GT5-ThreeKingdoms - there are two stages ± Stage 1...

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1 1 Three Kingdoms UGBA 143: Game Theory and Business Decisions 2 Three kingdoms Ancient China, around 200AD Empire was divided into three parts Three kingdoms: – Wei (under House of Cao) – Shu (under House of Liu) – Wu (under House of Sun) Main Question: – Who should ally with whom? 3 Three kingdoms Military strengths of the three kingdoms are: – Cao: 3 – Liu: 2 – Sun: 2 Each player had 3 strategies: Ally with Enemy1 to fight Enemy2; then fight Enemy1 Ally with Enemy2 to fight Enemy1; then fight Enemy2 Choose not to participate in any alliance An alliance can be formed only under mutual agreement 4 Rules of engagement If no alliance is formed: The probability of each player unifying the empire is proportional to their military strengths i.e. the probabilities are 3/7, 2/7, 2/7 5 Rules of engagement If an alliance is formed against an “outsider”,
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Unformatted text preview: there are two stages: ± Stage 1: Alliance versus Outsider Strength of the alliance is double the sum of the individual strengths Probability of winning is proportional to the strength of each side ± Stage 2 (only if Alliance defeats Outsider): Allies Fight Each Other ± Probability of winning is proportional to individual strengths 6 Bargaining with Transfers Now suppose that each side can “bargain” for an alliance with a specific “partner” In exchange for an alliance commitment, some portion of military strength is transferred to ally If the deal is accepted, military strengths are transferred and then the game proceeds If the deal is not accepted, military strengths remain at 2-2-3 The rest of the game proceeds as before...
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