuasian problem Player type & belief systems

GAME DESIGN for STRATEGY Payoffs reflect preference order. What if
GAME DESIGN for STRATEGY Payoffs reflect preference order. What if? 2 strategies. What if? 2 players. Then if Strategy I is the consensus……..? Cooperate Compete 1st preference (requires Trust & Commitment) Incentive to cheat 4th/Least preferred (Triggers punishment) Nash Equilibrium

Game Ends: Prisoners’ Dilemma
Preferences Enveloped by the Game Co-operate Trust & Commitment: Long-term Benefit Compete FMA: short-term gain SMA: short-term gain Game Ends: Prisoners’ Dilemma

Strategic Trade-Off Then if Strategy I is the consensus…… (i) There is an incentive to cheat (ii) Both players have to commit (iii) Players have to build trust Strategy I co-operate Strategy II defect/betray 2,2 0,3 3,0 1,1 Nash Equilibrium

Strategic Trade-Off in Pure Strategies Then if Strategy I Left and Strategy II Right are the consensus…… (i) There is no incentive to cheat (ii) Both players have to commit => Self-enforcing mechanism: prob ρ = (0,1) I: Drive on Left II: Drive on Right 1,1 Nash equilibrium 0,0 Nash Equilibrium

Traditional Trade-Off

Capacity and Credible Threat
Topics 1 & 2 to Topics 3 & 4 Capacity and Credible Threat Framework T/3 Commitment Camouflage

Oligopoly Games (n < 5) & 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 Nash Equilibrium. Every player plays her best strategy given the strategies of the other players. 22

Masterclass Games of Strategic Interaction
Pure Conflict The Prisoner’s Dilemma Self-enforcing mechanisms Bertrand price games (Sony v MS case) Cournot games with Pareto dominant strategies (EK and Qantas case) Evolutionary Stable Strategies (ESS) Coordination Game with Asymmetric Information: (Sony v Toshiba case)

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.

2000: Bertrand G1: PS2 v xBox 26 Oct 2000 US$299 Sony move (opening move) do-nothing from MS, waiting time imposed on Sony 15 Nov 2001 US$299 MS move no price differential, Sony bounded rational 14 May 2002 US$ Sony move retaliatory punishment move 15 May 2002 US$199 MS move Bertrand price reaction 13 May 2003 US$ Sony move engaging in price war 14 May 2003 US$179 MS move 29 Mar 2004 US$149 ‘point of balance’ game converging to Nash equilibrium US$149 or less 11 May 2004 US$ Sony move 2005:Cournot G2: PS3 v xBox Nov 2005 Xbox launched MS move 6 Feb 2006 MS move US$179 (Xbox one-shot move) 20 Apr US$ Sony move (PS2 one-shot move) 27 Apr 2006 MS move ( production: capacity signal) 8 May 2006 Sony move launch PS3 (end May: capacity signal)………..t -> ∞

PATTERN – 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 26 Oct 00 15 Nov 01 14 May 02 15 May 02 13 May 03 14 May 03 29 Mar 04 11 May 04 05 1 Nov 30 Oct 05 20 April 06 8 May 06 22 Nov 05 6 Feb 06 27 April 06 22 million Xbox shipped Xbox at $179 Microsoft Xbox launched at $299 Revised production schedule for Xbox 360 to million units by 30th June 2006 Xbox 360 launched at $399 Xbox at $199 Xbox at $179 Xbox at $149

Reasons to Play Reason 1 Reason 2 Reason 3 Law of One Price
Relevance of supply and demand: Say’s law for 21st century Elasticity & rival reaction as price discipline Reason 2 Individual behaviour; Heisenberg uncertainty principle Individuals are not like ‘white mice in an experiment’ Nudge behaviour Reason 3 Uncertainty about value Wages [price] and productivity[value] divergence: noise Capacity constraints

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 Folk Theorem and price hierarchy developed in Masterclass Note: Given that the winner raises price over time, the loser has no incentive to lower price. Reason: although the loser has always lost so far, which should push the loser to lower prices further, the loser knows that the winner is raising price, so that by not lowering price, the loser will win at the margins inside the price hierarchy.

