1. Chapter 1-1984 Book1 CONFLICT ANALYSIS: MODELS AND RESOLUTIONS

2. Chapter 1-1984 Book2 FAMILY TREE Classical game theory Metagame analysis Conflict analysis The graph model for conflict resolution

3. Chapter 1-1984 Book3 Genealogy of formal conflict models Cooperative Game Theory Metagame Analysis Drama Theory Conflict Analysis Graph Model for Conflict Resolution Normal Form Extensive Form... Game Theory Nonquantitative Approaches Quantitative Procedures

4. Chapter 1-1984 Book4 SPECIAL FEATURES OF CONFLICT ANALYSIS Option form for representing outcomes or states. Preference vectors using decimalized states allows stability calculations for a smaller conflict to be calculated by hand on one page. Preference vector provides a geometric interpretation of movement among outcomes. Stability due to sequential sanctioning is used to describe human behaviour under conflict. Stability caused by simultaneous sanctioning is also employed. Misperceptions can be studied using hypergame analysis.

5. Chapter 1-1984 Book5 Table P.1 Real World Conflicts Studied in the Book.

6. Chapter 1-1984 Book6 Table P.2 Topics in the Book.

7. Chapter 1-1984 Book7 Figure P.1 Paths of study.

8. Chapter 1-1984 Book8 CHAPTER ONE: INTRODUCTION TO CONFLICT ANALYSIS Explains how to apply conflict analysis to a two player game. The Cuban Missile Crisis of 1962 is studied.

9. Chapter 1-1984 Book9 CUBAN MISSILE CRISIS In 1959 Castro overthrew the Batista regime in Cuba. American property in Cuba was nationalized. In April 1961 the American sponsored invasion of Cuba failed at the Bay of Pigs. In 1962 the Russians installed nuclear missiles in Cuba. Americans wanted the missiles out of Cuba. Do conflict study for the situation in October 1962.

10. Chapter 1-1984 Book10 Figure 1.1 The general conflict analysis process.

11. Chapter 1-1984 Book11 STEPS IN MODELLING Select a point in time. Choose players and options. Remove infeasible outcomes. Develop a preference vector for each player by ordering outcomes from most preferred on the left to least preferred on the right.

12. Chapter 1-1984 Book12 US Air Strike1American Blockade0 strategy USSR Withdraw1Russian Escalate0strategy 1 or Y means yes. 0 or N indicates no. There are 2 4 = 16 possible outcomes. 12 of the 16 outcomes are feasible. PLAYERS AND OPTIONS OUTCOME OR STATE

13. Chapter 1-1984 Book13 INFEASIBLE OUTCOMES IN THE CUBAN MISSILE CRISIS The Russians will not withdraw their missiles and escalate at the same time. US Air Strike0101 - Blockade0011 - USSR Withdraw11111 Escalate11111 where a dash - means a 1 or a 0.

14. Chapter 1-1984 Book14 Evolution of the Cuban Missile Crisis from the status quo through an intermediate outcome to the final resolution. US Air Strike000 Blockade011 USSR Withdraw001 Escalate000 State026 Number Status Intermediate Equilibrium Quo Outcome

15. Chapter 1-1984 Book15 Table 1.1 Players, Options, and Outcomes for the Cuban Missile Crisis.

16. Chapter 1-1984 Book16 ECONOMIC NOTATION For hand calculations, convert binary outcomes to decimal numbers. EXAMPLE: Outcome (1 0 1 0) becomes 1 X 2 0 + 0 X 2 1 + 1 X 2 2 + 0 X 2 3 = 1 + 0 + 4 + 0 = 5

17. Chapter 1-1984 Book17 PREFERENCE VECTOR Ranking of outcomes from most preferred on the left to least preferred on the right. Ties are allowed. Ordinal preferences.

