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Understanding Partial Conflict Games and Nash Equilibrium

Learn about variable-sum games, dominant strategies, and Nash Equilibrium in the context of conflicts like the Arms Race example involving the US and North Korea. Explore the Prisoners' Dilemma and strategies for optimal outcomes.

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Understanding Partial Conflict Games and Nash Equilibrium

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  1. 1603/4 Partial-Conflict & Larger

  2. Partial conflict games are variable-sum games, in which the sum of pay-offs to the players at the different outcomes varies. Dominant strategy is the strategy that is MOST advantageous for the player in question. Nash Equilibrium – When no player can benefit by departing unilaterally (by itself) from its strategy associated with an outcome.

  3. Prisoners’ Dilemma is a two person variable-sum game in which each player has two strategies, cooperate or defect. Defect dominates cooperate for both players, even though the mutual-defection outcome, which is the unique Nash equilibrium in the game, is worse for both players than the mutual-cooperation outcome.

  4. Example: Arms race A = US arm in preperation for war (noncooperation) D = US disarm, or at least negotiate an arms-control agreement (cooperation) There are 4 possible outcomes when dealing with…North Korea. (D,D) both US & NK disarm which is the “next best” for both because, while advantageous to each, it also entails certain risks. (A,A) both US & NK arm Which is the “next worst” for both, because, they spend needlessly on arms and are comparatively no better off than at (D,D) (A,D) US Arms & NK disarms Which is “best” for US and “worst” for NK, because US gains a big edge over NK (D,A) US disarms & NK arms Which is “worst” for US and “best” for NK, because NK gains a big edge over US

  5. Example: Arms race A = US arm in preperation for war (noncooperation) D = US disarm, or at least negotiate an arms-control agreement (cooperation) There are 4 possible outcomes when dealing with…North Korea. (D,D) both US & NK disarm which is the “next best” for both because, while advantageous to each, it also entails certain risks. (A,A) both US & NK arm Which is the “next worst” for both, because, they spend needlessly on arms and are comparatively no better off than at (D,D) (A,D) US Arms & NK disarms Which is “best” for US and “worst” for NK, because US gains a big edge over NK (D,A) US disarms & NK arms Which is “worst” for US and “best” for NK, because NK gains a big edge over US NK A D Favor US A Arm US D Favor NK Disarm

  6. NK A D Favor US A Arm US D Favor NK Disarm Give ranks for each (dominant Strat.) NK A D (4,1) A (2,2) US D (1,4) (3,3)

  7. Game of Chicken P588: 18-23 Bre H T Fred H 1 -1 T -1 1

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