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) 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

Non Co-operative Strategic Games
Step 1 Player type and T/3 and value net Game Dimension: geography or product category Step 2 Elasticity & Unilateral Price Reaction Zero-Sum Constraints Step 3 Reserve Capacity & Credible Threat Camouflage & Commitment

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? Answer: I. Identity of near-rival II. Co-operate in order to compete III. Maximin strategy: second mover advantage (SMA)

Player type and signalling
Decisions (observed actions) 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 - Baumol model of TR max Scale and size: capacity & cost leadership Dividends as signals in a Marris model Algorithmic prices and ‘folk theorem’

CL Type : Capacity & Costs Equivalence
Excess capacity & inventory Reserve capacity & credible threat CL Type of Player Scale, Size and economies of scope Normalization of costs

Consumer preferences & demand Elastic & Inelastic Demand
Economic Foundations Classroom Discussion on Elasticity and on Capacity DEMAND Consumer preferences & demand Elastic & Inelastic Demand Baumol’s TR Test & Operating Leverage SUPPLY Capacity as a Credible Threat Productivity: Wages Imperfectly Measured STRATEGY Strategic Pricing Pizza Paradox Emirates Qantas Case Study

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 25-40% of the market share. Often linked with Stackelberg or ‘top-dog’ in Besanko.

Surprise and Noise (and Moon-shot/false flags)
Binary reaction: Will Player B react? Yes or No? If Yes, decision may be parked as ‘do-nothing strategy’ If NO, decision proceeds on error & mistakes Firsgt mover disadvantage Surprise: action ≠ type Cognitive Bias Noise Non-binary reaction: Player B will react. probability = ρ% Probability (1-ρ)% A.N.Other player will react? Who? Moon-shot and false flags Spherical competitors Decision taking on conjecture of likely reaction No Surprise if discounted with contingent risk profile

Thinking Strategically…
Principles of competition and cooperation. Chess and perfect information Backward induction and forward reasoning Timing in games Normal form and Extensive form one-shot v repeated play. FRPD

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 (Dynamic) 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)

The Relevance of Price (i) Price as a signal (ii) Costly price wars (iii) Failure of Law of One Price Hypothesis: BIN Price < END price Algorithmic pricing Are ‘onsumers’ irrational? Latent transaction costs Credible threats & belief systems

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 Signalling and Belief Systems

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 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

Entry Deterrent Strategy & Barriers to entry
Reputation of the incumbents Capacity building Entry function of the entrant De novo 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. Texas shoot-out ‘price hierarchy’ strategy

Bain Sylos-Labini: Limit Pricing Model Check Besanko or recommended textbook and McNutt pp85-88
Outline the entry game dimension: geography and segment as ‘relevant ‘ market-as-a-game Dominant incumbents v camouflaged entrant type Define strategy set for incumbents: with both commitment and punishment strategies. Allow entry and define the Nash equilibrium Extensive form preference - entry deterrent strategy v accommodation Class Exercise to construct payoff matrix.

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).

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. Player A Competitor B Competitor C Competitor D Near Rival Action 1 Lower price CV ≠ 0 CV = 0 B Action 2 Launch new product B or C Action 3 New innovation D Action 4 Action 5 Action 6……….. Probability ρ = (0,1) with B: ρ = 2/3

Strategy Profile: Find the Nash Trap
Class Exercise Strategy Profile: Find 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. Hypothesis 1 But if the entrant does not enter, fight and accommodate yield the same payoffs to both players (0,10). Hypothesis 2 If the entrant does not enter, it does not matter what the incumbent chooses to do. Albeit, defending with barriers to entry incurs legal costs and OC of management time. Hypothesis 3 The incumbent will not lower prices if the entrant does not enter. Uniquely, if price demand is inelastic.

Entry Strategy Decision Tree
Incumbent (no entry) payoff = 10 (or normalised to 1). With entry, payoff ( 2, 8) Probability: Payoff 2 realisable after price war and 8 on both expanding the market.