18. Chapter 1-1984 Book18 Table 1.2 Preference Vector for the US in the Cuban Missile Crisis.

19. Chapter 1-1984 Book19 Table 1.3 Preference Vector for the USSR in the Cuban Missile Crisis.

20. Chapter 1-1984 Book20 TYPES OF STABLE OUTCOMES 1.Rational (r) 2.Sequentially Sanctioned (s) 3.Unstable (u) 4.Simultaneously Sanctioned (u)

21. Chapter 1-1984 Book21 Solution Concepts and Human Behavior Solution Concepts Stability DescriptionsForesight Knowledge of Preferences Disimprovement Strategic Risk Nash stability (R) Focal DM (decision maker) cannot move unilaterally to a more preferred state. LowOwnNever Ignores risk General Metarational (GMR) All focal DM’s unilateral improvements are sanctioned by subsequent unilateral moves by others MediumOwnBy opponents Avoids risk; conser- vative Symmetric Metarational (SMR) All focal DM’s unilateral improvements are sanctioned, even after response by the focal DM. MediumOwnBy opponents Sequential Stability (SEQ) All focal DM’s unilateral improvements are sanctioned by subsequent unilateral improvements by others. MediumAllNever Takes some risks; satisfies Limited- move Stability (L n ) All DMs are assumed to act optimally and the maximum number of state transitions (h) is specified. VariableAllStrategic Accepts Risk; strategizes Non-myopic Stability (NM) Limiting case of limited move stability as the maximum number of state transitions increases to infinity. HighAllStrategic

22. Chapter 1-1984 Book22 UNILATERAL IMPROVEMENT Write UI’s below each outcome. EXAMPLE: From outcome 5, the US has UI’s to 4 and 6. 001 010 111Fixed 000Russian Strategy 465 UI

23. Chapter 1-1984 Book23 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

24. Chapter 1-1984 Book24 EQUILIBIA When an outcome has some type of stability for each player, it is a possible equilibrium or resolution. Mark each equilibrium with an E. If an outcome is unstable for at least one player, indicate this by an X.

25. Chapter 1-1984 Book25 Figure 1.1 The general conflict analysis process.

26. Chapter 1-1984 Book26 STABILITY ANALYSIS Individual Stability Equilibria

27. Chapter 1-1984 Book27 GENERAL DEFINITION OF STABILITY An outcome is stable for a particular player if it is not advantageous for the player to move away from the outcome. Stability can be induced in a number of different ways. A solution concept defines how stability is caused.

28. Chapter 1-1984 Book28 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

29. Chapter 1-1984 Book29 PREFERENCE VECTOR FORMAT Provides a geometric interpretation on how moves and counter- moves can take place among players. Allows for all stability calculations to be done on one page for smaller conflicts. Shows how the conflict can evolve from the status quo to the final equilibrium.

30. Chapter 1-1984 Book30 TYPES OF STABLE OUTCOMES Rational (r) Sequentially Sanctioned (s) Unstable (u) Simultaneously Sanctioned (u)

31. Chapter 1-1984 Book31 RATIONAL OUTCOME Outcome q is rational (r) for player A if A has no UI’s from q. EXAMPLES: –In Table 1.4 outcome 2 is rational for the US. –Outcome 6 is rational for the USSR. Write an r above these outcomes.

32. Chapter 1-1984 Book32 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

33. Chapter 1-1984 Book33 SEQUENTIALLY SANCTIONED OUTCOMES Outcome q is sequentially sanctioned for player A if for each UI from q a credible action can be taken by B to stop A from taking advantage of the UI.

34. Chapter 1-1984 Book34 EXAMPLE OF A SEQUENTIALLY SANCTIONED OUTCOME The US has UI from 6 to 4. The USSR has UI from 4 to 0. But 0 is less preferred to 6 by the US. The USSR has a credible action to deter the US from taking advantage of its UI. 6 is stable by sequential sanctioning for the US. Write s above 6.

35. Chapter 1-1984 Book35 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

36. Chapter 1-1984 Book36 TYPES OF STABLE OUTCOMES Rational (r) Sequentially Sanctioned (s) Unstable (u) Simultaneously Sanctioned (u)

37. Chapter 1-1984 Book37 UNSTABLE OUTCOME Outcome q is unstable (u) for player A if A has at least one UI from q for which B has no credible deterrent. If outcome q is unstable for A, player A will certainly not remain at that outcome and will take advantage of any undeterred UI.

