Bargaining in a Three-Person Game

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Abstract
Games are paradigms of many political events, especially those that involve partial or complete conflicts of interest among the participants. As paradigms, they display in relatively simple social interaction the same fundamental forces found in the more complex interactions of the grander political events whose structure they share. This is the feature of games that makes them attractive vehicles for both theorizing and experimentation in the social sciences. The scientific expectation is that, by studying the quasi-political interaction of games—where the variations among institutional, psychological, and ideological components of behavior are minimized—one will be able to understand more profoundly the basic political activities of bargaining, forming coalitions, and choosing strategies. This more profound understanding is a consequence of obtaining answers to the following questions:(1) What is the mathematical solution, that is, what amount of utility can players be expected to obtain, when it is assumed that players are rational and wish to maximize utility?(2) What is the strategy (or method of playing) that will ensure players of achieving the solution?An answer to the first question indicates what may be anticipated as the outcome of political events. If we know it, then, if also we can assume players are rational maximizers of utility, we can predict the political future with some confidence. An answer to the second question (about strategies) permits political engineers to give advice to politicians about how to behave successfully.