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 pp in McNutt Decoding Strategy] D. Results in A+B+C written up as an Aide Memoire for management. E. Strategy Profile compiled as Aide Memoire and presented as ‘Eyes Only Brief’ to the client.

Player’s Irrational Behaviour from Topic 3 to Topic 4
Learning curve/experience and speed of adjustment to the mature game Teams v Individuals Kreps’ Discontinuity effect Selten’s bounded rationality Relevance of Time and FRPD

Discussion of Strategy Set
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 pp

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 and Pre-game signalling Learning and updating beliefs

A-thinks that B-thinks that A-thinks
Enter & Attack Enter & Attack Compete FRPD Player A Player B Enter & Alliance Enter & Alliance

Extensive Decision Game Design I
(A, B) -1, -1 fight Player B retreat attacks 1,0 Player A avoids 0,1

Extensive Decision Game Design II
(A,B) -1, -1 fight Player B retreat attacks 1,0 Player A B believes A avoids 0,1 A fools B 2,0 2, -1

Market Systems & Evolutionary Strategy
Stage 1 Normal strategic form & Extensive form games Imperfect information on game dimension (enveloped) Incomplete information on player type & payoffs Stage 2 Dominant Strategy Prisoners’ Dilemma Limit Entry Games Stage 3 Nash Equilibrium & Payoff Dominant Kantian Altruistic Equilibrium Evolutionary Stable Strategy (Robins in the Garden) Co-operate in order to compete

Explanation of Nash Solution and Prisoners’ Dilemma
Thief of Nature Explanation of Nash Solution and Prisoners’ Dilemma Using this clip from a popular TV show ‘Golden Balls’ and with a link to supporting documentation on Blackboard Thief of Nature, we will explore the game dynamics later in the Masterclass.

TV Game Show ‘Golden Balls’ Split or Steal: signalling co-operation Ibrahim v Nick Nick: Split Nick: Steal Ibrahim: Split 6,800: 6,800 0:13,600 Ibrahim: Steal 13,600: 0 0: 0 Dominant Strategy Nash Equilibrium

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

Available on Blackboard
Classroom Discussion on Emirates & Qantas Case Study Co-operative outcome Counter-strategy Payoff-dominant NE outcome

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’ in the game Accommodation v entry deterrence Action as a Reaction, Observed Behaviour as ‘signalling’ type Pooling and separating equilibrium (on type) Camouflage and ‘false flags’ Nash equilibrium: ‘best you can do, given reaction of a competitor’

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 and also in Kaelo v2.0

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

Failure of Law of One Price
BIN Price < END price Discussion of first assignment Game Dimension Sufficiently Intelligent Algorithm v Rational ‘onsumer’

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. B Left Right A Top 3,3 1,2 Bottom 2,0 0,0 64

Alliance No Alliance/No JV Alliance/JV 2,2 Payoff-dominant 0,1 1,0 1,1 Risk-dominant

Sony fully committed to Blu-Ray?
What if: Sony fully committed to Blu-Ray? Toshiba Blu-Ray Toshiba HD-DVD Sony Blu-Ray 10,1 Pareto dominant Nash equilibrium with 10 = signal commit to Blue-Ray so Toshiba should also commit. 0,0 Sony HD-DVD 1,4 Nash equilibrium only if Sony commit to HD-DVD

Toshiba ‘thinking as’ Sony
What if: Toshiba ‘thinking as’ Sony commits to Blu-Ray Toshiba Blu-Ray Toshiba HD-DVD Sony Blu-Ray 5,5 Nash equilibrium 1,4 Sony HD-DVD 4,1 2,2

Play Games of Strategic Interaction
Conflict & The Prisoner’s Dilemma Trust & Commitment Play a Game

Minimax criteria. If you look at examples in the book Decoding Strategy pp we discuss this next slides for Near-rival v Apple but it can be applied also in any market-as-a-game Strategy Simply, identify the near rival [reacting first] and set up the game tree assuming that near-rival plays minimax, that is, confining you to the least of the greatest market shares in the game - so then you play maximin, to maximise the least loss. Deceiving Strategy (second mover advantage), once near-rival identified, play minimax