38. Chapter 1-1984 Book38 EXAMPLE OF AN UNSTABLE OUTCOME Analyze outcome 5 for the US. The US has UI’s to 4 and 6. If the US moves to 4 the USSR has UI to 0 which is less preferred to 5 by the US. Therefore, 4 is sanctioned. If the US goes to 6 the USSR stays at 6 since it is rational for the USSR. No sanction exists to stop the US from taking the UI from 5 to 6. Write u above outcome 5 for the US.

39. Chapter 1-1984 Book39 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

40. Chapter 1-1984 Book40 INDIVIDUAL STABILITY 1.Rational (r) 2.Sequentially Sanctioned (s) 3.Unstable (u) 4.Simultaneously Sanctioned (u)

41. Chapter 1-1984 Book41 SIMULTANEOUSLY SANCTIONED OUTCOME If outcome q is unstable for both A and B, stability could be induced by both players moving together. For a given player this occurs if the new outcome is less preferred to q by the player. Cancel instability by changing u to u.

42. Chapter 1-1984 Book42 STABILITY BY SIMULTANEOUS SANCTIONING Outcome 1 is unstable for both the US and USSR. 01Change US 10strategy. 00Fix Soviet 00strategy. 21 0 UI 1for US 1 011Fix US 600strategy. 10Change USSR 00strategy. 51 UI for USSR Get outcome 6 = 2 + 5 - 1. Since 6 is more preferred to 1 by both players, 1 remains unstable.

43. Chapter 1-1984 Book43 STABILITY BY SIMULTANEOUS SANCTIONING If outcome q is unstable for at least 2 players, check for stability by simultaneous sanctioning. When outcome q is unstable for m out of n players, simultaneous stability calculations are done for all possible combinations of 2 or more players for which q is unstable and for all combinations of UI’s which are not sequentially blocked.

44. Chapter 1-1984 Book44 SIMULTANEOUS SANCTIONING Let A i be the set of UI’s from q for player i which are not sequentially blocked, where a i  A i. Let M be the set of all players for which q is unstable where |M| ≥ 2. For every Γ  M, |Γ| ≥ 2, calculate p = ∑ a i – (|Γ| - 1)q where p is determined for every a i  A i for each player in the set Γ and all outcomes are decimalized. If anywhere during the calculations p is less preferred than q by i  Γ, then the UI given by a i  A i is blocked. If all a i  A i are blocked, q is stable for player i by simultaneous sanctioning. i ∈ Γi ∈ Γ Stability of State q for Player i

45. Chapter 1-1984 Book45 Figure 1.2 Stability of outcome q for player A in a two-player game.

46. Chapter 1-1984 Book46 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

47. Chapter 1-1984 Book47 EQUILIBRIA When an outcome has some type of stability for each player, it is a possible equilibrium or resolution. Mark each equilibrium with an E. If an outcome is unstable for at least one player, indicate this by an X.

48. Chapter 1-1984 Book48 PREDICTED EQUILIBRIA It can be proven mathematically that sequential sanctioning will always predict at least one equilibrium for an ordinal game. In practice, sequential sanctioning only predicts reasonable equilibria. For each real world case study, sequential sanctioning always forecasted the equilibrium which actually occurred. The other equilibria describe what could have happened if the conflict had evolved differently.

49. Chapter 1-1984 Book49 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

50. Chapter 1-1984 Book50 CUBAN CONFLICT Outcomes 4 and 6 are equilibria. From outcome 0 (status quo) US has a UI to 2. Russia has a UI from 2 to 6 which is the outcome that occurred historically. Note that 4 could have occurred if the Russians had been certain that the Americans would impose a blockade if the missiles remained in Cuba. Model as a hypergame.

51. Chapter 1-1984 Book51 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.

52. Chapter 1-1984 Book52 Evolution of the Cuban Missile Crisis from the status quo through an intermediate outcome to the final resolution. US Air Strike000 Blockade011 USSR Withdraw001 Escalate000 State026 Number Status Intermediate Equilibrium Quo Outcome

53. Chapter 1-1984 Book53 Table 1.4 Stability Analysis Tableau for the Cuban Missile Crisis.