A Principal's (Enforcer's) Optimal Extortion Empty Core Game: "Divide and Rule

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Working paper
Ricardo Nieva
Concordia University
We add a Principal (abstract enforcer) to any 2 person TU game in strategic form because of transaction costs or extorsion. The game yields in reasonable cases an empty core when there are no externalities in coalition formation and when the principal can choose any allocation on the frontier of the individual, rational and feasible set. The principal does so by inducing "The Simultaneous and Double Extorsion Game". Only one of the identical players and the princi- pal collude, iff the identical agents combined "might" is more than a threshold of the principal’s but less than 100%, i.e."divide and rule". The threshold de- pends on the limit to the degree of double extorsion. Strikingly, he would prefer to induce an empty core game with an extreme level of extortion instead of a nonempty core one. The result, ie. that only an identical agent and the prin- cipal collude, is robust to allowing for variable principal "might" or harrasing ability that might induce a cooperative game with externalities in coalition for- mation. As solution concept, we use an extension of Myerson’s (1978) Shapley value generalization to partition function games and the Aumann-Myerson link (1988) formation game.
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