A’s market shares Player B S4 S5 S6 S7 Row Minimum
Player B S4 S5 S6 S7 Row Minimum Maximin strategy by A Player A: S1 95 5 50 40 S2 60 70 55 90 S3 30 35 10 Column maximum Minimax strategy by B

Apple’s maximin = Near-Rival minimax Apple’s (global) market shares
Near Rival Strategy A Near Rival Strategy B Row min Apple Strategy 1 20 Smartphones games with entropy 60 Strategy 2 10 80 See next slide for camouflage deceiving play Column max Minimax Maximin

strategy without tactics is the slowest route to victory, tactics without strategy is the noise before defeat Sun Tzu The Art of War

Apple’s ‘loading the dice’ with minimax strategy Apple’s market shares adapted from pp152 in McNutt’s Decoding Strategy with camouflage, deceiving/fooling and mixed strategy Apple Strategy 1 Apple Strategy 2 Near Rival Strategy A 20 iPhone 7 in 2016….iPhone 10 Near-rival maximin play On smartphones/tablets 60 Apple’s minimax play (nano iPhone 2018/2019) or X Strategy B 80 10

Maximin Strategy & Dominant Strategy
Player type GAME STARTS FMA v SMA Maximin Strategy & Dominant Strategy Camouflage and Commitment Sub-game v FRPD Belief Systems Playbook PD Nash Equilibrium GAME ENDS

https://ncase.me/trust/
Post-Workshop 1.Readings from class 2. Final Online Lecture 3. Discussion Threads 4. Final Assessment Uploaded to BB

Game Ontology https://www. patrickmcnutt
Game Ontology Additional slides under development for a new book based on game theory and philosophy with practical application in design of a ‘panopticon’ prison with Adam Tarr architects at

Epistemic Game Design: beliefs; false flags; threat actors; loading the dice ‘Belief’ strategy from observed behaviour of competitors. The player’s type: pooling and separating equilibrium Finding the patterns in rival behaviour. Rational move: NPV Cost of Move < NPV Gain from observed patterns Markov payoff-only equilibria False flags and Updating belief systems. Signalling as moon-shot, noise and PLT. Revisit ‘empty city strategy’ Player type and fooling behaviour Payoff matrix with UI (useful idiot) or ET (external threat) and UT ‘unwitting thief’ to design a persuasive technology tool to play the game

All bets are off the table
(A,B) B Reciprocal Altruism Prisoners’ Dilemma A 1st Preference Pro-active No Regrets Tough commitment & Trust ? Descartes’ Game Change A lags behind, Costly Altruism for B unsustainable unilateral B lags behind, Costly Altruism for A 4th Preference Reactive Conflict All bets are off the table

Game Design..’reachable stability’: Texas ‘shootout’ strategy
Strategy as irrational reason if presented with an incredible threat. A thinks B will fight and B has reputation for fighting then A and B enter a ‘Texas shootout’: price hierarchy A undertakes a self-assessment of the threat from B, A signals a 50:50 alliance JV outcome and it is sustainable but the ‘reachable’ outcome (no price war) is stable because the rule of the alliance JV is to require each player to submit a bid (for the ‘reachable’ payoff), after which the winner has to buy out the loser at the average of their two bids. Contract of Incredible Threat: Suppose the reachable equilibrium is worth £100m, B offers their half of the payoff for £30m. A must decide to accept or decline the bid. If A accepts, B pays £30m and the equilibrium collapses. If A declines, A must pay B £30m and B must accept, leaving B with $80m. Discipline not to Cheat: Alternatively, both players enter sealed bids indicating the minimum price to end the alliance JV and whichever sealed bid is the higher ‘wins’ and buys the loser’s share at the price indicated in the loser’s sealed bid.

‘Habit is a great deadener’ Waiting for Godot Samuel Becket

Residential Workshop* Strategy & Competition Game Theory Perspective Patrick McNutt FRSA Visiting Fellow, Manchester Business School, UK Visiting Professor,

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Residential Workshop* Strategy & Competition Game Theory Perspective Patrick McNutt FRSA Visiting Fellow, Manchester Business School, UK Visiting Professor,

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